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The development of remote frequency transfer techniques, especially the appearance of optical clocks with unprecedented stability, has prompted geoscientists to study their applications in geodesy. Using remote frequency transfer technique, by frequency comparison of two optical clocks at two points P and Q connected by optical fibers, one can measure the signal's frequency shift between them, and the geopotential difference between them can be determined based on the gravity frequency shift equation. Given the orthometric height of P, the orthometric height of Q can be determined. Since the present stability of the optical clock has achieved 1 × 10−18 or better and comparing the frequency transfer via optical fiber provides stability at 10−19 level, the optical clock network enables determining the orthometric height at centimeter-level. This study provides a formulation to determine the height difference at one-centimeter level between two points on the ground based on the optical fiber frequency transfer technique.

The height obtained through the GNSS method is the ellipsoidal height and to have an efficient application in surveying it has to be converted into orthometric height. This paper aims to determine a local geoid model for a part of Duhok region based on the known orthometric height using GPS/levelling and assessing the precision performance of the two Earth gravitational models (EGM1996 and EGM2008) in the study area. The EGMs were adjusted based on root mean square errors, calculated from the differences between two geoid heights, GPS/levelling and EGMs. The Kriging interpolation method was used for creating a local geoid model based on GPS/levelling. The result from the adjusted geoid models to the survey data at 54 points revealed that the mean accuracy of geoidal heights at 0.08 m level is attainable. The precision performance of EGM96 is more precise than EGM08 by 14 mm in the area of interest.

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.

The regions around the world need to perform their results based on the local geoid. However, each region has different ground topography based on the amount of gravity in this region. Nowadays, the recent global Earth's gravity model of 2008 is successfully used for different purposes in geosciences research. This research presents an overview of the preliminary evaluation results of the new Earth Gravitation Model (EGM08) in the middle of Iraq. For completeness, the evaluation tests were also performed for EGM96 by examining 31 stations distributed over four Iraqi provinces. The national orthometric heights were compared with the GPS /leveling data obtained from these stations. This study illustrated that the GPS /leveling based on EGM08 data was better than that based on EGM96 data in terms of reducing the root mean square error (RMSE) of the differences between the orthometric heights and GPS/leveling data. The standard deviation (SD) values for the national orthometric heights and GPS heights were about 4 and 26cm, respectively. The results also show that there is a small difference in hight ranged (0.0013 - 0.1333 m) in Karbala, (0.0023 – 0.0062 m), in Najaf and (0.0173 – 0.0703 m), in Babylon. Due to the flat area, better results were obtained in Karbala and Najaf than Babylon. The EGM08 geoid method has shown to yield very close results to reality for various projects, thus its accuracy is acceptable.

Height is an important component in the determination of the position of a point. The study aimed at performing a comparative analysis of change between ellipsoidal height differences and the equivalent orthometric height difference of points. A hi-target Differential Global Positioning System (DGPS) was used to acquire GPS data with an occupation period of thirty (30) minutes on each point, which were processed using Hi-target Geomatics Office (HGO) software to obtain the ellipsoidal heights. An automatic level instrument was used to acquire leveling data, which were processed using the height of collimation method to obtain the orthometric heights. A total of fifty (50) points were occupied as common points for both the GPS and levelling observations at 20-meter intervals. The accuracy of the height difference was determined using standard deviation with the ellipsoidal height difference as 53.59cm and the orthometric height as 53.07cm respectively. A Root Mean Square Error value of 0.0621m was obtained as the accuracy of the change between the two height differences. Statistical analysis using the independent-sample Z test was used to analyze the data at a 5% significant level. The result shows no significant difference in the performance of the two height systems. It is worthy to note that GPS and spirit levelling height differences can be used interchangeably for any heighting in short distances for surveying and engineering applications.

The dramatic rise in warm temperatures in the Himalayan region has caused the formation and expansion of numerous supraglacial lakes, some of which pose a serious flood hazard for the downstream communities. In this study, we have investigated the risk of flood hazards associated with supraglacial lakes in the Hindu Kush, Karakoram and Himalayan ranges of Pakistan using Landsat 8 OLI (Operational Land Imager) data of 2013 and field observations. Among the total of 438 supraglacial lakes, the majority were identified in the Karakoram (378) followed by the Hindu Kush range (39). The concentration of lakes was high within 3500-4000 m elevation (168) followed by 4000-4500 m elevation range (116). The lakes had shown more than a two-fold increase during the 2001-2013 period in the three mountain ranges. The increase in lake number was pronounced over valley glaciers likely due to increasing hydro-glacial activity under changing climate. Two types of supraglacial lakes were identified based on geographic characteristics, for example those rolling over glaciers surface away from the margins (called rolling supraglacial lakes ‘RSLs’) and the lakes found near the margins of glaciers mostly stationary in nature (called static supraglacial lakes ‘SSLs’). Most of the glacial lakes outburst flood (GLOF) events have been observed from SSLs in this region. However, the hydrodynamic process exaggerating the risk of GLOF from supraglacial and englacial lakes needs in-depth research for effective disaster risk reduction in this region in future.

Many applications in geodesy, hydrography and engineering require geoid-related heights. Spirit leveling which is the traditional means of obtaining geoid- or mean sea level-related heights is slow, time-consuming and costly. Global Navigation Satellite Systems (GNSS) offer faster and relatively cheaper way of obtaining geoid-related heights when geoidal undulation is applied to ellipsoidal heights. However, difficulties involved in determining acceptable geoid height have seriously hampered the application of GNSS for leveling in Rivers State, thus necessitating the need to develop an acceptable geoid model which will serve as a means of conversion of GNSS-delivered ellipsoidal heights to their orthometric heights equivalent. In pursuance of this objective, a detailed gravimetric geoid has been evaluated for Rivers State, Nigeria. The computation of the geoid was carried out by the traditional remove-restore procedure. The Earth Geopotential Model 2008 (EGM08) was applied as the reference field for both the remove and restore parts of the procedures; spherical Fast Fourier Transform (FFT) was employed for the evaluation of the Molodenskii’s integral formula for the height anomaly, (ζ) to yield the quasi-geoid; while the Residual Terrain Modelling (RTM) was done by prism integration. The classical gravimetric geoid over Rivers State was obtained from the rigorously evaluated quasi-geoid by adding the quasi-geoid to geoid (N - ζ) correction it. The minimum and maximum geoid height values are 18.599 m and 20.114 m respectively with standard deviation of 0.345 m across the study area. Comparison of the gravimetric geoidal heights with the GPS/Leveling-derived geoidal heights of 13 stations across Rivers State, Nigeria showed that the absolute agreement with respect to the GPS/leveling datum is generally better than 7 cm root mean squares (r.m.s) error. Results also showed that combining both GPS heights and the computed Rivers State geoid model can give orthometric heights accurate to 3 cm post-fit using a 4-parameter empirical model. The geoid model can thus serve as a good alternative to traditional leveling when used with GPS leveling, particularly for third order leveling in the study area.

