Global Geopotential Models

The determination of gravimetric geoid models using gravity anomalies requires the computation of normal gravity on specific ellipsoids. For global models, the International Gravity Formula is applied to the WGS 84 ellipsoid, while local models use the ellipsoid adopted for geodetic computation in the region of study. In countries that use the Clarke 1880 ellipsoid, a theoretical gravity model is computed on this surface to establish a precise local geoid model. This paper formulates a local theoretical gravity model for calculation of theoretical gravity values on the Clarke 1880 spheroid using the Somiglinana's closed formula for normal gravity, angular velocity, gravitational constant, and the Clarke 1880 spheroid parameters. The model is presented in two forms (A and B) and compared to ensure accuracy. Both forms of the model are suitable for accurate normal gravity computation on the Clarke 1880 ellipsoid.

This research investigates the performance of six satellite-only GOCE-based Global Geopotential Models (GGMs) released between 2018 and 2023. They include the WHU-SWPU-GOGR2022S, GOSG2S, Tongji-GMMG2021S, GO_CONS_GCF_2_TIM_R6, IGGT_R1C, and GOSG01S models. The assessment has been carried out using 221 first-order observed gravity stations in Egypt where 16 of them are of absolute gravity measurements. In addition, the assessment comprises the World Gravity Map 2012 (WGM 2012) as another unique open-source of gravity information worldwide. The accomplished findings have demonstrated that the WHU-SWPU-GOGR2022S model produces the least standard deviation of ±11.272 mGal over the available absolute gravity stations. On relative gravity points, the GOSG2S is the accurate GGM a with standard deviation equals ±15.480 mGal. Even though the WGM 2012 is not a GOCE-based GGM it has produced standard deviations of ±7.598 and ± 12.296 mGal at absolute and relative gravity locations respectively. Thus based on the available datasets and attained results, it can be concluded that the WGM 2012 and the WHU-SWPU-GOGR2022S GGM precisely describe the Earth's gravitational field over Egypt in particular. Furthermore, it is recommended to utilize those two sources of free-air gravity anomalies in geodetic activities chiefly for local geoid modelling.

Tez (Doktora) -- İstanbul Teknik Üniversitesi, Fen Bilimleri Enstitüsü, 2007Thesis (PhD) -- İstanbul Technical University, Institute of Science and Technology, 2007Bu çalışmada, GPS tekniğinden elde edilen elipsoidal yüksekliklerin bölgesel düşey datumdaki ortometrik yüksekliklere dönüştürülmesinde lokal geoit modeli çözümlerinin kullanımı araştırılmıştır. Araştırma iki kısımdan oluşmaktadır. Birinci kısımda Türkiye ulusal geoitleri TG99A ve TG03 ile Avrupa gravimetrik geoidi EGG97 beş adet lokal bölgedeki GPS/nivelman verileri kullanılarak test edilmiştir. Daha sonra bu modeller GPS/nivelman noktalarında geoit yükseklik farkları kullanılarak hesaplanan yüzey modelleri ile ulusal düşey datuma uydurulmuş ve bağımsız GPS/nivelman verileri yardımıyla sonuçlar test edilmiştir. Bölgesel geoit modelleri ile gerçekleştirilen bu testlerden başka lokal GPS/nivelman geoit modelleri hesaplanmış doğrulukları irdelenmiştir. Test edilen ve yeni hesaplanan geoit modellerinin doğrulukları karşılaşt...

GOCE has contributed important gravity information towards the definition and realization of the new North American height reference system. In addition to the new gravimetric geoid models based on GOCE, offsets of the classical levelling-based vertical datums in North America, namely CGVD28 in Canada and NAVD88 in the USA and Mexico, can be computed with respect to a global equipotential surface defined by means of a GOCE-based geoid. Although the two datums will eventually be replaced by a common and continent-wide vertical datum (and in fact the new Canadian height datum established in 2013 is already geoid based), their connection and unification is of great interest to the scientific and user communities.

GPS (Global Positioning System) is a passive, all-weather satellite-based navigation and positioning system, which is designed to provide precise three dimensional position and velocity, as well as time information on a continuous worldwide basis. The ability of GPS for providing high-precision vertical component of relative coordinates could be exploited for monitoring, and hence mapping, the sea level. In this case, the local nature of GPS measurements could nicely supplement the temporal and spatial resolution of satellite altimetry measurements which has a more or less global nature. This paper would describe and discuss the concept and method of monitoring sea level using GPS, and the technical and operational aspects that should be taken into account in implementing this technique. The paper would also discuss the prospect of using this GPS-based approach for monitoring sea level in Indonesia, along with its potential related applications. The paper would be sum up with some concluding remarks and recommendations. I.

The vertical height system in Kenya is anchored on a single levelling-based tidal gauge, which is referred to as mean sea level. The fusion of existing height systems into the world height system is one of the primary objectives of the International Height Reference System (IHRS) implementation. Computing the datum offset with regard to the global IHRS datum and the zero-height geopotential value can help achieve this goal in part. This paper studies the approach of using a Global Geopotential model (GGM) with the GNSS-levelling as a convenient method for vertical datum offsets' computation that may connect two or more vertical datums. To reduce the geoid omission error of the GGMs, an optimized GGM is developed and utilized up to a maximum of 3600 • and order. For the first time, the numerical analyses of this work reveal the zero-height geopotential and its associated standard error of the Kenyan vertical datum, from which the datum offsets with the IHRS were estimated. Values of 62636850.996 ± 0.104m 2 s − 2 and − 24.5 ± 1.04cm were obtained as the geopotential of the zero-height and vertical datum offset with respect to the global value, respectively.

This study investigates to use GPS/Levelling measurements of Kuwait and four heuristic regression methods including Least Square Support Vector Regression (LSSVR), Gaussian Process Regression (GPR), Kernel Ridge Regression (KRR), and Multivariate Adaptive Regression Splines (MARS) for modelling local geoid undulation. The accuracy of the models was compared by geoid undulation of gravitational observations and Global Geopotential Models (GGMs). The results show that the KRR model is suitable for Kuwait geoid model, its error of percentage is 0.018 and 0.124% relative to gravity and GPS/Levelling geoid undulation models, respectively. Furthermore, the comparison of KRR model with GGMs models signifies its accuracy.

