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Park, Kwang-Cheol, Young-Hwan Lim, Jong-In Lim, and Won-Hyung Park. "Performance Improvement for Increased Communication Speed in Anonymous Network using GeoIP." Journal of Society for e-Business Studies 16, no. 4 (November 30, 2011): 75–85. http://dx.doi.org/10.7838/jsebs.2011.16.4.075.
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Pahlevi, Arisauna M., Ibnu Sofian, Dyah Pangastuti, and Antonius B. Wijanarto. "UPDATING MODEL GEOID INDONESIA." Seminar Nasional Geomatika 3 (February 15, 2019): 761. http://dx.doi.org/10.24895/sng.2018.3-0.1063.
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Geoid merupakan referensi tinggi di Indonesia sesuai amanat Peraturan Kepala BIG (Perka BIG) nomor 15 Tahun 2013 tentang Sistem Referensi Geospasial Indonesia (SRGI). Melalui website http://srgi.big.go.id/srgi2, BIG secara bertahap memenuhi kebutuhan masyarakat terkait dengan sistem referensi geospasial termasuk di dalamnya informasi model geoid Indonesia. Model geoid Indonesia yang dihasilkan pada tahun 2013 merupakan model geoid Indonesia yang diolah berbasis pulau. pada tahun 2018, dilakukan updating model geoid Indonesia. Tujuannya untuk menghasilkan model geoid Indonesia secara keseluruhan atau terintegrasi di seluruh wilayah Indonesia. Data yang digunakan adalah; Data spherical harmonic beberapa model geoid global sebagai data gelombang panjang, data gelombang menengah menggunakan Data DTU-10, data gayaberat airborne wilayah Pulau Sulawesi, Kalimantan dan Papua. Sedangkan data gelombang pendek menggunakan Data SRTM-15 meter. Metode yang digunakan dalam pemodelan geoid adalah metode Fast Fourier Transform (FFT). Data-data tersebut diolah dengan menggunakan perangkat lunak gravsoft yang telah dimodifikasi di sesuaikan dengan kebutuhan Indonesia. Validasi model geoid dilakukan dengan membandingkan nilai geoid gravimetrik hasil pengolahan model geoid dari data gayaberat, dengan nilai geoid geometrik dari pengukuran GNSS di pilar Tanda Tinggi Geodesi (TTG). Dari pengolahan data, menghasilkan model geoid dari beberapa data komponen gelombang panjang yang berbeda. Model geoid dengan standar deviasi terkecil adalah model geoid yang diperoleh dari kombinasi komponen gelombang panjang EGM2008 - derajat 2190 dengan nilai standar deviasi 0.2283. Metode pemodelan geoid secara menyeluruh di seluruh wilayah Indonesia lebih relevan dilakukan di negara kepulauan seperti Indonesia, dikarenakan lebih memudahkan unifikasi model geoid antara darat dan laut.
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Truong, Nguyen Ngoc, and Tran Van Nhac. "Determination of the constant Wo for local geoid of Vietnam and it’s systematic deviation from the global geoid." Tạp chí Khoa học và Công nghệ biển 17, no. 4B (December 15, 2017): 138–44. http://dx.doi.org/10.15625/1859-3097/17/4b/13001.
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Constant Wo, defining the geoid, has important applications in the area of physical geodesy. With the development of artificial Earth satellite, constant Wo for the global geoid approximating the oceans on Earth can be calculated from an expansion of spherical harmonics - Stokes constants determined by observation of perturbations in artificial satellite’s orbits. However, the Stokes constants are limited, therefore the geoid constant Wo could not be calculated for local geoid (state geoid) from the mentioned expansion of spherical harmonics. In this paper, we present a method to determine the constant Wo for local geoid of Vietnam, using generalized Bruns formula and Neyman boundary problem. The initial data used are Faye gravity anomalies surveyed on land and sea of Southern Vietnam. The constant Wo is then used to calculate the systematic deviation of the local geoid of Vietnam from the global geoid EGM - 96.