The geoid is used as a transformation linkage between ellipsoidal heights (h) determined from DGPS observations and orthometric heights (H). Widespread acceptability and adoption of GPS in local geospatial data acquisitions require the development of a local geoid model (N) for use to obtain orthometric heights in the absence of a national geoid model. Geoid model can be developed by gravimetric approach; global geopotential model (GGM); geometric technique among others. The conventional approach to GPS measurements is the use of one base reference station for field measurements. It has several drawbacks e.g. in signal range/coverage, accuracy degradation of results, etc. Based on Grashof's law of stability of triangles, this study was therefore based on dual reference base stations to improve on DGPS signal range and stability of results. Pro-online matrix solver was applied to the least squares observation equations of the two modelled FCT surfaces (multi - quadratic and bicubic) to determine polynomial coefficients. The geoid undulation was computed and orthometric height generated for production of a topographical plan at 1m contour interval for elevation data in surveying, engineering and environmental applications. Skill =1 and bias = 0 were computed to confirm the predictive capability of the models and that no bias/errors were introduced into the respective modelling exercise. Diagnostic test also confirmed the viability and feasibility of providing vertical datum surface for FCT by this approach. Standard deviation (σ) as accuracy indicator was computed and the multi-quadratic model with σ =11cm was the better geoid surface for modelling of orthometric height in the FCT by the geometric method.

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 gravimertric and quasi-geoid determination project using the resources of Selcuk 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 software developed by the Karlsruhe Applied Sciences. The principle of the DFHRS software is based on the parametric model of N(φ, λ, h) as a continuos polynomial height reference surface (HRS). Following the quasi-geoid computation, when we reach the requested accuracy level, namely better than 5 cm, then it will have been shown that the GNSS based determination of orthometric heights (H) is much faster, easier to handle and much more economic, in comparison to classical geodetic levelling. On the other hand, it is possible to obtain a gravimetric geoid better than 10 cm accuracy by using global models and gravity data with 1-2 mGal accuracy. And you can only check such geoid only with GNSS/Levelling heights which provide better accuracies. Thus, 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. Consequently, in this paper, all works carried out within the framework of this project and the reached preliminary results will be presented.

Islamic studies, including fiqh, using an integration-interconnection approach with other sciences are important to do to get a more complete perspective. One of them is the interconnection of “hisab-rukyat” fiqh with geodesy. In general, the study of the Qibla direction, the beginning of prayer times, the beginning of the qamariah month, and eclipses in “hisab-rukyat” fiqh, uses the general formula of spherical trigonometry with a round earth reference. Round earth references in the study of the region differ from the real condition of the earth in the form of an ellipsoid as described in geodesy. To get more valid results, it is important to convert latitude and place height. The latitude of the place obtained by reference or GPS is the geodetic latitude with the earth reference in the form of an ellipsoid, whereas the spherical trigonometry formula refers to the shape of a round Earth. The place height obtained through GPS is the ellipsoid height, not the desired orthometric height (above the average surface of sea water). By converting these data, studies of the “hisab-rukyat” fiqh can be more valid. By increasing the validity of the calculation results, the interconnection between “hisab-rukyat” fiqh and geodesy appears in the form of complementation, meaning that data and findings of geodesy can complement data and analysis in “hisab-rukyat” fiqh, so that it is possible to draw more valid conclusions.

Geoid modelling is a fundamental procedure in geomatics and geosciences applications to estimate the orthometric heights from the ellipsoidal heights measured using Global Navigation Satellite Systems (GNSS) observations. In case of no local geoid model is available for any area, a Global Geopotential Model (GGM) is utilized for height conversion. However; the availability of too many GGMs, more than 160 models, makes the selection of the most acceptable one is a significant task. This paper aims to develop a straightforward scheme to acquire, manipulate, and investigate the accuracy of GGMs, within a Geographic Information Systems (GIS) environment. Four GGMs, namely XGM2016, GECO, EIGEN-6C4, and EGM2008, have been utilized in Egypt. Accomplished results show that the standard deviations of the investigated GGMs' discrepancies, over Egypt, range from ± 10.90 mGal to ± 13.10 mGal for gravity anomalies, and from ± 0.23 m to ± 0.30 m for geoid heights. In order to pick up the optimum GGM, a dimensionless reliability index is computed for each GGM. Based on the investigated GGMs, the available datasets, and also the proposed criteria applied in analyzingresults in this paper, we can conclude that the EGM2008 is still the most suitable GGM for representing the gravitational field over Egypt with an average reliability index of 5.10. The proposed efficient GIS-based process is practically beneficial for height conversion in several geodetic, environmental, surveying, and mapping applications in Egypt.

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.

The aqueducts built by the ancient Romans are among the most impressive evidence of their engineering skills. The water inside the aqueducts was transported for kilometers, exploiting only the slight but constant differences in altitude throughout the route. To keep the differences in height constant, the aqueducts could proceed underground or aboveground on well-known arched structures that supported lead, ceramic or stone pipes. In order to reconstruct the characteristics of these structures, it is necessary to carry out an accurate survey of the orthometric heights, and therefore the most suitable technology is geometric levelling. In this case, however, it is not applicable, and therefore here we propose an alternative methodology. The final goal of this work was to estimate the flow of some sectors of these aqueducts preserved in the area south of the city of Rome. This has two main purposes: The first is to reconstruct the flow rate of these aqueducts for historical studies, the second is to check how much the orthometric heights have changed over the centuries, in order to reconstruct the movements from a geophysical and geodynamic point of view. The latter analysis will be developed in a following phase of this research. For this purpose, a high-precision geomatic survey was carried out in the area under study, partly retracing a survey already carried out in 1917 whose purpose and methodologies are not known. The area has been affected by a gradual subsidence over centuries, including since 1917. The observed sections of the aqueducts showed average inclinations, slightly lower than the 2 per thousand that is reported in the literature for similar aqueducts. The measurements carried out allowed the flow rate of the two specific aqueducts to be estimated more accurately, both as they were originally and in the presence of deposits that have accumulated during the years of use of the aqueducts. The reconstruction of the initial geometry will later be used as a reference to estimate how much the geodynamic deformations of the area have deformed the aqueducts themselves.