In this study, a thorough validation of the recently released Global Geopotential Models (GGMs) has been carried out by comparing all models with both the free-air (FA) gravity anomaly observations and GPS/Levelling data in Kuwait. First, the gravity functional in terms of FA gravity anomalies and geoid heights that derived from GGMs and compared with the ground-based data before applying the Spectral Enhancement Method (SEM). The findings indicate that the combined GGMs, generally, fit the ground data better than the satellite-only GGMs due to the existing spectral gaps. Second, the FA gravity anomalies and geoid heights, obtained from GGMs at maximum Spherical Harmonics (SH) degree/order (d/o) for the combined models and from spherical harmonics d/o ranging from 100 to their maximum d/o, with a step of 10 d/o for the satellite only GGMs, were compared with the corresponding ones from terrestrial data using the SEM. For the FA gravity signal, the EIGEN-6C4 manifested the best results of combined GGMs with differences characterised with a mean of 0.967 mGal and a Standard Deviation (STD) of 2.845 mGal, while TIM_R5 at SH (d/o) 200 showed the best results with a mean of satellite only GGMs with a mean if 1.008 mGal and a STD of 2.657 mGal. In the case of the evaluation of the geoidal height with GPS/levelling, XGM2016 manifested the best results of combined GGMs with differences characterised with a STD of 0.234 m. For the satellite only GGMs, the best results have been obtained from SPW_R5 at SH d/o 250 with a STD 0.207 m.

Digital Elevation Model (DEM) is crucial to a wide range of surveying and civil engineering applications worldwide. Some of the DEMs such as ASTER, SRTM1 and SRTM3 are freely available open source products. In order to evaluate the three DEMs, the contribution of EGM96 are removed and all DEMs heights are becoming ellipsoidal height. This step was done to avoid the errors occurred due to EGM96. 601 points of observed ellipsoidal heights compared with the three DEMs, the results show that the SRTM1 is the most accurate one, that produces mean height difference and standard deviations equal 2.89 and ±8.65 m respectively. In order to increase the accuracy of SRTM1 in EGYPT, a precise Global Geopotential Model (GGM) is needed to convert the SRTM1 ellipsoidal height to orthometric height, so that, we quantify the precision of most-recent released GGM (five models). The results show that, the GECO model is the best fit global models over Egypt, which produces a standard deviation of geoid undulation differences equals ±0.42 m over observed 17 HARN GPS/leveling stations. To confirm an enhanced DEM in EGYPT, the two orthometric height models (SRTM1 ellipsoidal height + EGM96) and (SRTM1 ellipsoidal height + GECO) are assessment with 17 GPS/leveling stations and 112 orthometric height stations, the results show that the estimated height differences between the SRTM1 before improvements and the enhanced model are at rate of 0.44 m and 0.06 m respectively.

According to the wide spread use of satellitebased positioning techniques, especially Global Navigation Satellite Systems (GNSS), a greater attention has been paid to the precise determination of geoid models. As it is known, leveling measurements require high cost and long time in observation process that make it not convenient for the practical geodetic purposes. Thus obtaining the orthometric heights by GNSS is the most conventional way of determining these heights. Verifying this goal was the main objective behind the current research. The current research introduces a numerical solution of geoid modeling by applying a surface fitting for a few sparse data points of geoid undulation using minimum curvature surface (MCS). The MCS is presented for deriving a system of linear equations from boundary integral equations. To emphasize the precise applicability of the MCS as a tool for modeling the geoid in an area using GPS/leveling data, a comparison study between EGM2008 and MCS geoid models, is performed. The obtained results showed that MCS technique is a precise tool for determining the geoid in Egypt either on regional and/ or local scale with law distortion at check points.

The Italian official height system is defined through a high precision levelling network established and maintained by the Istituto Geografico Militare - IGM. During the last 20 years, IGM has performed levelling campaigns on almost the whole peninsular area of Italy with the aim of both densifying the existing network and updating the reference heights. This paper reports about the procedure applied to correct the levelling observations for the gravity effects and the assessment on the results. The needed gravity values were predicted from the Italian gravity dataset (IGD), and both from EGM2008 and XGM2019e high resolution global gravity models. A new formulation of the normal correction as well as the standard orthometric correction were applied. The IGD derived corrections proved to be effective by reducing the misclosure error of critical loops below the tolerance level. Gravity data derived from EGM2008 and XGM2019e proved to be too poor for the correction purposes, as it was ...

GGMs GNSS/Levelling Geoid Statistical values This paper focuses on making a comparing of GNSS/Levelling data and data obtained from global geopotential models. For comparison, geoid undulations obtained by GNSS/Levelling method and geoid undulations obtained from global geopotential models have been used. As global geopotential models, SGG-UGM-2, XGM2019e_2159, GO_CONS_GCF_2_TIM_R6e, ITSG-Grace2018s, EIGEN-GRGS.RL04.MEAN-FIELD, GOCO06s, GO_CONS_GCF_2_TIM_R6, GO_CONS_GCF_2_DIR_R6 GGMs are used. The data sets used in the improvements of the models are altimetry, satellite, location data and topography. The disparities between the geoid undulations obtained from the GNSS/Levelling method and geoid undulations obtained from global geoid models have been taken. Some statistical criteria for these differences have been calculated. These criteria, such as smallest, biggest, average, standard deviation, Root Mean Square RMS statistical values of deviations between GNSS/Levelling geoid and global geopotential models, are taken into consideration when comparing the models. According to the comparison, the global gravity field model that best fits the GNSS/Levelling is selected.

The GOCE satellite mission is one of the main achievements of the satellite geodesy for the Earth's gravitational field recovery. Three different approaches have been developed for the estimation of harmonic coefficients from gradiometry data measured on board of GOCE-satellite. In this paper a special version of the space-wise method based on the second method of Neumann for fast determination of the harmonic coefficients C nm , S nm of the Earth's gravitational potential is given based on the radial gravity gradients of the EGG_TRF_2 product, except of two polar gaps filled by radial gradients from the EGM2008 gravity model. In the pre-processing stage GOCE-based second degree radial derivatives were averaged to the regular grid through Kalman static filter with additional Gaussean smoothing of residual radial derivatives. All computations are made by iterations. As the first step the determination of the preliminary NULP-01S model up to degree/order 220 derived from the Gaussean grid of the GOCE radial derivatives with respect to the WGS-84 reference field was developed based only one of the radial gradients EGG_TRF_2 in the EFRF-frame. In the second iteration the same algorithm is applied to build the NULP-02S gravity field model up to degree/order 250 using the same Gaussean grid with respect to the NULP-01S reference field. The NULP-02S model was verified by means of applying various approaches for the construction of the gridded gravity anomalies and geoid heights in the Black Sea area using processing of datasets from six altimetry satellite missions. Comparison of different models with GNSS-levelling data in the USA area demonstrates the independent verification of achieved accuracy of the constructed NULP-02S Earth's gravity field model.

