Geoid Model Research Articles

A Comparison of Orthometric Heights Calculated from (GPS/Leveling) and (EGM08) Methods Based–GIS

Interest in the study of global gravitational models has increased recently all over the world because it is necessary for height datum transformations. Today the International Center for Global Earth Models (ICGEM) provides the largest collection in the world produced through gravitational data from the gravitational satellite’s missions CHAMP, GRACE, and GOCE … Etc. To allow easy access through the internet with its more intelligent technologies, it is one of the International Gravity Organization’s services. While the Global Positioning System (GPS) has become one of the most preferred technologies in engineering surveying, a major dilemma in GPS survey lies in oval-based elevations. At the same time, orthometric heights are commonly used in the engineering field. Therefore, it is necessary to convert the measured heights by satellites assigned to the elliptical surface into orthometric heights and supported to the geoid surface (mean sea level) through an accurate geodetic model. The differences between orthometric measurement heights from DGPS/leveling data (obtained from 57 points in the study area) are increasingly used by professionals geographical information systems(GIS). However, the local determination of Geoid is necessary for better accuracy of the orthometric height from DGPS. This paper aims to introduce a modern technique for determining elevation, avoiding cumbersome and time-consuming spirit leveling operations. Fast vertical positioning can be obtained using DGPS with geoid models. The Root Mean Square Error (RMSE) is ± 0.19 m with high precision of DGPS derived with EGM08; thus, the more it describes the Earth’s gravitational field in more detail.

Sensitivity of Enhanced SRTM for Sea-Level Rise Variation on Egyptian Coasts

The accuracy of digital elevation models (DEMs) is very critical to planning adaptation strategies for coastal areas under changing scenarios of global climate and sea-level rise. This research assesses the accuracy of the interferometric DEM from the SRTM mission as it is one of the free available DEMs that have been widely used in many applications. The SRTM model is enhanced using the best fit global geoid model for Egypt instead of EGM96 and by applying a mathematical scale factor formula. This research aims to obtain a higher vertical accuracy of the SRTM model that achieves the requirements for coastal inundation studies with minimum field measurement data. The methodology approach consists of three phases. In the first phase, the enhancement scale factor formulas were derived using uniformly distributed ground control points (GCPs) at two different terrains data in Egypt. The second phase contains the evaluation and validation process. It was observed that the enhanced accuracy achieved ranged from 45% to 60 % based on the type of terrains. In the last phase, the sensitivity of these DEMs to sea-level projections using the recent available local tide gauge data was analyzed. It is recommended to investigate this method approach to determine the optimal size and distribution of reference ground control points needed to adjust various free open DEMs of low vertical accuracy for further studies and other applications.

Evaluating two numerical methods for developing a local geoid model and a local digital elevation model for the Red Sea Coast, Egypt

Global Navigation Satellite System (GNSS) provides ellipsoidal heights, whereas engineering projects need orthometric heights of points. Thus, to take advantage of GNSS in engineering work, the relation between orthometric and ellipsoid height must be determined as a function of position by geoid modeling. The Red Sea coastal cities have various natural potentials that render them economically promising cities that are attractive to numerous investors and visitors alike. Over the past years, there has been an increased governmental awareness of setting up large projects in these cities. With the increasing utilization of GNSS in a number of these projects, there is an imperative need to develop a local geoid model in this region. This study is an attempt to use a geometric method for the study area in order to develop a local geoid model and a local digital elevation model. In addition, the performance of EGM2008, SRTM, and ASTER is evaluated. In order to develop the local geoid model, the polynomial regression method and Artificial Neural network (ANN) technique are employed. Performance evaluation of the studied methods is based on a compilation of various statistical parameters and goodness-of-fit measures, followed by a comparison of methods outputs. The study indicates significant improvements in the local geoid model when using both methods. Additionally, the model resulting from the ANN appears more reliable compared to the calculated model using polynomial regression. In this study, the accuracy of EGM2008 is about ±0.466 m. Moreover, regarding the global digital elevation model, ASTER outperforms SRTM by about ±0.905 m.