International audience; The importance of the local geoid model for the computation of accurate geoid heights, as well as orthometric heights used for engineering constructions, necessitated its establishment in areas, regions or countries. Consequently, this study establishes the local geometric geoid model of Busoga, Uganda, using the geometric method. A total of 26 points were used in the study, 20 points for the development of the model and 6 test points. GNSS observations were acquired with Trimble GNSS dual-frequency receivers and processed with Bernese (V5.2) and Spectra Precision Survey Office (v4.1) software to obtain the coordinates and ellipsoidal heights of the points. Differences between the existing orthometric and ellipsoidal heights were computed to obtain the geoid heights. The Least squares adjustment technique was applied to determine the fit, as well as the Bicubic and Multiquadratic models' parameters. The Root Mean Squares Error (RMSE) index was used to compute the accuracy of the models. The geoid models were compared with their RMSE, as well as accuracy to determine which of them is more suitable for application in the study area. The comparison result shows that the Multiquadratic geoid model is more suitable for implementation in the study area. A Microsoft Excel program was developed for the application of the model in the study area.; L'importance du modèle du géoïde local pour le calcul des hauteurs précises du géoïde, ainsi que des hauteurs orthométriques utilisées pour les constructions d'ingénierie, a nécessité son établissement dans des zones, des régions ou des pays. Par conséquent, cette étude établit le modèle géoïde géométrique local de Busoga, en Ouganda, en utilisant la méthode géométrique. Un total de 26 points a été utilisé dans l'étude, 20 points pour le développement du modèle et 6 points de test. Les observations GNSS ont été acquises avec des récepteurs bifréquences Trimble GNSS et traitées avec les logiciels Bernese (V5.2) et Spectra Precision Survey Office (v4.1) pour obtenir les coordonnées et les hauteurs ellipsoïdales des points. Les différences entre les hauteurs orthométriques et ellipsoïdales existantes ont été calculées pour obtenir les hauteurs du géoïde. La technique d’ajustement des moindres carrés a été appliquée pour déterminer l’ajustement, ainsi que les paramètres des modèles bicubique et multiquadratique. L'indice d'erreur quadratique moyenne (RMSE) a été utilisé pour calculer la précision des modèles. Les modèles du géoïde ont été comparés à leur RMSE, ainsi que la précision pour déterminer lequel d'entre eux est le plus approprié pour une application dans la zone d'étude. Le résultat de la comparaison montre que le modèle du géoïde multiquadratique est plus adapté à une mise en œuvre dans la zone d'étude. Un programme Microsoft Excel a été développé pour l'application du modèle dans la zone d'étude.

Comparison of orthometric heights obtained from the combination of GPS/Levelling survey method with that obtained from Lidar, Srtm, and Astergdem data is an area of research which is of great interest to Geomaticians. This area of research makes possible the discovery of other suitable methods of determining orthometric height which can be selected for use depending on the region, extent and nature of the terrain where the project is to be executed.The X, Y, Z coordinates and the geoidal heights for all the existing controls within university of Lagos were determined using the GPS/ Levelling survey method, the required orthometric height (H) was then obtained as the differences between ellipsoidal and geoidal heights. Extracting orthometric heights for the X and Y coordinates of observed control points overlaid on each of Lidar, Srtm and Astergdem required the use of spatial analysis tool in an arc map environment. From the profile plot (Figure 3.5) of all the orthometric heights, the heights relationship was easy established. From the descriptive statistics test (Table 3.4), the one way ANOVAs test at 1% and 5% level of significance (Table 3.8), the number of points in other methods whose orthometric height is closed to that of Levelling/GPS method (Table 3.7) and correlation test on the various orthometric heights obtained (Table 3.5) it is obvious that all the applied methods operates at different spatial resolutions, of all the four methods, GPS/Levelling method was the most reliable and most accurate method followed by lidar method, then by astergdem method and Srtm has the least. In a nutshell, Orthometric heights generated by method of Lidar are very close to that generated by GPS/Levelling method at several stations, thus method of Lidar was considered as the most suitable alternative to GPS/Levelling method, whenever the use of later method cannot be easily accomplished.

Engineering projects require orthometric heights of points where as Global Navigation Satellite System (GNSS) provide height above ellipsoid. Thus, to make use of GNSS in engineering surveying, the relationship between ellipsoidal height and orthometric height as a function of position needs to be established through geoid modeling. In this study, an attempt has been made to develop a geoid model using the geometric method. Observations were taken in a network of sixteen stations spread over 600 km2 around Dehra Dun, India. GPS observations were taken using dual frequency geodetic GPS receivers and leveling done using digital levels with 0.1 mm accuracy. Orthometric height of stations from developed model have been found to be near to those from field levelling which is considered most accurate. Further, the values have been compared with those obtained from the recent GOCE–GRACE–LAGEOS geoid model EIGEN6C3stat. It has been found that the geometric model provides far better accuracy than that obtained from the global geoid model. Therefore, it can be concluded that the geometric method of geoid modeling can better be used for reduction of GPS observed ellipsoidal height to orthometric height in a local area. This model may gainfully be employed in a project area as a substitute for densification of leveling lines, thereby reducing the project cost substantially.