The gravity field is important to determine the size and shape of the earth, to determine the heights, to investigate the structure of the crust, and to explore the mineral wealth. A lot of gravity observations have been taken in Egypt. Those gravity observations are taken over a long-time span with different gravimeters, different references, and different processing methodologies. Those huge amounts of data need to be filtered and unified before using them in precise geoid determination. In the advent of satellite missions for gravity field determination and the yielded global gravity models with good resolution and precision, filtering the terrestrial observed gravity and improving the global gravity models should be done. In this research, the recent Global Geopotential Models (GGMs) will be used in filtering the terrestrial gravity anomalies, and then the reliable terrestrial anomalies will be used in improving the global model gravity anomalies. Four recent GGMs (EGM2008, XGM2019e_2159, GOCO06s, and SGG-UGM 2) are validated using terrestrial gravity anomalies to determine which model best fits the Earth's external gravity field in Egypt. Thousands of terrestrial gravity anomalies are collected as different data sets, so one of the aims of this research is to unify them using the common points among them. Finally, gravity anomalies are used to obtain their corresponding undulation values using a simple model. The obtained results of this study are recommended when collecting all the gravity observations taken all over Egypt to compute precise gravimetric geoid.

, GETECH Ltd. at the University of Leeds, is acknowledged for providing gravity data to the thesis research. Also, Steve Kenyon is thanked for providing the SRTM data. I acknowledge the International Gravimetric Bureau (BGI) for providing a part of the data used in this thesis. I am grateful to my parents Öznur and Mustafa Özöner, and my sister Özge Özöner, for their continuous support, generosity and encouragement during such a long and difficult period. They always did their best to keep me motivated and made me feel that I am very precious for them. They have always believed that I could succeed and this has made me stronger. Never ending thanks are given to them. My parents-in-law Fatmana and Mehmet Erol gave me their support and encouraged me all the time during this study, I am grateful to this. Last, but with great importance, I would like to thank my husband, Serdar Erol, who made this stressful period bearable with his understanding, kindness and patience. His endless support, help, encouragement and love made this thesis possible. I always feel the luckiest person because I share my life with him.

The International Service for the Geoid (ISG, https://www.isgeoid.polimi.it/) 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. 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, 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), 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). 1 Introduction The geoid, an equipotential surface of the Earth gravity field (Heiskanen and Moritz, 1967, Sansò and Sideris, 2013) has important applications in engineering for the definition of physical heights (Sansò et al., 2019), for example to compute them from ellipsoidal heights observed by GNSS techniques, and in geosciences, for example to determine the ocean geostrophic currents (Bingham et al., 2008, Knudsen et al., 2011). Because of its definition, the geoid is naturally modelled as a surface at a global level, typically through a truncated spherical harmonic expansion. The use of base functions on a spherical domain is justified by the fact that the geoid undulation is an anomalous quantity with respect to a given reference ellipsoid, while the

The last geopotential model EGM2008 has been compared with gravity and GPS/leveling data over the Central Mediterranean area. In this area, the gravity field has sharp variations due to strong topography/bathymetry signals and to relevant geophysical features. More than 300.000 gravity values covering the whole area have been considered in the comparisons. These data were used in the last Italian geoid computation and have been validated for datum consistency and for outliers. Further comparisons have been carried out using GPS/leveling data which are homogeneously distributed over the Italian Peninsula. About 1000 available values have been used in the comparison. The results show that, in this area, EGM2008 fits gravity and GPS/leveling data better than other existing global models. The geopotential model performances have been also compared with those of the last Italian geoid estimate, the ITALGEO05 geoid which has been computed in 2005. The statistics of the residuals with GPS/leveling data show that EGM2008 and ITALGEO05 have comparable accuracies, even though EGM2008 is slightly better.

In this paper, some features of the local disturbing potential model developed by the GGI method (based on Geophysical Gravity Inversion) were analyzed. The model was developed for the area of the Western Carpathians covering the Polish-Slovak border. A detailed assessment of the model's property was made regarding the accuracy of the disturbing potential values (height anomalies), gravity values, complete Bouguer anomalies (CBA), and differences between geoid undulations and height anomalies (N − ζ). Obtained accuracies of the GGI quasigeoid model (in terms of standard deviation of the residuals to the reference quasigeoid models) were at the level of ±2.2 cm for Poland and ±0.9 cm for the Slovak area. In terms of gravity, there was shown dependence of the accuracy of the GGI model on the digital elevation model (DEM) resolution, the point height, the density of gravity data used, and used reference density of topography model. The best obtained results of gravity prediction were characterized by an error of approximately 1 mGal. The GGI approach were compared with classical gravity prediction methods (using CBA and topographic-isostatic anomalies supported by Kriging prediction), getting very similar results. On the basis of the GGI model, CBA and differences (N − ζ) were also determined. The strong dependence of resolution of the CBA model obtained by GGI approach, on the size of the constant density zones, has been demonstrated. This significantly reduces the quality of such a model. The crucial importance of the topographic masses density model for both determined values (CBA and (N − ζ)) was also indicated. Therefore, for determining these quantities, all available information on topographic mass densities should be used in modelling.