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Pisetskaya, Olga, and Alexander Yarmolenko. "Problem of Determining a Geoid." Baltic Surveying 8 (October 31, 2018): 85–92. http://dx.doi.org/10.22616/j.balticsurveying.2018.011.
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The issue of the study of the problem of determining the geoid and quasi-geoid models is considered. Development of methods for constructing an exact geoid model using different dimensions. Analysis of the calculation of normal heights using satellite measurements, construction of geoid and quasi-geoid models by different methods is performed. Based on the results of the analytical review of existing methods for determining the geoid, it was proposed to use various data (geodetic heights, mixed gravity anomalies, anomalous potential) to construct this model, which allows building a model of a geoid with millimetre accuracy. The possibility of using the collocation method is considered. The task is to develop a methodology for constructing a geoid model using a network of low density gravity points and using pure and mixed gravity anomalies, which allows us to solve the problem of finding potential by solving the Laplace equation or using wavelets.
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Reguzzoni, Mirko, Daniela Carrion, Carlo Iapige De Gaetani, Alberta Albertella, Lorenzo Rossi, Giovanna Sona, Khulan Batsukh, et al. "Open access to regional geoid models: the International Service for the Geoid." Earth System Science Data 13, no. 4 (April 21, 2021): 1653–66. http://dx.doi.org/10.5194/essd-13-1653-2021.
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Abstract. The International Service for the Geoid (ISG, https://www.isgeoid.polimi.it/, last access: 31 March 2021) provides free access to a dedicated and comprehensive repository of geoid models through its website. In the archive, both the latest releases of the most important and well-known geoid models, as well as less recent or less known ones, are freely available, giving to the users a wide range of possible applications to perform analyses on the evolution of the geoid computation research field. The ISG is an official service of the International Association of Geodesy (IAG), under the umbrella of the International Gravity Field Service (IGFS). Its main tasks are collecting, analysing, and redistributing local, regional, and continental geoid models and providing technical support to people involved in geoid-related topics for both educational and research purposes. In the framework of its activities, the ISG performs research taking advantage of its archive and organizes seminars and specific training courses on geoid determination, supporting students and researchers in geodesy as well as distributing training material on the use of the most common algorithms for geoid estimation. This paper aims at describing the data and services, including the newly implemented DOI Service for geoid models (https://dataservices.gfz-potsdam.de/portal/?fq=subject:isg, last access: 31 March 2021), and showing the added value of the ISG archive of geoid models for the scientific community and technicians, like engineers and surveyors (https://www.isgeoid.polimi.it/Geoid/reg_list.html, last access: 31 March 2021).
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Lukoševičius, Viktoras. "DFHRS-BASED COMPUTATION OF QUASI-GEOID OF LATVIA." Geodesy and Cartography 39, no. 1 (April 12, 2013): 11–17. http://dx.doi.org/10.3846/20296991.2013.788827.
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In geodesy, civil engineering and related fields high accuracy coordinate determination is needed, for that reason GNSS technologies plays important role. Transformation from GNSS derived ellipsoidal heights to orthometric or normal heights requires a high accuracy geoid or quasi-geoid model, respectively the accuracy of the currently used Latvian gravimetric quasi-geoid model LV'98 is 6–8 cm. The objective of this work was to calculate an improved quasi-geoid (QGeoid) for Latvia. The computation was performed by applying the DFHRS software. This paper discusses obtained geoid height reference surface, its comparisons to other geoid models, fitting point statistics and quality control based on independent measurements.
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Pa’suya, M. F., A. H. M. Din, J. C. McCubbine, A. H. Omar, Z. M. Amin, and N. A. Z. Yahaya. "GRAVIMETRIC GEOID MODELLING OVER PENINSULAR MALAYSIA USING TWO DIFFERENT GRIDDING APPROACHES FOR COMBINING FREE AIR ANOMALY." ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences XLII-4/W16 (October 1, 2019): 515–22. http://dx.doi.org/10.5194/isprs-archives-xlii-4-w16-515-2019.