Extraction of underground minerals causes subsidence of the ground surface due to gravitational forces. The subsidence rate depends on the type of extracted ore, as well as its shape, thickness, and depth. Additionally, the embedding and overburden rock properties influence the time needed for the deformations to reach the surface. Using the results of geodetic deformation monitoring, which supply the information on pattern and magnitude of surface deformation, the performance of the mine may be evaluated. The monitoring can supply information on the actual rock mass behaviour during the operation and in many cases during the years after the mining operations have ceased. Geodetic methods of deformation monitoring supply information on the absolute and relative displacements (changes in position in a selected coordinate system) from which displacement and strain fields for the monitored object may be derived. Thus, geodetic measurements provide global information on absolute and relative displacements over large areas, either at discrete points or continuous in the space domain. The geodetic methods are affected by errors caused by atmospheric refraction and delay of electromagnetic signal. Since geodetic measurements allow for redundancy and statistical evaluation of the quality of the data, they generally provide reliable results. Usually, the designed accuracy of deformation measurements should allow for the detection of at least one third of the expected maximum deformations over the desired time span at the 95% probability level. In ground subsidence studies in mining areas, 10 mm accuracy at 95% level in both vertical and horizontal displacements is typically required. In the case of salt mines, the process of ground subsidence in viscous rock is slow, therefore, subsidence monitoring surveys may be performed once a year. In subsidence determination, two techniques are commonly used: leveling and satellite positioning. The satellite positioning technique is used to determine the 3D (horizontal coordinates and height) or 2D position of monitored points (only horizontal coordinates). When comparing the heights determined from satellite and leveling surveys, it has to be noted that the leveling heights are referred with respect to the geoid (orthometric heights), while heights determined from satellite surveys are referred with respect to the ellipsoid (ellipsoidal height). In the case of satellite surveys, the accuracy of horizontal position is typically 2&ndash, 3 times better than vertical. The analysis of the optimal session duration lead to the conclusion that in order to achieve the sub-cm accuracy of horizontal coordinates at 95% confidence level, the satellite positioning session length using Global Positioning System (GPS) should be at least three hours long. In order to achieve the sub-cm accuracy of height coordinate at 95% confidence level in a single observation session, the GPS session length should be at least twelve hours long.

A precise orthometric height (H) and orthometric height difference (ΔH) determination is required in many fields like construction, geodesy and geophysics. H is often obtained from an ellipsoidal height (h) and geoid height (N) of a geoid model (GM) because this computation does not have the spirit leveling restrictions on long distances. However, the H accuracy depends on the GM local area adaptation, and current global geoid models (GGMs) have not been yet evaluated for Costa Rica. Therefore, this paper aims to determine which GGM maintains a better fit with a GPS/levelling baseline that contains the gravity full spectrum. A 74 km baseline was measured using GPS, spirit leveling and gravity measurements to validate the N computed from EGM2008, EIGEN-6C4, GECO, EGM96, GGM05C and GOCO05C. First, an absolute N assessment was made, where geoid height from the GGMs (NGGM) were directly compared to the geometric geoid heights (Ngeo) obtained from GPS and spirit levelling. A bias fit (Nbias) of about 2 m was computed from this comparison for most GGMs with respect to the local vertical reference surface (W0). By subtracting the Nbias, a relative geoid height (ΔN) assessment was designed to compare the differences between GGM relative geoid height (ΔNGGM) and geometric relative geoid height (ΔNgeo) on segments along the baseline. The ΔN comparison shows that EGM2008, EIGEN-6C4 and GECO better represent the Costa Rican Central Pacific Coastal Zone and over long distances, ΔH can be computed with a decimeter to centimeter precision. La determinación de alturas ortométricas (H) y diferencias de altura ortomética (ΔH) precisas es requerida en campos como construcción, geodesia y geofísica. La H puede obtenerse midiendo altura elipsoidal (h) y calculando altura geoidal (N) de un modelo geoidal (GM), evitando limitaciones de la nivelación geodésica en largas distancias. Sin embargo, la precisión de H dependerá de la adaptación del GM al sitio, y la adaptación de los modelos geoidales globales (GGMs) actualmente se desconoce para Costa Rica. Por eso, este artículo busca determinar cuál GGM mantiene mayor congruencia con una línea base de GPS /Nivelación que contenga el espectro de gravedad completo. Para esto, se midió una línea base de 74 km utilizando GPS, nivelación geodésica y mediciones gravimétricas, para validar el N calculado con EGM2008, EIGEN-6C4, GECO, EGM96, GGM05C y GOCO05C. Primero, se evaluó el valor absoluto de N, donde N de los GGMs (NGGM) se comparó directamente con N geométrica (Ngeo) obtenida con GPS y nivelación geodésica. Obteniendo un sesgo (Nbias) cercano a 2 m para la mayoría de GGMs respecto de la superficie de referencia vertical local (W0). Al sustraer el Nbias, se aplicó una evaluación de la altura geoidal relativa (ΔNGGM) respecto de la altura geoidal geométrica relativa (ΔNgeo) en segmentos a lo largo de la línea base. La comparación de ΔN mostró que EGM2008, EIGEN-6C4 y GECO representan de mejor forma la zona costera del Pacífico Central de Costa Rica, y que en largas distancias es posible obtener ΔH con precisiones decimétricas a centimétricas.

A dual-port annular antenna with polarization diversity is proposed for smartwatch application. A modified T-shape monopole is integrated with an annular ring antenna. The two antennas are fed by coplanar waveguide (CPW) line and slot line, respectively. Both the two ports cover 2.4 GHz WLAN bandwidth. Besides, the back shell of smartwatches and the human tissue model are considered. The numerical results show that the two ports has orthometric radiation patterns. The antenna is analyzed both in free space and on human body. The gain and radiation efficiency is higher than 1.1 dBi and 30 % in the on body scenario.

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.

Objective The present study aimed to evaluate the precision of the torque applied by 0.022" self-ligating brackets of different brands, the precision of parallelism between the inner walls of their slots, and precision of their slot height. Eighty brackets for upper central incisors of eight trademarked models were selected: Abzil, GAC, American Orthodontics, Morelli, Orthometric, Ormco, Forestadent, and Ortho Organizers. Images of the brackets were obtained using a scanning electron microscope (SEM) and these were measured using the AutoCAD 2011 software. The tolerance parameters stated in the ISO 27020 standard were used as references. The results showed that only the Orthometric, Morelli, and Ormco groups showed results inconsistent with the ISO standard. Regarding the parallelism of the internal walls of the slots, most of the models studied had results in line with the ISO prescription, except the Morelli group. In assessing bracket slot height, only the Forestadent, GAC, American Orthodontics, and Ormco groups presented results in accordance with the ISO standard. The GAC, Forestadent, and American Orthodontics groups did not differ in relation to the three factors of the ISO 27020 standard. Great variability of results is observed in relation to all the variables.