In this paper, some features of the local disturbing potential model developed by the GGI method (based on Geophysical Gravity Inversion) were analyzed. The model was developed for the area of the Western Carpathians covering the Polish-Slovak border. A detailed assessment of the model's property was made regarding the accuracy of the disturbing potential values (height anomalies), gravity values, complete Bouguer anomalies (CBA), and differences between geoid undulations and height anomalies (N − ζ). Obtained accuracies of the GGI quasigeoid model (in terms of standard deviation of the residuals to the reference quasigeoid models) were at the level of ±2.2 cm for Poland and ±0.9 cm for the Slovak area. In terms of gravity, there was shown dependence of the accuracy of the GGI model on the digital elevation model (DEM) resolution, the point height, the density of gravity data used, and used reference density of topography model. The best obtained results of gravity prediction were characterized by an error of approximately 1 mGal. The GGI approach were compared with classical gravity prediction methods (using CBA and topographic-isostatic anomalies supported by Kriging prediction), getting very similar results. On the basis of the GGI model, CBA and differences (N − ζ) were also determined. The strong dependence of resolution of the CBA model obtained by GGI approach, on the size of the constant density zones, has been demonstrated. This significantly reduces the quality of such a model. The crucial importance of the topographic masses density model for both determined values (CBA and (N − ζ)) was also indicated. Therefore, for determining these quantities, all available information on topographic mass densities should be used in modelling.

Terrestrial measurements can provide accurate gravity data, but it is costly and time-consuming for large and remote area. Airborne gravity measurements have actually been carried out in Indonesia since 2008 by Technical University of Denmark (DTU) in collaboration with the Geospatial Information Agency (BIG). Purpose of the project was to develop a geoid model used for converting elevations from GPS/GNSS measurements that refers to ellipsoid to orthometric elevations that refer to sea level. The data can actually be explored so that it can be used for geophysical and other geoscience purposes, but the data must be carefully treated and extracted into observational gravity data. This study aims to improve the accuracy of gravity airborne data to produce an accurate complete Bouguer anomaly map. The data used in this study were airborne gravity data over Province of Southeast Sulawesi collected on September 29, 2008 to October 1, 2008.  Variation in flight height at the time of conse...

Requirement for a high resolution geoid model has increased substantially during the last few decades especially with the advent of Global Positioning System (GPS). Many countries across the world have already developed their own geoidal model which serve as the means of deriving orthometric heights from GNSS observations. On the other hand, the need for transformation of the ellipsoidal heights derived from GNSS observations to the physical orthometric heights has forced geodesists to determine the high precision local geoid heights. Besides, because orthometric heights are used in engineering and GIS applications, local quasi-geoid determination studies have become especially important. As it is well known, Turkey is situated on a tectonically very active region and earthquakes occurring in different times cause deformations in heights of levelling points of Turkish National Vertical Network. On the other hand, National Mapping Agency of Turkey (GDM: General Directorate of Mapping) which is responsible for the establishment and maintenance of national geodetic networks compute geoid models for whole Turkey and release them for public use in different periods. These GDM-computed geoid models are called "hybrid geoid" models. Hybrid geoid models are computed with the combination of gravimetric geoid models and geoid heights on the GPS_levelling points. And it is also known that the absolute accuracies of these geoid models are nearly at the 10 cm level or even worse. But, the requested accuracy is about better than 5 cm. Hence, in order to prove that the required accuracy levels can be achieved, a local gravimetric and quasi-geoid determination project using the resources of Selçuk University was initiated. Project area has been planned to cover a limited part of Central Anatolia including Konya. Necessary basic data (gravity, levelling etc.) for this project have been obtained in the field by performing observations/measurements. Some other necessary data such as absolute gravity values have been obtained from GDM. And as the next phase, high accuracy (better than 5 cm) local gravimetric and quasi-geoid models will be computed for the limited part of Central Anatolia using the above mentioned data. In order to be able to reach this goal suitable geoid computations softwares must be used. In this project, we will use DFHRS developed by the Karlsruhe Applied Sciences and GRAVSOFT softwares. According to the results to be obtained from this project, a more comprehensive project will be launched and the project area will be expanded. Thus, additional gravity, levelling and GNSS measurements will be carried out in the new project area for the determination of a high accuracy regional gravimetric geoid.

Several post-processing methods have been developed over the last years in order to take into consideration topography within satellite-based solar radiation maps using digital elevation models (DEM). If the main part of these procedures is to estimate the obstructed horizon around each DEM point of a given region so as to consider terrain-based shading effects, the size of the area can also limit this implementation. That is why we have developed a new efficient horizon model based on the DEM retrieved during the Shuttle Radar Topography Mission (SRTM). In order to be usable at any world location with the same expected accuracy, this model is only derived from mathematical statements without any kind of empirical approximation. Validation against in situ horizons and comparison with some other models have finally shown this one presents both better accuracy (RMSE of 1.555 • against 1.712 • or more) and lower computation time (at least 4 times faster). Furthermore, in the case of very large areas, we propose an optimization procedure allowing the user to knowingly alter the modeling error in order to reduce processing time. Finally, using in situ data, we have also developed a method for predicting the repercussion of the original SRTM DEM error on the final horizon precision.

Satellite data sets are an asset in global gravity collections; their characteristics vary in coverage and resolution. New collections appear often, and the user must adapt fast to their characteristics. Their use in geophysical modeling is rapidly increasing; with this in mind we compare two of the most densely populated sets: EIGEN-6C4 and GGMplus. We characterize them in terms of their frequency histograms, Free Air anomalies, power spectrum, and simple Bouguer anomalies. The nature of the digital elevation models used for data reduction is discussed. We conclude that the GGMplus data set offers a better spatial resolution. To evaluate their effect in geophysical modelling, we chose an inland region with a prominent volcanic structure in which we perform 3D inversions of the respective Bouguer anomalies, obtaining density variations that in principle can be associated with the geologic materials and the structure of the volcanic edifice. Model results are analyzed along sections of the inverted data; we conclude that the GGMplus data set offers higher resolution in the cases analyzed.