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Abstract. We investigate the use of the KTH Method to compute gravimetric geoid models of Malaysian Peninsular and the effect of two differing strategies to combine and interpolate terrestrial, marine DTU17 free air gravity anomaly data at regular grid nodes. Gravimetric geoid models were produced for both free air anomaly grids using the GOCE-only geopotential model GGM GO_CONS_GCF_2_SPW_R4 as the long wavelength reference signal and high-resolution TanDEM-X global digital terrain model. The geoid models were analyzed to assess how the different gridding strategies impact the gravimetric geoid over Malaysian Peninsular by comparing themto 172 GNSS-levelling derived geoid undulations. The RMSE of the two sets of gravimetric geoid model / GNSS-levelling residuals differed by approx. 26.2 mm. When a 4-parameter fit is used, the difference between the RMSE of the residuals reduced to 8 mm. The geoid models shown here do not include the latest airborne gravity data used in the computation of the official gravimetric geoid for the Malaysian Peninsular, for this reason they are not as precise.
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Infante, Claudia, Claudia Tocho, and Daniel Del Cogliano. "ANALYSIS OF ISOSTATICALLY-BALANCED CORTICAL MODELS USING MODERN GLOBAL GEOPOTENTIAL MODELS." Boletim de Ciências Geodésicas 23, no. 4 (December 2017): 623–35. http://dx.doi.org/10.1590/s1982-21702017000400041.
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Abstract: The knowledge of the Earth's gravity field and its temporal variations is the main goal of the dedicated gravity field missions CHAMP, GRACE and GOCE. Since then, several global geopotential models (GGMs) have been released. This paper uses geoid heights derived from global geopotential models to analyze the cortical features of the Tandilia structure which is assumed to be in isostatic equilibrium. The geoid heights are suitably filtered so that the structure becomes apparent as a residual geoid height. Assuming that the geological structure is in isostatic equilibrium, the residual geoid height can be assimilated and compared to the isostatic geoid height generated from an isostatically compensated crust. The residual geoid height was obtained from the EGM2008 and the EIGEN-6C4 global geopotential models, respectively. The isostatic geoid was computed using the cortical parameters from the global crustal models GEMMA and CRUST 1.0 and from local parameters determined in the area under study. The obtained results make it clear that the isostatic geoid height might become appropriate to validate crustal models if the structures analyzed show evidence of being in isostatic equilibrium.
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Eshagh, Mehdi. "Error calibration of quasi-geoidal, normal and ellipsoidal heights of Sweden using variance component estimation." Contributions to Geophysics and Geodesy 40, no. 1 (January 1, 2010): 1–30. http://dx.doi.org/10.2478/v10126-010-0001-9.
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Error calibration of quasi-geoidal, normal and ellipsoidal heights of Sweden using variance component estimation Errors of estimated parameters in an adjustment process should be scaled according to the size of the estimated residuals or misclosures. After computing a quasi-geoid (geoid), its biases and tilts, due to existence of systematic errors in the terrestrial data, are removed by fitting a corrective surface to the misclosures of the differences between the GNSS/levelling data and the quasi-geoid (geoid). Variance component estimation can be used to re-scale or calibrate the error of the GNSS/levelling data and the quasi-geoid (geoid) model. This paper uses this method to calibrate the errors of the recent quasi-geoid model, the GNSS and the normal heights of Sweden. Different stochastic models are investigated in this study and based on a 7-parameter corrective surface model and a three-variance component stochastic model, the calibrated error of the quasi-geoid and the normal heights are 6 mm and 5 mm, respectively and the re-scaled error of the GNSS heights is 18 mm.
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Kao, Szu-Pyng, Fang-Shii Ning, Chao-Nan Chen, and Chia-Ling Chen. "USING PARTICLE SWARM OPTIMIZATION TO ESTABLISH A LOCAL GEOMETRIC GEOID MODEL." Boletim de Ciências Geodésicas 23, no. 2 (June 2017): 327–37. http://dx.doi.org/10.1590/s1982-21702017000200021.