The Global Navigational Satellite Systems, particularly the Global Positioning System has emerged as state of the art technology for providing precise horizontal and vertical location of points on surface of the earth. The vertical location is with respect to the Reference spheroid and known as ellipsoidal height. However in most of the application areas the heights considered are the orthometric heights (Mean Sea Level heights) with respect to the Geoid. The GPS-derived ellipsoidal heights are converted to corresponding orthometric heights using either a global or a local geoid model. Geoid model is a mathematical relation between the geoidal separation (N) and the horizontal location of a point. The accuracy of the conversion of ellipsoidal heights to orthometric heights depends on the accuracy of the geoid model. The objective of this study is to develop a local geoid model for a region of about 100 × 100 km2 area in Botswana in order to assess the accuracy of orthometric heights obtained from ellipsoidal heights. The geometric method is used for computation of the geoidal separation of control points from available orthometric heights and thereafter these points are used along with their horizontal coordinates and the geoidal separation to develop a surface model using a second degree polynomial as well as a TIN model. From the study it appears that an accuracy of about 20 cm in orthometric heights can be achieved by employing suitable number of well planned control points and an appropriate mathematical model in development of the geoid model.

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.

This study aims to analyze the accuracy for feasibility study of Network-RTK(VRS) surveying inside and outside of Korean CORS network. The southwest coast of Korea where some part of mainland and islands are outside of CORS network is chosen as the test area. To evaluate the accuracy of VRS surveying at surveying points, several Unified Control Points (UCPs) inside and outside of Korean CORS network were selected as the points in the test area. The feasibility of VRS surveying was analyzed by investigating the errors related to the location of points inside and outside of CORS network and the difference of 3-dimensional coordinates observed on different date. As the results of this study, the orthometric height errors of points outside of CORS network based on KNGeoid14 were improved about 5.0 cm in RMSE in comparison with KNGeoid13. The height errors of VRS surveying were considered to be less relevant to the results from PDOP and number of satellites (GPS and GLONASS). However, the orthometric errors caused by the geoidal height of KNGeoid and the ellipsoidal height of VRS surveying at points located outside of CORS network need to be addressed carefully for control surveying. When a point surveyed twice on different date, the difference of the ellipsoidal height of the point outside of CORS network was larger than that of the point inside of CORS network.

GNSS/Leveling technology makes it possible to get geoidal height geometrically using GNSS and Leveling technology. GNSS/Geoid technology refers to a technology for obtaining orthometric height by subtracting geoidal height achieved by Geoid technology from ellipsoidal height achieved by GNSS technology. The purpose of this study is to verify the accuracy of the ellipsoidal height determination in order to verify the accuracy of the orthometric height determination by the GNSS/Geoid technology. For the study, a test bed was selected in Kyungnam province and GNSS Static surveying was accomplished in the test bed and then the GNSS data was processed in accordance with various analysis conditions. So, it was verified the accuracy of the ellipsoidal heights determination in accordance with the surveying conditions under the GNSS Static surveying. According to the research results, to ensure the 3cm goal accuracy of the ellipsoidal height determination, it should be surveyed by four fixed points on the survey area periphery and more than two hours of the GNSS occupation time, And also, it was found that should be limited to a baseline distance of 20km under the GNSS Static surveying.

Orthometric heights, useful for many engineering and geoscience applications, can be obtained by GPS (Global Positioning System) surveys only when an accurate geoid undulation model (that supplies the vertical separation between the geoid and WGS84 ellipsoid) is available for the considered topic area. Global geoid height models (i.e., EGM2008), deriving from satellite gravity measurements suitably integrated with other data are free available on web, but their accuracy is often not sufficient for the user’s purposes. More accurate local models can nevertheless be acquired, but often only for a fee. GPS/levelling surveys are suitable for determining a local, accurate geoid model, but may be too expensive. This paper aims to demonstrate that GNSS (Global Navigation Satellite System) Permanent Station documents (monographs), freely available on the web and supplying orthometric and ellipsoidal heights, permit to calculate precise geoidal undulations useful to perform global geoid modelling on a local area. In fact, in this study 25 GNSS Permanent Stations (GNSS PS), located in North-Western Italy are considered: the differences between GNSS PS geoidal heights and the corresponding EGM2008 1′ × 1′ ones are used as a starting dataset for Ordinary Kriging applications. The resulting model is summed to the EGM2008 1′ × 1′, obtaining a better-performed model of the interest area. The accuracy tests demonstrate that the resulting model is better than EGM2008 grids to produce contours from a GPS dataset for large-scale mapping.

International audience; As the surface adopted for geodetic computation is a mathematical surface which is different from the physical surface, the geoid adopted as a reference for vertical coordinate system, the ellipsoidal heights obtained from GPS observation are transformed to practical heights known as orthometric heights. The transformation of the ellipsoidal heights to orthometric heights requires the knowledge of the geoid-ellipsoid separation at the point of observation. Since the geometric method requires the computation of geoid heights of points from GPS observation and geodetic levelling carried out over long distances which is labour intensive and prone to human errors, the accurate geoid heights of the points should be obtained from gravity measurement and a geometric geoid surface fitted to the gravimetric geoid heights. This paper presents detailed procedures for determining local gravimetric-geometric geoid model of an area or a region. The detailed procedures which consist of selection of suitable/evenly distributed points, DGPS and gravity observations of selected points, processing of DGPS and gravity observations, computation of gravimetric geoid heights of the points, fitting of geometric geoid surface to the computed gravimetric geoid heights and computation of accuracy of the geoid model are presented in sequential order.

In the last few years, satellite-based positioning techniques, such as the Global Positioning System (GPS), proved their abilities in various geodetic fields. Height determination, as one of such applications, requires a more likely correct geoid model to provide reliable geoid heights for transformation of the ellipsoidal heights to orthometric heights. An important step is then to establish such a model by optimal combination of the available geoid models. This can be achieved via variance component estimation (VCE) methods, which provide appropriate weights to GPS and leveling observations as well as the geoid models. The authors demonstrate the efficacy of the least-squares VCE (LS-VCE) to this problem. The algorithm is applied to real data sets in Shahin-Shahr, Isfahan, Iran, to evaluate the EGM2008 and GGMplus Earth geopotential models and a regional geoid model (named IRGeoid10) in terms of agreement to the GPS/leveling observations and introduce the more likely correct model over the case-...