We improve the accuracy of global geoid models (GGMs) by utilizing deep convolutional neural networks (CNNs) and empirical rules. The geoid heights obtained from the global geopotential models (GGM), EGM2008, and XG2019, are validated using geometrical geoid heights obtained from GNSS/leveling data. We used AlexNet, LeNet, and VGG16 CNN models to investigate the improvement of geoid accuracy and found that VGG16 model shows the most signiĄcant improvement among all the models. The VGG16 model improves the geoid accuracy of EGM2008 and XGM2019e by about 39 cm. Additionally, we apply empirical rules for outliers detection to eliminate unreliable GNSS/leveling data and found that this further improves the geoid accuracy by 13 cm for EGM2008 and 12 cm for XGM2019e. We also used a 7-parameter stochastic model to remove existing systematic errors, impacting 9 mm on AlexNet and VGG16. Keywords geoid • CNNs • EGM2008 • XGM2019e • AlexNet • LeNet • VGG16 • outliers removal. 1 Introduction The geoid is considered a crucial geodetic reference surface since it represents a connection between different surfaces and height systems. The geoid connects the orthometric and ellipsoidal heights geometrically through a simple mathematical relationship (Heiskanen and Moritz, 1967). However, the computation of each of these heights has its complexity and challenges. For instance, the geoid calculation has different considerations regarding the M. Nasser * Corresponding author

One of the main challenges in physical geodesy today is achieving the 1-centimetre gravimetric quasi-geoid model, since a model of such accuracy could be used in the definition and realisation of the height reference frame. One of the main obstacles in this challenge is the lack of terrestrial gravity data or its uneven distribution. Therefore, the main question arises: what density of gravity points is necessary in order to obtain a gravimetric quasi-geoid model with an accuracy of 1 centimetre or even better? In this simulated study, the results show a trend of decreasing RMS related to the sparser dataset used in computation, leading to the conclusion that the determination of the sub-centimetre quasi-geoid model is no longer a theory, but can be achieved with the exact density of terrestrial gravity data: gravity observation stations have to be distributed no farther than 500 m from one another. When dealing with a very rough topography, the distance should be even shorter.

The development of a high-resolution and high accuracy geoid model is becoming nowadays a fundamental component of any modern geodetic infrastructure. The Kingdom of Saudi Arabia (KSA) has devoted the last decade a significant number of resources and manpower to collect high-quality land and airborne gravity data as well as GNSS/Levelling observations to create a state-of-the-art geoid model as a fundamental part of the Saudi Arabia National Spatial Reference System (SANSRS). In that frame, this work focuses on the collected gravity, terrain, and GNSS/Levelling data for the area under study, and their pre-processing in terms of horizontal, vertical and gravity reference system homogenization, blunder detection and removal. Given the availability of these data the latest gravimetric geoid model for the KSA is developed.The gravity data pre-processing relied on the available metadata to collect information about the horizontal, vertical and gravity reference system. Hence, all this in...

Nowadays the Global Positioning System (GPS) is one of the most favorite techniques in practical geodesy. A major dilemma in GPS surveying lies in its ellipsoidal-based type of heights, while in engineering practice orthometric heights are usually utilized. Thus, it is important to convert GPS heights into orthometric heights through applying an accurate geoid model. The objectives of this paper are to model a local geoid in the study area using GPS/levelling technique, and to evaluate the performance of several Global Geopotential Models (GGMs) particularly the OUS-91A, EGM96 and EGM2008 in the study area, which is located in the northern Egypt at Rosetta zone area. The accomplished results show that the EGM 2008 represents the most precise global geopotential model to be used for geoid determination in Egypt. Furthermore, the achievable accuracy of local geoid determination in the study area after using regression method models is ranges between 0.059 meter to -0.083 meter, with a...

An optimum Global Geopotential Model (GGM) is required either to represent the long wavelength of the Earth's gravitational field in gravimetric geoid modelling or to act as a stand-alone national geoid in some developing countries. Thus, the current research aims to investigate the performance of seven recent high-order GGMs over Egypt utilizing the most recent precise Global Navigation Satellite Systems(GNSS)/Levelling datasets. Attained results showed that the investigated GGMs perform differently over Egypt with an accuracy level varying between ±0.249 m for the SGG-UGM-1 model and ±0.300 m for the GECO model. Removing outliers in the terrestrial dataset reveal significant improvements, in terms of standard deviations. Consequently, the performance of the investigated GGMs has been modified where the EIGEN-6C4 model became the best model with a standard deviation equals ±0.172 m. Furthermore, a 3D spatial correction surface has been constructed and has been added to the original EIGEN-6C4 model to get an enhanced version of the global EIGEN-6C4. Over checkpoints, the average error of the enhanced model equals −0.018 m with a standard deviation equal ±0.011 m. That means that incorporating terrestrial geodetic data into the global EIGEN-6C4 model has increased its accuracy in Egypt by almost 36 %. Accordingly, such developed enhanced GGM represent the optimum stand-alone geoid model in Egypt. Nevertheless, such accuracy levels of GGMs do not fulfill the requirements of high-accuracy surveying and civil engineering applications. That concludes that a precise national geoid model is still crucial. It is recommended that all available geodetic datasets should be collected from all governmental and private organizations to construct a national geodetic database that would be implemented in modelling an Egyptian local geoid.

The orthometric height has an essential role in a variety of civil engineering projects and it is defined as the length of the curved plumbline from a point (on the earth surface) to its intersection with the geoid surface. Leveling process is considered as the most accurate technique for obtaining these heights. However, regardless of its potentials, it is tedious, costly, and time consuming. Recently many organizations and research centers have developed multi Global Geopotential Models (GGMs) depending on several types of available gravity and height datasets to estimate orthometric heights from GNSS measurements. In this study, we present an evaluation and assessment of the accuracy of five of recent and popular GGM S : XGM2016, XGM2019e, EIGEN-6C4, GO_CONS_GCF_2_TIM_R6e, and EGM2008 using actual 145 GNSS/leveling points and 96 terrestrial gravity points. The goal of this research is to find the best fit model along the study area located along the coastal zones of Egypt with distances of about 1,970 km for further determination of geoid modeling at regional scale. The selection of these areas basically was due to their developmental, urban, and economical importance and their continuous need for protection works to fight against the coastal erosion caused by climate change and global warming. The results indicated that for geoid undulation, GO_CONS_GCF_2_TIM_R6e model is the best fit GGM for the estimation of geoid model along Mediterranean Sea coastal line, while XGM2019e_2159 model is the best suitable for coastal line of the Red Sea. And regarding the gravity anomalies, the most reliable GGMs for this study area are XGM2019e_2159 and EIGEN-6C4 for Bouguer and free-air gravity anomaly, respectively.

The orthometric height has an essential role in a variety of civil engineering projects and it is defined as the length of the curved plumbline from a point (on the earth surface) to its intersection with the geoid surface. Leveling process is considered as the most accurate technique for obtaining these heights. However, regardless of its potentials, it is tedious, costly, and time consuming. Recently many organizations and research centers have developed multi Global Geopotential Models (GGMs) depending on several types of available gravity and height datasets to estimate orthometric heights from GNSS measurements. In this study, we present an evaluation and assessment of the accuracy of five of recent and popular GGMS: XGM2016, XGM2019e, EIGEN-6C4, GO_CONS_GCF_2_TIM_R6e, and EGM2008 using actual 145 GNSS/leveling points and 96 terrestrial gravity points. The goal of this research is to find the best fit model along the study area located along the coastal zones of Egypt with dist...