A hybrid binary grey wolf optimizer for selection and reduction of reference points with extreme learning machine approach on local GNSS/leveling geoid determination

Modeling and optimization from natural phenomena and observations of the physical earth is an extremely important issue. In the light of the developments in computer and artificial intelligence technologies, the applications of learning-based modeling and optimization techniques in all kinds of study fields are increasing. In this research, the applicability of four different state-of-the-art metaheuristic algorithms which are Particle swarm optimization (PSO), Tree-Seed Algorithm (TSA), Artificial Bee Colony (ABC) algorithm, and Grey Wolf Optimizer (GWO), in local GNSS/leveling geoid studies have been examined. The most suitable geoid model has been tried to be obtained by using different reference points via the well-known machine learning algorithms, Artificial Neural Network (ANN) and Extreme Learning Machine (ELM), at the existing GNSS/leveling points in Burdur city of Turkey. In this study, eight different hybrid approaches are proposed by using each metaheuristic algorithm together with machine learning methods. By using these hybrid approaches, the model closest to the minimum number of reference points has been tried to be obtained. Furthermore, the performance of the hybrid approaches has been compared. According to the comparisons, the hybrid approach performed with GWO and ELM has achieved better results than other proposed hybrid approaches. As a result of the research, it has been seen that the most suitable local GNSS/Leveling geoid can be determined with a lower number of reference points in an appropriate distribution.

Open access to regional geoid models: the International Service for the Geoid

Abstract. The International Service for the Geoid (ISG, https://www.isgeoid.polimi.it/, last access: 31 March 2021) provides free access to a dedicated and comprehensive repository of geoid models through its website. In the archive, both the latest releases of the most important and well-known geoid models, as well as less recent or less known ones, are freely available, giving to the users a wide range of possible applications to perform analyses on the evolution of the geoid computation research field. The ISG is an official service of the International Association of Geodesy (IAG), under the umbrella of the International Gravity Field Service (IGFS). Its main tasks are collecting, analysing, and redistributing local, regional, and continental geoid models and providing technical support to people involved in geoid-related topics for both educational and research purposes. In the framework of its activities, the ISG performs research taking advantage of its archive and organizes seminars and specific training courses on geoid determination, supporting students and researchers in geodesy as well as distributing training material on the use of the most common algorithms for geoid estimation. This paper aims at describing the data and services, including the newly implemented DOI Service for geoid models (https://dataservices.gfz-potsdam.de/portal/?fq=subject:isg, last access: 31 March 2021), and showing the added value of the ISG archive of geoid models for the scientific community and technicians, like engineers and surveyors (https://www.isgeoid.polimi.it/Geoid/reg_list.html, last access: 31 March 2021).

Contribution of GRAV-D airborne gravity to improvement of regional gravimetric geoid modelling in Colorado, USA

This paper studies the contribution of airborne gravity data to improvement of gravimetric geoid modelling across the mountainous area in Colorado, USA. First, airborne gravity data was processed, filtered, and downward-continued. Then, three gravity anomaly grids were prepared; the first grid only from the terrestrial gravity data, the second grid only from the downward-continued airborne gravity data, and the third grid from combined downward-continued airborne and terrestrial gravity data. Gravimetric geoid models with the three gravity anomaly grids were determined using the least-squares modification of Stokes’ formula with additive corrections (LSMSA) method. The absolute and relative accuracy of the computed gravimetric geoid models was estimated on GNSS/levelling points. Results exhibit the accuracy improved by 1.1 cm or 20% in terms of standard deviation when airborne and terrestrial gravity data was used for geoid computation, compared to the geoid model computed only from terrestrial gravity data. Finally, the spectral analysis of surface gravity anomaly grids and geoid models was performed, which provided insights into specific wavelength bands in which airborne gravity data contributed and improved the power spectrum.