The assessment of hydrologic dynamics in rivers, lakes, reservoirs and wetlands requires measurements of water level, its temporal and spatial derivatives, and the extent and dynamics of open water surfaces. Motivated by the declining number of ground-based measurement stations, research efforts have been devoted to the retrieval of these hydraulic properties from spaceborne platforms in the past few decades. However, due to coarse spatial and temporal resolutions, spaceborne missions have several limitations when assessing the water level of terrestrial surface water bodies and determining complex water dynamics. Unmanned Aerial Vehicles (UAVs) can fill the gap between spaceborne and ground-based observations, and provide high spatial resolution and dense temporal coverage data, in quick turn-around time, using flexible payload design. This study focused on categorizing and testing sensors, which comply with the weight constraint of small UAVs (around 1.5 kg), capable of measuring the range to water surface. Subtracting the measured range from the vertical position retrieved by the onboard Global Navigation Satellite System (GNSS) receiver, we can determine the water level (orthometric height). Three different ranging payloads, which consisted of a radar, a sonar and an in-house developed camera-based laser distance sensor (CLDS), have been evaluated in terms of accuracy, precision, maximum ranging distance and beam divergence. After numerous flights, the relative accuracy of the overall system was estimated. A ranging accuracy better than 0.5% of the range and a maximum ranging distance of 60 m were achieved with the radar. The CLDS showed the lowest beam divergence, which is required to avoid contamination of the signal from interfering surroundings for narrow fields of view. With the GNSS system delivering a relative vertical accuracy better than 3–5 cm, water level can be retrieved with an overall accuracy better than 5–7 cm.

The means for determining reference surfaces when using satellite-based positioning techniques differs from the way they are determined using classical terrestrial positioning techniques. The height of any point on earth, as determined by a global positioning system (GPS), is based on the World Geodetic System of 1984 datum, but when using classical terrestrial measurements this height is based on the geoid. However, GPS-derived ellipsoidal heights must initially be transformed into orthometric heights for practical applications. We use geoid models developed with geoid heights for the height transformation, because orthometric height determination methods using classical techniques require time and manpower. In this study, the performances of polynomials, radial basis functions (RBFs) and multilayer perceptron (MLP) neural network algorithms used in local geoid surface modelling were evaluated in the study area. Upon analysis of statistical results, the artificial neural network method was observed to give better results than the other two methods.

This paper proposes a high-efficiency and continuous levelling method for linear objects, such as highways and railways, by applying a vehicle-borne GPS/INS kinematic surveying system which integrates the Global Positioning System (GPS) and the Inertial Navigation System (INS). Generally, the raw ellipsoid height directly outputted by GPS/INS needs to be transformed to the local orthometric height. However, because of various systematic errors and random errors, such as the measuring error and the quasi-geoid model error, the accuracy of the orthometric height would rarely meet engineering requirements. To solve this problem, a novel sliding least-squares collocation (SLSC) model based on ground control points was constructed to improve the accuracy of GPS/INS kinematic levelling. Two data sets collected from the Chang Ying highway located in Jilin province, China, were used to validate the proposed method. The experimental results indicate that the proposed method improves the trajectory points’ orthometric height accuracy by at least 160%.

Various corrector surface models are proposed to mitigate systematic height errors to fit the orthometric heights determined by combining the Tainan City real-time kinematic (RTK) global positioning system (GPS) network and the local geoid model data to the published orthometric heights. Several data sets for Tainan City were tested and analyzed. Two geometric geoid models and one gravimetric-geometric geoid model were generated using the GPS and leveling data. Consequently, three types of orthometric heights were determined (Models I, II, and III). The selection of the optimal corrector surface model for different models was based on a series of statistical tests. The test results show that (1) the selection of the optimal corrector surface model is highly related to the geoid model generating method, hence the optimal corrector surface models are a fifth-degree polynomial for Models I and II and a seven-parameter similarity transformation for Model III; and (2) the determined orthometric height ...

Controls are coordinated horizontal or vertical positional data for land and geographic information systems forming a framework to which surveys are started, referenced and adjusted. Controls on KNUST campus were established over three decades ago with new ones being added as and when t h e y a r e required. Conventional survey methods like trilateration, triangulation and traversing were used and are still being used for densification of controls. These approaches involve the use of low precision instruments such as analogue/optical theodolites and leveling equipment. Since the establishment of these controls, t h e y have not been investigated but t h e y are being used for p r o j e c t development. A modern method that uses satellite positioning techniques such as GPS is currently in operation and has numerous advantages in the establishment of control networks. GPS control surveys were carried-out on seven controls and ellipsoidal coordinates were obtained in the World Geodetic System 84 reference frame. The Cartesian coordinates were projected onto the Universal Transverse Mercator frame. A two dimensional conformal transformation was done using existing KNUST boundary coordinates to Ghana National coordinates based on the War Office ellipsoid. Precise Level routines were carried out on the seven controls for the computations of orthometric heights. The method of least squares adjustment, root mean square errors (RMSE), standard errors (SE) and residuals derived were used to analyse the differences in horizontal positions and heights of the controls. The linear displacement between the computed and the existing coordinates were within the range of 0.015m to 0.014m. The RMSE were 0.048 and 0.106, whiles the SE were also 0.057 and 0.125 for the northings and eastings respectively. The computed and existing heights differed between -0.075m and -0.004m with a mean downward movement of 0.011m. Keywords: Surveying; coordinates; control points; GPS; precise level

GPS (Global Positioning System) technique has become a major tool in contemporary surveying and geodesy. This concerns mostly measurements of horizontal point coordinates, where centimeter-level accuracies are usually required and easily achievable. For the height component, however, these requirements are higher and millimeter-level accuracy is necessary. On the other hand, the intrinsic precision of GPS-derived heights is clearly lower comparing to the horizontal components. This is due to unfavorable satellite geometry, adverse effects of the troposphere or GPS antenna phase center offset and variations. In order to overcome these effects one has to carefully model all the error sources and rigorously process the GPS data. This paper presents studies on the optimal GPS data processing strategy suitable for precise leveling. This was done through the extensive testing and selection of the most appropriate observational session duration, ambiguity resolution strategy, network geometry, troposphere and ionospheric delay reduction methods, signal linear combination, elevation angle cut-off, etc. The analyzed processing strategies were evaluated through the processing of a test network. The test network consisted of 19 monitored points and 5 control points, and covered the area of 20 km x 60 km. The obtained results show that the precise GPS leveling with the selected optimal processing strategy allows for about 3 mm repeatability of height measurements when processing 4-hour long sessions. In our opinion GPS leveling may serve as fast and cost-effective replacement of classic geometric leveling, especially in applications where the heights in orthometric or normal height systems are not necessary. This is the case in, e.g., ground deformation studies.