The Italian official height system is defined through a high precision levelling network established and maintained by the Istituto Geografico Militare - IGM. During the last 20 years, IGM has performed levelling campaigns on almost the whole peninsular area of Italy with the aim of both densifying the existing network and updating the reference heights. This paper reports about the procedure applied to correct the levelling observations for the gravity effects and the assessment on the results. The needed gravity values were predicted from the Italian gravity dataset (IGD), and both from EGM2008 and XGM2019e high resolution global gravity models. A new formulation of the normal correction as well as the standard orthometric correction were applied. The IGD derived corrections proved to be effective by reducing the misclosure error of critical loops below the tolerance level. Gravity data derived from EGM2008 and XGM2019e proved to be too poor for the correction purposes, as it was ...

Requirement for a high resolution geoid model has increased substantially during the last few decades especially with the advent of Global Positioning System (GPS). Many countries across the world have already developed their own geoidal model which serve as the means of deriving orthometric heights from GNSS observations. On the other hand, the need for transformation of the ellipsoidal heights derived from GNSS observations to the physical orthometric heights has forced geodesists to determine the high precision local geoid heights. Besides, because orthometric heights are used in engineering and GIS applications, local quasi-geoid determination studies have become especially important. As it is well known, Turkey is situated on a tectonically very active region and earthquakes occurring in different times cause deformations in heights of levelling points of Turkish National Vertical Network. On the other hand, National Mapping Agency of Turkey (GDM: General Directorate of Mapping) which is responsible for the establishment and maintenance of national geodetic networks compute geoid models for whole Turkey and release them for public use in different periods. These GDM-computed geoid models are called "hybrid geoid" models. Hybrid geoid models are computed with the combination of gravimetric geoid models and geoid heights on the GPS_levelling points. And it is also known that the absolute accuracies of these geoid models are nearly at the 10 cm level or even worse. But, the requested accuracy is about better than 5 cm. Hence, in order to prove that the required accuracy levels can be achieved, a local gravimetric and quasi-geoid determination project using the resources of Selçuk University was initiated. Project area has been planned to cover a limited part of Central Anatolia including Konya. Necessary basic data (gravity, levelling etc.) for this project have been obtained in the field by performing observations/measurements. Some other necessary data such as absolute gravity values have been obtained from GDM. And as the next phase, high accuracy (better than 5 cm) local gravimetric and quasi-geoid models will be computed for the limited part of Central Anatolia using the above mentioned data. In order to be able to reach this goal suitable geoid computations softwares must be used. In this project, we will use DFHRS developed by the Karlsruhe Applied Sciences and GRAVSOFT softwares. According to the results to be obtained from this project, a more comprehensive project will be launched and the project area will be expanded. Thus, additional gravity, levelling and GNSS measurements will be carried out in the new project area for the determination of a high accuracy regional gravimetric geoid.

In this study, 96 bench marks and unified control points across South Korea were selected as GPS/Leveling stations, GPS surveying was conducted in the Network-RTK (VRS) method and the results were utilized to calculate geometric geoidal heights. These geometric geoidal heights were utilized in the evaluation of the geoid models comprising global gravity field models, such as EGM2008 and EIGEN-6C4, and South Korean geoid models, such as KNGoeid13 and KNGeoid14. In addition, geoid model KNGeoid14, which was found to have the highest accuracy and precision through the evaluation, was utilized to calculate GPS derived orthometric heights, and the results were evaluated to review the possibility of orthometric height surveys using the GPS/ Geoid method. As for the results of the study, in the evaluation of the global gravity field models, the standard deviations of EGM2008 and EIGEN-6C4 were shown to be almost the same as the values were 7.0 cm and 7.1 cm respectively, and geoid model KNGeoid14 was found to have been improved compared to KNGeoid13 as its RMS and standard deviation were shown to be smaller than those of KNGeoid13. In addition, differences in the orthometric height values of 96 points derived in the GPS/Geoid method were analysed using geoid model KNGeoid14, and, in the results, the average error was shown to be 3.9 cm and the standard deviations was shown to be 5.2 cm so that the possibility of utilization of the GPS/Geoid method in orthometric height surveys with the decimeter accuracy could be identified.

The development of a high-resolution and high accuracy geoid model is becoming nowadays a fundamental component of any modern geodetic infrastructure. The Kingdom of Saudi Arabia (KSA) has devoted the last decade a significant number of resources and manpower to collect high-quality land and airborne gravity data as well as GNSS/Levelling observations to create a state-of-the-art geoid model as a fundamental part of the Saudi Arabia National Spatial Reference System (SANSRS). In that frame, this work focuses on the collected gravity, terrain, and GNSS/Levelling data for the area under study, and their pre-processing in terms of horizontal, vertical and gravity reference system homogenization, blunder detection and removal. Given the availability of these data the latest gravimetric geoid model for the KSA is developed.The gravity data pre-processing relied on the available metadata to collect information about the horizontal, vertical and gravity reference system. Hence, all this in...

Each gravity observation technique has different parameters and contributes to different pieces of the gravity spectrum. This means that no one gravity dataset is able to model the Earth’s gravity field completely and the best gravity map is one derived from many sources. Therefore, one of the challenges in gravity field modelling is combining multiple types of heterogeneous gravity datasets.  The aim of this study is to determine the optimal method to produce a single gravity map of the Canterbury case study area, for the purposes of use in geoid modelling.  This objective is realised through the identification and application of a four-step integration process: purpose, data, combination and assessment. This includes the evaluation of three integration methods: natural neighbour, ordinary kriging and least squares collocation.  As geoid modelling requires the combination of gravity datasets collected at various altitudes, it is beneficial to be able to combine the dataset using an...