A local lithospheric structure model for Vietnam derived from a high-resolution gravimetric geoid

High-resolution Moho and lithosphere–asthenosphere boundary depth models for Vietnam and its surrounding areas are determined based on a recently released geoid model constructed from surface and satellite gravity data (GEOID_LSC_C model) and on 3ʹʹ resolution topography data (mixed SRTM model). A linear density gradient for the crust and a temperature-dependent density for the lithospheric mantle were used to determine the lithospheric structure under the assumption of local isostasy. In a first step, the impact of correcting elevation data from sedimentary basins to estimate Moho depth has been evaluated using CRUST1.0 model. Results obtained from a test area where seismic data are available, which demonstrated that the sedimentary effect should be considered before the inversion process. The geoid height and elevation-corrected sedimentary layer were filtered to remove signals originating below the lithosphere. The resulting Moho and lithosphere–asthenosphere boundary depth models computed at 1ʹ resolution were evaluated against seismic data as well as global and local lithospheric models available in the study region. These comparisons indicate a consistency of our Moho depth estimation with the seismic data within 1.5 km in standard deviation for the whole Vietnam. This new Moho depth model for the study region represents a significant improvement over the global models CRUST1.0 and GEMMA, which have standard deviations of 3.2 and 3.3 km, respectively, when compared to the seismic data. Even if a detailed geological interpretation of the results is out of scope of this paper, a joint analysis of the obtained models with the high-resolution Bouguer gravity anomaly is finally discussed in terms of the main geological patterns of the study region. The high resolution of our Moho and lithosphere–asthenosphere boundary depth models contribute to better constrain the lithospheric structure as well as tectonic and geodynamic processes of this region. The differences in Moho depth visible in the northeast and southwest sides of the Red River Fault Zone confirmed that the Red River Fault Zone may be considered the boundary between two continental blocks: South China and Indochina blocks. However, no remarkable differences in lithosphere–asthenosphere boundary depth were obtained from our results. This suggests that the Red River Fault Zone developed within the crust and remained a crustal fault.

Collocation and FFT-based geoid estimation within the Colorado 1 cm geoid experiment

In the frame of the International Association of Geodesy Joint Working Group 2.2.2 “The 1 cm geoid experiment”, terrestrial and airborne gravity datasets along with GPS/leveling data were made available for the comparison of different geoid modeling methods and techniques in the wider area of Colorado, USA. We discuss the methods and procedures we followed for computing gravimetric quasi-geoid and geoid models and geopotential values from the available datasets. The procedures followed were based on the remove-compute-restore approach using XGM2016 as a reference geopotential model. The higher frequencies of the gravity field were computed via the residual terrain correction, using (a) the CGIAR-CSI SRTM digital elevation model with the classical technique and (b) a spectral one. Least-Squares Collocation was used for the downward continuation of the airborne data and for gridding. Finally, the geoid models were obtained by applying Least-Squares Collocation and spherical FFT-based methods, while the influence of the orthometric height correction on geoid heights was taken into account by employing simple and complete Bouguer reductions. All results were evaluated with available GPS/leveling benchmarks. Moreover, potential values were determined in support of the International Height Reference System/Frame. From the results acquired, a final accuracy of 5–7 cm for the determined geoid models was achieved depending on the adopted method and data combination, without considering the accuracy of the GPS/leveling data used for their evaluation. The contribution of the airborne gravity data was deemed as limited in combination solutions although the airborne only solution provided equal level of accuracy to the terrestrial and the combined ones. Better consistency was obtained on the points of the GSVS17 line, when compared to the GPS/leveling data, where an accuracy of 2.4 cm and 2.8 cm was reached for the FFT and LSC based methods, respectively.

High-resolution geoid modeling using least squares modification of Stokes and Hotine formulas in Colorado