This paper focuses on studying long distance height datum transfer across seas by a method, using GPS/leveling and gravimetric geoid fitting with an additional parameter. The method combines earth gravitational model EGM2008 with ellipsoidal height derived from GPS, to determine the height datum difference between a mainland and an island. Fitting function is given as a polynomial surface. An iteration algorithm by using different regularization parameters is adopted to solve the ill-conditioned matrix in the normal equation. The precision of the additional parameter is estimated. The feasibility of the proposed method is validated by practical data of two bridge constructions. It can obtain the height datum parameter and quasi-geoid model successively. The objective of long distance height datum transfer is then achieved. Comparing the computed value with known value, the results show that the inconsistencies of the height datum difference are small. No matter how many the differences are, they can be computed precisely. Precision of the computed height datum can satisfy the engineering requirement of the height. Therefore it can be applied in practical engineering, or to validate the reliability of other methods for long distance leveling. This method is low cost, efficient and reliable, and can be generally used in geodesy.

Civil engineering projects require the orthometric height of points (i.e., the height of points above geoid). Thus, to make use of the Global Navigation Satellite System (GNSS) in engineering surveying, geoid undulation (i.e., the separation between an ellipsoid and geoid surface) must be known. In this study, an attempt has been made to determine the geoid undulation using the astro-geodetic method. Observations were taken in a network of seven stations spread over 300 km2 around Dehra Dun, India. Astronomical observations of seven stars belonging to different constellations were taken with a theodolite having a least count of 1.0 s. Global positioning system (GPS) observations were taken using dual-frequency geodetic GPS receivers with a 0.1-mm-accurate digital level. Values of astro-geodetic geoid undulations (of stations) have been found close to that computed from field levelling. Further, the values have been compared with those obtained from global geoid models such as EIGEN6C3stat and EGM2...

A method for automatically measuring the imaging quality parameters of an image intensifier based on orthometric phase-shifting gratings (OPSG) is proposed. Two sets of phase-shifting gratings, one with a fringe direction at 45° and the other at 135°, are successively projected onto the input port of the image intensifier, and the corresponding deformed patterns modulated by the measured image intensifier on its output port are captured with a CCD camera. Two phases are retrieved from these two sets of deformed patterns by a phase-measuring algorithm. By building the relationship between these retrieved phases, the referential fringe period can be determined accurately. Meanwhile, the distorted phase distribution introduced by the image intensifier can also be efficiently separated wherein the subtle imaging quality information can be further decomposed. Subsequently, the magnification of the image intensifier is successfully measured by fringe period self-calibration. The experimental results have shown the feasibility of the proposed method, which can automatically measure the multiple imaging quality parameters of an image intensifier without human intervention.

The performance of Earth Gravitational Model 2008 (EGM2008) is evaluated over Nairobi County and its environs using GPS/levelling and free-air gravity anomalies. The data used include 18 GPS/levelling and 97 gravity points. The heights in Kenya are referred to the mean sea level and they are generally considered as orthometric heights. Hence the height anomalies obtained from tide-free EGM2008 model are converted to geoid undulations using a conversion model supplied with EGM2008. The standard deviation of the differences between EGM2008 implied and GPS/levelling geoid undulations at the 18 points is ±11.6 cm while the standard deviation of the differences between EGM2008 implied free-air and observed free-air gravity anomalies at the 97 points is ±10.7 mGal. These results indicate a high potential for EGM2008 in geoid modelling over Kenya. An initial high-resolution gravimetric geoid model over Kenya can be developed by combining EGM2008 and local gravity data sets. Keywords: EGM2008, geoid undulations, free-air gravity anomalies, GPS/levelling, Nairobi County and its environs

Precise information of geoid undulations is essential for obtaining the orthometric heights from Global Positioning System (GPS) measurements over any region; apart from providing the information of subsurface density distribution. This paper presents computation of geoid undulations over a part of southern Indian region from terrestrial gravity and elevation data using remove–restore technique that involves spherical Fast Fourier Transform (FFT) to compute ‘Stokes’ coefficients. Computed geoid undulations are compared with geoid obtained from global geopotential models such as EGM2008 and EIGEN-GRACE02S and measured GPS-levelling records at 67 locations. Statistical analysis of comparison suggests that the computed gravimetric geoid model has a good match with the geoid determined from GPS-levelling with rms of 0.1 m whereas EGM2008 has 0.46 m. The differences of GPS-levelling with EGM2008 at majority of stations fall in the range of ±0.5 m, which indicates that EGM2008 may be used for orthometric height determination with an accuracy of

Accurate orthometric heights in a national vertical datum can be determined economically using GPS heights and gravimetrically computed geoid undulations. If this national vertical datum should be tied to a global geoid, then both the datum offset as well as the difference between the GPS ellipsoid and the globally best-fitting ellipsoid should be known. This paper elaborates on the theory and procedures to obtain the datum offset for South Korea’s national vertical datum on the basis of the global model, EGM08. Among several GPS/leveling data sets slightly different estimates are obtained, with the estimate, 26.5 +/− 1.3 cm (above the global zero-tide geoid) obtained using over 800 data points distributed in South Korea. The uncertainty is a level of precision, not absolute accuracy, and the discrepancies between estimates using different subsets of the data indicate the presence of small unsolvable biases among them. An alternative procedure to determine orthometric heights using the modern principles is also proposed that makes the vertical datum completely independent of the global geoid in the traditional way and obviates the estimation of these offsets.

Developing the Nabucco engineering infrastructure was the most challenging task imaginable and required state-of-the-art technologies. For this purpose, a Nabucco-Global Positioning System (GPS) Network was established. It is 762 km long. Nine-hundred and two ground control unit points were established. In order to provide the relationship with ITRF96 datum, it was surrounded by TFNGN (Turkish Fundamental National GPS Network) and TNVCN (Turkish National Vertical Control Network) checkpoints. GPS observations were evaluated in the form of a unique network. After being reduced to projection segments, coordinates in ED50 datum were provided between datums by 2D-Helmert Transformation. Orthometric heights related to the GPS Network were obtained by the improvement of TG-03 data based on a GPS/leveling procedure. The objective of the study is to present the results of a comprehensive engineering project which involved many geodetic considerations including GPS, orthometric heights, and geoid undulations and g...