The main goal of the study is the calculation of a high resolution dataset that models the geoid for Greece using several kind of data collected by the Hellenic Military Geographical Service (HMGS). In situ gravity measurements and GPS/levelling on triangulation points plays a central role in the formation of covariance and cross-covariance functions used for the calculation of high frequency residuals. Also global models such as EGM2008 and EIGEN-6C4 contribute in the analysis of collected data and in the removal of low frequencies. A database of older gravity measurements completes and guarantees the data coverage of the whole region leading to a high resolution exported product. The whole project is based on the Remove-Compute-Restore (RCR) technique and the Least Squares Collocation (LSC) method is used at its core during the computation of the residual geoid height. In order to fulfill the RCR technique topographic corrections have been calculated on each measured point and the indirect effect has been computed for the total region. Rasters of the above have been extracted for visualization and analysis. The final product has been transformed through a parametric model for orthometric height adaption. Several scripts have been developed in Matlab and Python for the reckonings as no commercial or scientific software was used. Data combination and visualization in raster format has been made using the ESRI ArcGIS software. The study concludes to three different beta geoid height models depending on the RCR usage for further discussion and which will be evaluated in the light of new data collection.

The aim of this study is to analyze the best fitting geoid model for an arbitrary selected area of investigation. The Digital Finite Element Height Reference Surface (DFHRS) method, developed by Hochschule Karlsruhe has been chosen to define the height reference surface for the territory of Kosovo, which should be defined as national vertical datum. This approach allows the conversion of ellipsoidal heights determined by GPS into the standard heights, which refer to the height reference surface (HRS) of an orthometric, or normal surface system. The DFHRS is defined as continues HRS in arbitrary large areas by bivariate polynomials over an irregular grid (Jager, Schneid 2001). The DFHRS approach uses wide range of the input data (Geometric and Physical) and in our case there were 30 GPS/leveling height data as well as physical derivatives from different global geopotential models. The proposed approach has been successfully applied and results are compared to actual normal heights an...

The purpose of this paper is to determine a high-precision the Republic of Albania geoid model
in order to convert the ellipsoidal heights into orthometric heights. The Digital Finite-Element Height
Reference Surface method was used to solve this problem. The following models were chosen as the Republic
of Albania global geopotential models: EGM96, EGG97 and EGM2008. Calculations of mentioned models
were performed for 151 points of the Republic of Albania territory using the Digital Finite-Element Height
Reference Surface method to determine the height reference surface. The minimum, maximum, mean values,
standard deviation and mean quadratic error of the models in question were identified. The results showed that
EGM96 had a standard deviation of 8 cm, EGG97 had a standard deviation of 4.8 cm and EGM2008 had a
standard deviation of 4.2 cm as the best model. Thus, it was proved that EGM2008 has topographic distribution
and fits well in the extension of the territory of the Republic of Albania.

The existing Bouguer anomaly map, which covers the territory of the Republic of Slovenia is a few decades old. Since then, quite a few new gravimetric measurements (data) for the territory of Slovenia as well as high quality digital terrain models that are needed for creating such a map have been made available. The methodology and standards for creating gravity anomaly maps are also changing. Thus, the national Bouguer anomaly map was updated. There were some gross errors detected in the set of old gravimetric data. Additionally, the influence of new updated gravimetric data was analyzed. The comparison of the various maps and the analysis of the influence of input gravimetric data indicates that the new gravimetric data of Slovenia has a significant influence on the creation of the gravimetric anomaly maps for Slovenia (even over 30 mGals at some points).

This paper presents an attempt to consider whether it is possible to determine a geoid at the centimetre level in the territory of Egypt based on recently available global and local gravity field data. The paper has two main objectives. Firstly, the paper overviews previously published geoid solutions, while the second objective investigates the performance of the recent global geopotential models (GGM) in Egypt. The existing geoid solutions have illustrated that there is an insufficient distribution of data which is sampled inconsistently. At this time, data deficiency still exists, and to overcome it, we have selected a "data window" and applied the Least Square Collocation (LSC) technique. The outcome from LSC was interesting and acceptable, and we obtained a "sample" geoid that has a standard deviation of 11 cm for the external control points.

Requirement for a high resolution geoid model has increased substantially during the last few decades especially with the advent of Global Positioning System (GPS). Many countries across the world have already developed their own geoidal model which serve as the means of deriving orthometric heights from GNSS observations. On the other hand, the need for transformation of the ellipsoidal heights derived from GNSS observations to the physical orthometric heights has forced geodesists to determine the high precision local geoid heights. Besides, because orthometric heights are used in engineering and GIS applications, local quasi-geoid determination studies have become especially important. As it is well known, Turkey is situated on a tectonically very active region and earthquakes occurring in different times cause deformations in heights of levelling points of Turkish National Vertical Network. On the other hand, National Mapping Agency of Turkey (GDM: General Directorate of Mapping) which is responsible for the establishment and maintenance of national geodetic networks compute geoid models for whole Turkey and release them for public use in different periods. These GDM-computed geoid models are called "hybrid geoid" models. Hybrid geoid models are computed with the combination of gravimetric geoid models and geoid heights on the GPS_levelling points. And it is also known that the absolute accuracies of these geoid models are nearly at the 10 cm level or even worse. But, the requested accuracy is about better than 5 cm. Hence, in order to prove that the required accuracy levels can be achieved, a local gravimetric and quasi-geoid determination project using the resources of Selçuk University was initiated. Project area has been planned to cover a limited part of Central Anatolia including Konya. Necessary basic data (gravity, levelling etc.) for this project have been obtained in the field by performing observations/measurements. Some other necessary data such as absolute gravity values have been obtained from GDM. And as the next phase, high accuracy (better than 5 cm) local gravimetric and quasi-geoid models will be computed for the limited part of Central Anatolia using the above mentioned data. In order to be able to reach this goal suitable geoid computations softwares must be used. In this project, we will use DFHRS developed by the Karlsruhe Applied Sciences and GRAVSOFT softwares. According to the results to be obtained from this project, a more comprehensive project will be launched and the project area will be expanded. Thus, additional gravity, levelling and GNSS measurements will be carried out in the new project area for the determination of a high accuracy regional gravimetric geoid.