The Colorado geoid experiment was initiated and organized as a joint study by the Joint Working Group (JWG) 2.2.2 (1-cm geoid experiment) of the International Association of Geodesy (IAG) in 2017, and different institutions and research groups contributed to this study. The aim of this experiment was to clarify the repeatability of gravity potential values as International Height Reference System (IHRS) coordinates from different geoid determination approaches carried out with the same input dataset. The dataset included the terrestrial and airborne gravity observations, a digital terrain model, the XGM2016 global geopotential model and GPS/leveling data for model validations belonging to a mountainous area of approximately 550 km × 730 km in Colorado, US. The dataset was provided by National Geodetic Survey (NGS) department. In this frame, this article aims providing a discussion on Colorado geoid modeling through individual experimental results obtained by Istanbul Technical University-Gravity Research Group (ITU-GRG). This contribution mainly focused on modeling the Colorado geoid using the least squares modifications of Stokes and Hotine integral formulas with additive corrections. The computations using each formula were carried out using ITU-GRG software, including the solution variants based on terrestrial-only, airborne-only and combined gravity datasets. Then, the calculated experimental geoid models were validated using historical and recently measured profile-based GPS/leveling datasets, and they were also compared with the official solutions submitted by different institutions for the “1-cm geoid experiment” of IAG JWG 2.2.2. For all validation results, the Hotine and Stokes integral formulas yielded similar performances in terms of geoid accuracy; however, the models computed using the combined data had better accuracy than those using the terrestrial-only and airborne-only solutions. The geoid model solutions using the combined data had an accuracy of 2.69 cm for the Hotine method and 2.87 cm for the Stokes method in the test results using GPS/leveling data of the GSVS17 (Geoid Slope Validation Survey 2017) profile. Airborne data from the Gravity for the Redefinition of the American Vertical Datum (GRAV-D) project contributed significantly towards improving the geoid model, especially in the mountainous parts of the area.

Realistic dynamic topography through coupling geoid and hydrodynamic models of the Baltic Sea

Accurate and compatible sea level data are now more important than ever before, especially in semi-enclosed sea areas that are highly exploited and surrounded by many countries, such as the Baltic Sea. Obtaining accurate sea level data is however, not only hindered by resolution deficiencies and systematic and random errors from the various available sources (e.g. satellite altimetry (SA), tide gauges (TG), hydrodynamic models (HDM), etc.), but most importantly by variations in and insufficient knowledge of the vertical reference datums. This study demonstrates that by incorporating the geoid (equipotential surface of the earth, that represents a stable vertical datum) along with a network of tide gauges and hydrodynamic models it is possible to obtain accurate and realistic sea level data.A simplified method is developed that calculates the bias between TG and HDM and identifies an optimum time period to be utilized, given the associated accuracy required. A bias period of 0–6 h results in a standard deviation of less than 5 cm at all participating TG stations. The method is tested in the estuarine water body of the Gulf of Finland (in the eastern section of the Baltic Sea). Results show that without the bias correction, the mean dynamic topography from a westerly to easterly direction along the gulf, varied from −12.7 to −8.2 cm (a difference of 4.5 cm) whilst after bias correction the model varied from 18 cm to 25.4 cm (a difference of 7.4 cm). Both these scenarios demonstrate an increasing eastward trend. Nevertheless, a major difference in quantification exists and to a first approximation, this may vary by as much as a factor of almost 2. The analysis also intrinsically identified critical areas where drastic changes in dynamic topography occur and the associated seasons. Thus, the utilization of more stable vertical reference, such as the geoid, displays promising results, that essentially allows better quantification of more realistic parameters (e.g. sea level trends, extreme value analysis etc.). In addition, it allows identification of hydrodynamic modelling imperfections and that a coherent compatibility with other sources of sea level data (e.g. SA, Global Navigational Satellite Systems etc.) is now possible. This accuracy and conformity in sea level data are urgently required for a comprehensive understanding of climate change, marine engineering and navigation applications.