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There exist a number of methods for approximating the local geoid surface and studies carried out to determine a local geoid. In this study, performance of geoid by PSO method in modeling local geoid was presented and analyzed. The ellipsoidal heights (h), derived from GPS observations, and known orthometric heights from first-order benchmarks were first used to create local geometric geoid model, then the PSO method was used to convert ellipsoidal heights into orthometric heights (H). The resulting values were used to compare between the spirit leveling and GPS methods. The adopted PSO method can improve the fitting of local geometric geoid by quadratic surface fitting method, which agrees with the known orthometric heights within ±1.02cm
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Erol, Serdar, Emrah Özögel, Ramazan Alper Kuçak, and Bihter Erol. "Utilizing Airborne LiDAR and UAV Photogrammetry Techniques in Local Geoid Model Determination and Validation." ISPRS International Journal of Geo-Information 9, no. 9 (September 2, 2020): 528. http://dx.doi.org/10.3390/ijgi9090528.
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This investigation evaluates the performance of digital terrain models (DTMs) generated in different vertical datums by aerial LiDAR and unmanned aerial vehicle (UAV) photogrammetry techniques, for the determination and validation of local geoid models. Many engineering projects require the point heights referring to a physical surface, i.e., geoid, rather than an ellipsoid. When a high-accuracy local geoid model is available in the study area, the physical heights are practically obtained with the transformation of global navigation satellite system (GNSS) ellipsoidal heights of the points. Besides the commonly used geodetic methods, this study introduces a novel approach for the determination and validation of the local geoid surface models using photogrammetry. The numeric tests were carried out in the Bergama region, in the west of Turkey. Using direct georeferenced airborne LiDAR and indirect georeferenced UAV photogrammetry-derived point clouds, DTMs were generated in ellipsoidal and geoidal vertical datums, respectively. After this, the local geoid models were calculated as differences between the generated DTMs. Generated local geoid models in the grid and pointwise formats were tested and compared with the regional gravimetric geoid model (TG03) and a high-resolution global geoid model (EIGEN6C4), respectively. In conclusion, the applied approach provided sufficient performance for modeling and validating the geoid heights with centimeter-level accuracy.
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Bolkas, D., G. Fotopoulos, and M. G. Sideris. "Referencing regional geoid-based vertical datums to national tide gauge networks." Journal of Geodetic Science 2, no. 4 (December 1, 2012): 363–69. http://dx.doi.org/10.2478/v10156-011-0050-7.
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AbstractThe objective of this study is to investigate the best means for referencing a regional geoid-based vertical datum to a network of tide gauges. In this study, a network of 27 tide gauge stations scattered along the coasts of Canada are used in order to assess the replacement of the conventionally derived Canadian Geodetic Vertical Datum of 1928 with a geoid-based datum. This is in-line with the future implementation plan of Canada’s geoid-based vertical height system. A mixed least-squares adjustment was performed for various scenarios, including satellite-only global geoid models, combined global geoid models and regional geoid models. In addition, various sea surface topography and vertical ground motion models were tested for estimating orthometric heights. The resulting approximation of a local equipotential surface is compared to previously published values and considerations for referencing a geoid-based vertical datum to tide gauge networks are emphasized.
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Kim, Kwang Bae, Hong Sik Yun, and Ha Jung Choi. "Accuracy Evaluation of Geoid Heights in the National Control Points of South Korea Using High-Degree Geopotential Model." Applied Sciences 10, no. 4 (February 21, 2020): 1466. http://dx.doi.org/10.3390/app10041466.