At present, one of the methods used to determine the height of points on the Earth's surface is Global Navigation Satellite System (GNSS) leveling. It is possible to determine the orthometric or normal height by this method only if there is a geoid or quasi-geoid height model available. This paper proposes the methodology for local correction of the heights of high-order global geoid models such as EGM08, EIGEN-6C4, GECO, and XGM2019e_2159. This methodology was tested in different areas of the research field, covering various relief forms. The dependence of the change in corrected height accuracy on the input data was analyzed, and the correction was also conducted for model heights in three tidal systems: "tide free", "mean tide", and "zero tide". The results show that the heights of EIGEN-6C4 model can be corrected with an accuracy of up to 1 cm for flat and foothill terrains with the dimensionality of 1 Â 1 ; 2 Â 2 ; and 3 Â 3. The EGM08 model presents an almost identical result. The EIGEN-6C4 model is best suited for mountainous relief and provides an accuracy of 1.5 cm on the 1 Â 1 area. The height correction accuracy of GECO and XGM2019e_2159 models is slightly poor, which has fuzziness in terms of numerical fluctuation.

Vertical deflection can be determined by geometrical and physical measurement. In geometrical way, vertical deflection is obtained by comparing astronomical coordinate and geodetical coordinate. In physical way, vertical deflection can be computed from gravity measurement. In the past, vertical deflection was computed from gravity anomaly data. Gravity anomaly data measurement is difficult because it need reduction of gravity from surface of the earth to the geoid using orthometric height from spirit level measurement. In modern era, gravity anomaly data may be replaced by gravity disturbance data whose only required gravity and GNSS (Global Navigation Satellite System) measurement. This research aims to determine vertical deflection in Semarang City from terrestrial gravity disturbance data. The gravity data were measured in March of 2016. Formula of Vening Meinesz that usually used for vertical deflection was replaced by new formula that generated from derivation of function of Ho...

Terrestrial measurements can provide accurate gravity data, but it is costly and time-consuming for large and remote area. Airborne gravity measurements have actually been carried out in Indonesia since 2008 by Technical University of Denmark (DTU) in collaboration with the Geospatial Information Agency (BIG). Purpose of the project was to develop a geoid model used for converting elevations from GPS/GNSS measurements that refers to ellipsoid to orthometric elevations that refer to sea level. The data can actually be explored so that it can be used for geophysical and other geoscience purposes, but the data must be carefully treated and extracted into observational gravity data. This study aims to improve the accuracy of gravity airborne data to produce an accurate complete Bouguer anomaly map. The data used in this study were airborne gravity data over Province of Southeast Sulawesi collected on September 29, 2008 to October 1, 2008.  Variation in flight height at the time of conse...

This paper evaluates a combined geoid model in the area of Fagnano Lake located in Tierra del Fuego, Argentina. The model includes GPS/levelling points, gravity data and GPS buoy observations on the lake. The GPS buoy information allowed to determine a mean lake level (MLL) surface which was used to extend the geoid model to an area with restricted access by land (Del Cogliano et al. 2007). An approach to optimize the selection and distribution of the MLL data is developed in order to use them as input in the Equivalent Source Technique, and to combine them with different types of observations. Furthermore, the global geopotential model EGM2008 is validated in the remote lake area. This model does not include observed gravity data in this region. Its behaviour is compared to the results of our observations along the levelling lines. Differences of several decimetres are found when EGM2008 geoid undulations are compared to geoid undulations derived from observations in this region. In the areas where EGM2008 relies on real gravimetric observations, differences between model and observations are only of a few centimetres. The comparison of the EGM2008 model with our observations reveals the effect of missing or not representative gravity information may have on the estimation of geoid undulations in high mountain regions. The data on which EGM2008 is based in the Fagnano Lake area does not result from gravimetric observations on land. Therefore, we consider them as not representative and we show that their effect can be significant in such areas.

Original scientific paper Modern scientific research is largely focused on interdisciplinary aspect of individual technical disciplines in research and scientific approach in discovering new insights. In the field of geo-sciences, there is a wide range of mutual methods of measuring physical parameters needed for the determination of geologic and structural composition of the underground area, the density of surface layers, the Earth's gravity field, i.e. local gravity changes. This paper explains the influences of topography of the Earth masses in the determination of vertical deflections needed for the transformation of the heights by means of trigonometric levelling methods in the real gravity field acceleration.

The virtual point-mass method has been widely used in dealing with the approximation of the local gravity field which is a difficult problem in internal currently. In this paper, the approximation theory of point-mass model is briefly introduced, and the characteristics of the elements in the coefficient matrix for the model construction are analyzed by numerical calculation. The observations of gravity anomaly is simulated from EGM2008 with degree and order 720 and the approximated region is 32~34 N o o and 103~105 E o o. A four-tier point-mass model which is on the base of the geopotential model with degree and order 36 from low frequency to high frequency is applied to approximate the local earth's gravity field. The results of the experiments show that the truncation error of gravity disturbance created by using the point-mass model is less than 2 mGal on the radial direction and there is an optimal truncation error for some certain spectrum gravity field in the space.

The determination of heights above mean sea level by spirit-leveling is known to be a difficult task as it is time-consuming, tedious and expensive. Knowledge of a reliable geoid model for transformation of heights in a particular region is therefore vital. The published quality estimates of Global Geopotential Models are presented as a global average and thus not representative of its performance in a particular region. Evaluation of EIGEN-6C4 and EGM2008 has been performed to ascertain its quality in determination of orthometric heights in Uganda.
The evaluation of EIGEN-6C4 and EGM2008 geoid models involved the determination of their accuracy in obtaining geoid heights and therefore orthometric heights. This provided a validation of the quality of both geoid models in transformation of heights that was done by using GNSS and
levelling data at seven fundamental benchmarks in Uganda. Also, a test for the suitability of EIGEN-6C4 in determination of heights with physical meaning is performed for a road section from Lira to Abim. This was done by relative evaluation of the geoid model with respect to a reference control station.
The determination of the accuracy of the geoid models using GNSS and levelling data provided a smaller Standard Deviation of 0.158m and mean of -0.774m for EIGEN-6C4 compared to that of EGM2008 representing a better fit to the reference surface due to the GNSS and levelling data.
While testing for suitability of EIGEN-6C4 for geodetic applications, the Root Mean Square Error per kilometer of 5.3mm for a baseline length of approximately 9km in the test for suitability of EIGEN-6C4 for orthometric height determination shows an acceptable levelling misclosure.
The potential of EIGEN-6C4 geoid model has been demonstrated in determination of heights with physical meaning and as such plausible results to provide confidence in its adoption for geodetic and engineering applications. The quality of EIGEN-6C4 for practical applications is dependent on the quality of datasets used in its development and evaluation. It is recommended that further tests for applicability be performed in other regions of Uganda.