ПРО ПРЕДСТАВЛЕННЯ АКФ STHA-ПОЛІНОМАМИ ДЛЯ МОДЕЛЮВАННЯ РЕГІОНАЛЬНОГО ГРАВІТАЦІЙНОГО ПОЛЯ ЗЕМЛІ

The current Baltic height system in Ukraine is outdated and requires modernization. The current resolution of Cabinet of Ministers of Ukraine states that the implementation of topographic, geodetic and cartographic works starting from January 1, 2023 will be carried out using UELN/EVRS2000 height system. For successful integration of our height system into European one, it is necessary to construct a high-precision model of geoid surface on territory of Ukraine, which should fit well with European geoid model EGG2015. This will allow using advanced satellite technologies to determine gravity-dependent heights. The main methods of constructing regional gravitational field of Earth include method of geopotential decomposition into series of spherical functions with fractional indices (in particular, STHA-method) and least-squares collocation method. However, to date, no relationship has been established between them. The construction of ACF using STHApolynomials, which wavelength is much shorter than Legendre polynomials and depends on area of studied region, will significantly improve accuracy of regional models of Earth's gravitational field. The approach to construction of ACF using STHA-polynomials can be very promising precisely because wavelength of these functions coincides with area of studied region, and all other properties coincide with properties of Legendre polynomials. That is why it is necessary to perform ACF calculations using Legendre polynomials and STHApolynomials and analyze results. The solution of this problem is realized by constructing and analyzing covariance and cross-covariance functions of geopotential functionals using Legendre polynomials and STHA-polynomials according to Tscherning-Rapp model. A number of covariance and crossover-covariance functions are calculated and compared using Legendre polynomials and STHA-polynomials according to Tscherning-Rapp model. The values of geoid heights obtained from GNSS-observations at points of SGN of I, II and III classes in territory of Lviv region are taken as input data. A method for constructing a local ACF using STHA-polynomials is proposed and tested. STHA-polynomials have been found to be significantly more efficient than Legendre polynomials because their domain coincides with that of region under study. For example, it is shown that for Lviv region decomposition of covariance functions in a series by Legendre polynomials up to order 600 is equivalent to decomposition in a series by STHA-polynomials up to order 8.

Accuracy Analysis of Indonesian Geoid Model Based On Grids

Providing geospatial data and information services like the Indonesian geoid model is one of the important things on implementation of The Regulation of Head of the Geospatial Information Agency (BIG) No. 15 of 2013 about Indonesia Geospatial Reference System 2013 (SRGI2013). The geospatial information service requires innovation to fulfill the needs of the user. The provision of Indonesian geoid model with various grid resolutions is one of the forms of renewal that designed to meet the needs of users based on the accuracy level that needed. Each geoid model with a different grid resolution will produce different geometries as well. Therefore, the value of geoid undulation on a certain coordinate will be different according to the grid resolution. Based on that case, this paper will analyze the accuracy of The Indonesian geoid model based on the various grid resolution. Grids resolution that used in this case is 36”, 1’, 2.5’, and 5’. The accuracy of the geoid model is obtained from the standard deviation of the difference between geometric undulation values and gravimetric undulation values in 186 control points. The result of this study shows that Indonesian geoid model with the grid resolution 36”, 1’, 2.5’, and 5’ have the geoid accuracy 5.129 cm, 6.472 cm, 9.584 cm, dan 13.942 cm sequentially. Based on that result, we can conclude that the less grid resolution of geoid model will produce a higher accuracy of the geoid model. In addition, this study could be a consideration for every user to use the Indonesian geoid model based on their need and specification.

Про точність моделей (квазі)геоїда відносно системи висот UELN/EVRS2000

Nowadays the Baltic Height System 1977 operates in Ukraine, the starting point of which is the zero of the Kronstadt banchmark. However, the current height system in Ukraine is morally obsolete primarily due to the great distance from the zero-point of height (about 2 thousand km) and the difficulty of adapting to the use of satellite surveying methods. Therefore, today it does not correspond to the level of development of modern geospatial technologies and it needs to be modernized. The most optimal way to modernize the height network of Ukraine is its integration into the United European Leveling Network UELN, the zero point of which is the Amsterdam banchmark. Within the framework of such integration it is necessary to create a high-precision geoid model for the territory of Ukraine, connected to the UELN/EVRS2000 height system. Aim. The purpose of the work is to compare the accuracy of different geoid/quasigeoid models and the global gravitational field of the Earth on the Western Ukraine area (border region) relative to the heights of points in the height system UELN/EVRS2000, where GNSSleveling is performed, and to determine the most optimal model in relation to which a high-precision geoid model can be created, consistent with the UELN/EVRS2000 height system.Method. To obtain the heights of leveling points on the Ukraine area in the UELN/EVRS2000 height system we performed I class leveling on two lines from the fundamental benchmarks on the territory of Ukraine (heights are known in the Baltic height system 1977) to I class benchmarks on the Poland area (UELN/EVRS2000 height system). GNSS-leveling in static mode (1-second sampling observations for more than 6 hours) was performed on all fundamental and ground benchmarks, as well as horizontal marks. Results. The heights of the quasigeoid at 26 points are obtained from the performed measurements. The heights are compared with three global models of the Earth’s gravitational field: EGM2008, EIGEN-6C4 and XGM2019e_2159 (the maximum order of all these models is 2190), as well as with the European geoid EGG2015. It is established that the best accuracy (≈ 7 cm) allows to obtain the European geoid EGG2015. Scientific novelty and practical significance. For the first time the accuracy of the Earth’s gravitational field models and geoid models on the Ukraine area is investigated at points where the height in the UELN/EVRS2000 height system is known. We established that when constructing a high-precision quasigeoid using the “Remove–Restore” procedure, it is best to use the European geoid EGG2015 as a systematic component.