According to the wide spread use of satellite-based 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.

Precise terrain elevation information is required in various remote sensing and Engineering projects. There are many technologies to derive the terrain elevation information like GPS, ground surveys, LiDAR, Photogrammetry. GPS is the most widely used technology to obtain information due to its ease of operation. However the usage of ellipsoidal heights, i.e. with respect to WGS84 has limited usage in hydrological applications. GPS heights must be converted into orthometric heights for use in hydrological applications, and this requires geoid undulation information. These geoid undulations can be deduced from earth gravity models. There are various earth gravity models available for ready usage like EGM96, EGM2008, GFZ96 in the public domain. This paper discusses the improvements observed in deriving orthometric heights using EGM2008 over its predecessor model EGM96. The utilization of the new model in topographical mapping projects are also presented.

The aim of the present study is the employment of the artificial neural network (ANN) model in the estimation and evaluation of geoid heights. For that reason, a number of control points with known orthometric heights in the region of North Greece were measured by GPS and used to test the presented algorithms. The derived ANN geoid heights are compared to those produced by a well-known conventional method through a combined gravimetric geoid. In order to evaluate the computed heights, numerical tests were carried out for points distributed inside and at the borders of the study area. The obtained results show that the ANN model is a competitive approach with certain advantages.

The orthometric height (OH) system plays a key role in geodesy, and it has broad applications in various fields and activities. Based on general relativity theory (GRT), on an arbitrary equi-geo- potential surface, there does not exist the gravity frequency shift of an electromagnetic wave signal. However, between arbitrary two different equi-geopotential surfaces, there exists the gra- vity frequency shift of the signal. The relationship between the geopotential difference and the gravity frequency shift between arbitrary two points P and Q is referred to as the gravity frequency shift equation. Based on this equation, one can determine the geopotential difference as well as the OH difference between two separated points P and Q either by using electromagnetic wave signals propagated between P and Q, or by using the Global Positioning System (GPS) satellite signals received simultaneously by receivers at P and Q. Suppose an emitter at P emits a signal with frequency f towards a receiver at Q, and the received frequency of the signal at Q is , or suppose an emitter on board a flying GPS satellite emits signals with frequency f towards two receivers at P and Q on ground, and the received frequencies of the signals at P and Q are and , respectively, then, the geopoten-tial dif- ference between these two points can be determined based on the geopotential frequen- cy shift equation, using either the gravity frequency shift ? f or ? , and the corresponding OH difference is further determined based on the Bruns’ formula. Besides, using this approach a unified world height datum system might be realized, because P and Q could be chosen quite arbitrarily, e.g., they are located on two separated continents or islands.

Iran is a mountainous country with large lateral density variations of its crust. Constant density value is commonly used to determine the geoid models as well as topographic corrections. The effect of lateral density variation in the geoid can reach up to 14 cm in Iran which is not negligible in a precise geoid modelling. Also, the current height datum of Iran is based on the orthometric system but the effect of gravity variation was not applied in height parameter. Furthermore, the height systems of most neighbouring countries are defined as normal height. Connection of networks can be useful for the unification of height datum, geodynamics researches and optimal adjustment of levelling network. The new quasi-geoid model based on a recent EGM2008 global geo-potential model was created to solve the mentioned problem. The main purpose of the present study is to discuss the results of a research project in which a gravimetric quasi-geoid model for Iran was computed based on the least-squares modification of Stokes' formula. The evaluation is made using 475 GPS/levelling height anomalies covering the major parts of the country except the mountainous areas to the North and West. After a 7-parameter fit, the most promising attempt achieved a RMS value of 19 cm for the residuals based on the GPS/levelling data.

The geopotential-value approach is utilized in this study to estimate the average offsets of local vertical datums (LVDs) in New Zealand realized in the system of normal-orthometric heights. The LVD offsets are taken relative to the World Height System (WHS). We adopt the geoidal geopotential value W 0 = 62,636,856 m2 s−2 for a definition of WHS. The conversion of heights between different permanent tide systems is taken into consideration. The geopotential-value approach utilizes Molodensky’s theory of the normal heights. The normal-orthometric heights at global positioning system (GPS)-leveling points are thus first converted to the normal heights. The normal to normal-orthometric height correction is computed and applied along the leveling lines using the leveling data, and the gravity disturbances are computed approximately from the EGM08 global geopotential model. The numerical study is conducted for 18 LVDs in the North and South Islands of New Zealand. The LVD offsets are estimated from EGM08 to GPS-leveling data. The estimated average LVD offsets vary between 1 cm (Wellington 1953 LVD) and 37 cm (One Tree Point 1964 LVD).

The aim of this study is to present the results of several 'external' quality tests for the most recent (at the time of writing this paper) global geopotential models (GGMs) using precise GPS and leveled orthometric heights over the area of Greece. The tested GGMs include the GRACE-based combined model GGM03C, the latest EIGEN-type combined models EIGEN-GL04C and EIGEN-GL05C, the ultra-high resolution model EGM08 that was released last year by the US National Geospatial-Intelligence Agency, and also the older NASA/NIMA/OSU's EGM96 model. The evaluation tests are based on comparisons of absolute and relative geoid undulations that are computed from the selected GGMs and the external GPS/levelling data. The test network covers the entire part of the Hellenic mainland and it consists of more than 1500 benchmarks which belong to the Hellenic national triangulation network, with direct levelling ties to the Hellenic vertical reference frame. The spatial positions of these benchmarks have been recently ...

The aim of this article is to review the potentiality and reliability of the integrated usage of global positioning system (GPS), terrestrial laser scanner (TLS), and total station survey measurements in the geomorphologic studies. Test surveys based on these techniques were done in the area of “Tana della Volpe” blind valley and in the adjacent “Monticino” quarry, near Brisighella, Ravenna, Northern Apennines, Italy. Such sites are characterized by peculiar geomorphologic attributes such as the presence of slope, karst, and anthropic forms. We surveyed about 18,000 GPS points and about 42,200,000 TLS points in a total of 22 scans. The processing of the survey’s whole data set produced three distinct arrays of three-dimensional (3D) coordinates complemented by orthometric heights. Moreover, an integrated multistep procedure was implemented based on the following premises: (1) the removal of points not referred to the bare earth surface; (2) the combination of three coordinate sets into a single one referr...