An alternative geoid model for Africa using the shallow-layer method

The aim of the current investigation is to determine an alternative geoid model for Africa using the shallow-layer method. The shallow-layer method, following the basic definition of the geoid, differs essentially from the traditional geoid determination techniques (Stokes and Molodensky) that it doesn’t need real gravity data. It comes from the definition of the geoid. Here, the shallow-layer method is used to determine a 5′ × 5′ geoid model for Africa covering the latitudes between −36°N and 39°N and longitudes from −20°E to 53°E The Earth Gravitational Model (EGM2008), the global topographic model (DTM2006.0), the global crustal model (CRUST1.0) and the Danish National Space Center data set (DNSC08) global models have been used to construct and define the shallow layer and its interior structure. A combination of prism and tesseroid modelling methods have been utilized to determine the gravitational potential produced by the shallow-layer masses. The validation and tests of the computed shallow-layer geoid have been done at two different levels. First, a comparison between the computed shallow-layer geoid and the recently developed AFRgeo2019 gravimetric geoid for Africa (based on real gravity data) has been carried out. Second, a comparison of the computed shallow-layer geoid with several geoid models computed using different global geopotential models has been performed. The results show that the computed shallow-layer geoid behaves similarly to those determined by the global geopotential models. Differences between the shallow-layer and the AFRgeo2019 gravimetric geoids are generally small (below 0.5 m) at most of the African continent

Sea Topography of the Ionian and Adriatic Seas Using Repeated GNSS Measurements

The mean sea surface topography of the Ionian and Adriatic Seas has been determined. This was based on six-months of Global Navigation Satellite System (GNSS) measurements which were performed on the Ionian Queen (a ship). The measurements were analyzed following a double-path methodology based on differential GNSS (D-GNSS) and precise point positioning (PPP) analysis. Numerical filtering techniques, multi-parametric accuracy analysis and a new technique for removing the meteorological tide factors were also used. Results were compared with the EGM96 geoid model. The calculated differences ranged between 0 and 48 cm. The error of the results was estimated to fall within 3.31 cm. The 3D image of the marine topography in the region shows a nearly constant slope of 4 cm/km in the N–S direction. Thus, the effectiveness of the approach “repeated GNSS measurements on the same route of a ship” developed in the context of “GNSS methods on floating means” has been demonstrated. The application of this approach using systematic multi-track recordings on conventional liner ships is very promising, as it may open possibilities for widespread use of the methodology across the world.

Validating Geoid Models with Marine GNSS Measurements, Sea Surface Models, and Additional Gravity Observations in the Gulf of Finland

Traditionally, geoid models have been validated using GNSS-levelling benchmarks on land only. As such benchmarks cannot be established offshore, marine areas of geoid models must be evaluated in a different way. In this research, we present a marine GNSS/gravity campaign where existing geoid models were validated at sea areas by GNSS measurements in combination with sea surface models. Additionally, a new geoid model, calculated using the newly collected marine gravity data, was validated. The campaign was carried out with the marine geology research catamaran Geomari (operated by the Geological Survey of Finland), which sailed back and forth the eastern part of the Finnish territorial waters of the Gulf of Finland during the early summer of 2018. From the GNSS and sea surface data we were able to obtain geoid heights at sea areas with an accuracy of a few centimetres. When the GNSS derived geoid heights are compared with geoid heights from the geoid models differences between the respective models are seen in the most eastern and southern parts of the campaign area. The new gravity data changed the geoid model heights by up to 15 cm in areas of sparse/non-existing gravity data.

Regional geoid determination in Tierra del Fuego including GPS levelling

A regional geoid model for the Argentine part of the Isla Grande de Tierra del Fuego, established in previous works on the basis of GPS levelling, suffers a lack of observation data in the remote south-western investigation area. In order to improve the data distribution in this region, the mean lake level of Lago Fagnano has been regarded as a natural indicator for the local geoid. Using a GPS buoy and pressure tide gauges, a method to determine the mean lake surface topography with respect to the ellipsoid has been developed. It is shown that the obtained lake level geometry is essentially controlled by the regional gravity field. The derived information on the mean lake level has been included in the geoid model, which results in a more detailed and plausible representation of the regional geoid.

Determination of Orthometric Height using GNSS and EGM Data: a Scenario of the Federal University of Technology Akure

The advent of Global Navigation Satellite System (GNSS) and Earth Gravitational Model (EGM)particularly Global Positioning System (GPS) has modernized geodetic surveying in providing horizontal and vertical positions of points with a sub-meter level of accuracy over the reference ellipsoid. The GPS gives ellipsoidal heights which makes the conversion of the heights to orthometric heights possible by incorporating a geoid model. The conventional method of determining orthometric height is tedious, time-consuming, and labour intensive. This study entails the determination of orthometric height using GNSS and EGM data. A total of forty-nine (49) stations selected within the study area were occupied for GPS observation using South DGPS instrument in static mode for the position and ellipsoidal height determination. The geoidal height values of the GPS derived data were computed using GeoidEval utility software with reference to three different EGMs (EGM2008, EGM96 and EGM84). In order to determine the orthometric heights of the selected stations, the difference between the EGM geoidal height values (NEGM) and the ellipsoidal heights were computed. The results show that the orthometric height obtained with respect to EGM2008 gives better results with a standard deviation of 9.530m and a standard error of 1.361m. The study reveals that the use of GNSS and EGM data for orthometric height determination is less expensive, less tedious, accurate and time-saving compared to the conventional approach of geodetic and spirit levelling.

Optimum Combinations of GGM and GDEM Models for Precise National Geoid Modelling

This study aims to develop a Local Geoid Model (LGM) for Egypt to determine the optimal combinations of global models with Global Navigation Satellite Systems (GNSS/Levelling) data. A precise national geodetic dataset, four Global Geopotential Models (GGMs), and three global Digital Elevation Models (DEMs) have been utilized. Hence, twelve gravimetric LGMs have been developed using the Least-Square Collocation (LSC) method fitted to GNSS/Levelling data and judged over 100 checkpoints. Results revealed that improvements in local geoid accuracy are attributed mainly to GGMs models representing the long wavelength of the Earth's gravitational field. Regarding DEMs, the accuracy of LGMs does not significantly depend on the utilized DEM. Based on the available data, the attained optimum geoid of Egypt has been developed with a standard deviation, equals 0.129 m.

Vertical Accuracy Assessment of Open Access Digital Elevation Models Using GPS

In this study, the vertical accuracy of the Shuttle Radar Topography Mission Digital Elevation Model Version 2.0 (SRTM30), the Advanced Spaceborne Thermal Emission and Reflection Radiometer Global DEM Version 2.0 (ASTER GDEM2), and Advanced Land Observing Satellite World 3D Digital Surface Model Version 2.1 (ALOS AW3D30) was statistically assessed using GPS data. The Tashkent geodynamical polygon was chosen as a study region, where the land surface can reflect as both natural (tectonic) and man-made (Charvak reservoir load effect) processes. The geometric approach using GPS/leveling stations and EGM96 GGM-based geoid undulations was applied for local geoid modeling. RMSE of ~7.48 m, ~6.90 m, and ~8.24 m was obtained for SRTM30, ASTER GDEM2, and ALOS AW3D30, respectively. ASTER GDEM2 proved to be the most accurate DEM with absolute vertical accuracy LE90 of 11.35 m and ME of 5.25 m and it is very suitable for geodetic and hydrological studies in this mountainous area.