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Precise geoid heights are not as important for understanding Earth’s gravity field, but they are important to geodesy itself, since the vertical datum is defined as geoid in a cm-level accuracy. Several high-degree geopotential models have been derived lately by using satellite tracking data such as those from Gravity Recovery and Climate Experiment (GRACE) and Gravity Field and Steady-State Ocean Circulation Explorer (GOCE), satellite altimeter data, and terrestrial and airborne gravity data. The Korean national geoid (KNGeoid) models of the National Geographic Information Institute (NGII) were developed using the latest global geopotential models (GGMs), which are combinations of gravity data from satellites and land gravity data. In this study, geoid heights calculated from the latest high-degree GGMs were used to evaluate the accuracy of the three GGMs (European Improved Gravity model of Earth by New techniques (EIGEN)-6C4, Earth Gravitational Model 2008 (EGM2008), and GOCE-EGM2008 combined model (GECO)) by comparing them with the geoid heights derived from the Global Navigation Satellite System (GNSS)/leveling of the 1182 unified control points (UCPs) that have been installed by NGII in South Korea since 2008. In addition, the geoid heights derived from the KNGeoid models were compared with the geoid heights derived from the GNSS/leveling of the 1182 UCPs to assess the accuracy of the KNGeoid models in terms of relative geoid heights for further gravimetric geoid determination studies in South Korea. As a result, the EGM2008 model could be selected as the suitable GGM from among the three GGMs for determining a gravimetric geoid model for South Korea.
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Soycan, Metin. "Improving EGM2008 by GPS and leveling data at local scale." Boletim de Ciências Geodésicas 20, no. 1 (March 2014): 3–18. http://dx.doi.org/10.1590/s1982-21702014000100001.
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The development of the Earth Gravitational Model 2008 (EGM2008) model is a significant contribution for modeling the Earth's gravity and geoid. Recently, it can be confidently used versus geometric models following a simple refinement procedure. Several studies show that, EGM2008 can reach the accuracy of regional or local geoid models after modeling the differences between the GPS-leveling geoid heights and EGM2008 derived geoid heights at identified control points. The study focuses on a corrector surface fitting (CSF) approach based on radial basis functions (RBF) as improvement procedure for EGM2008. A detailed mathematical model and solution algorithm of the proposed model is given, and it has been applied in different test areas covering the city borders of Bursa, Konya, Denizli and Gaziantep in Turkey. Accuracy of the improved model was evaluated in scattered check points within test regions. The geoid heights of all check points obtained by GPS-leveling measurements were compared with the geoid heights obtained from improved model. The discrepancies between the calculated and measured geoid heights were analyzed and discussed.
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Hughes, C. W., and R. J. Bingham. "An oceanographer’s guide to GOCE and the geoid." Ocean Science Discussions 3, no. 5 (September 20, 2006): 1543–68. http://dx.doi.org/10.5194/osd-3-1543-2006.
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Abstract. A review is given of the geodetic concepts necessary for oceanographers to make use of satellite gravity data to define the geoid, and to interpret the resulting product. The geoid is defined, with particular attention to subtleties related to the representation of the permanent tide, and the way in which the geoid is represented in ocean models. The usual spherical harmonic description of the gravitational field is described, together with the concepts required to calculate a geoid from the spherical harmonic coefficients. A brief description is given of the measurement system in the GOCE satellite mission, scheduled for launch shortly, followed by a description of a reference ellipsoid with respect to which the geoid may be calculated. Finally, a recipe is given for calculation of the geoid relative to any chosen ellipsoid, given a set of spherical harmonic coefficients and defining constants.
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Manandhar, Niraj, and Shanker K.C. "Geoid Determination and Gravity Works in Nepal." Journal on Geoinformatics, Nepal 17, no. 1 (June 4, 2018): 7–15. http://dx.doi.org/10.3126/njg.v17i1.23003.
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Gravimetric geoid plays the important role in the process of local/regional geoidal undulation determination. This approach uses the residual gravity anomalies determined by the surface gravity measurement using the gravimeter together with best fit geopotential model, with the geoid undulations over the oceans determined from the method of satellite altimetry. Mass distribution, position and elevation are prominent factors affecting the surface gravity. These information in combination with geopotential model helps in satellite orbit determination, oil, mineral and gas exploration supporting in the national economy. The preliminary geoid thus computed using airborne gravity and other surface gravity observation and the accuracy of computed geoid was likely at the 10-20cm in the interior of Nepal but higher near the border due to lack of data in China and India. The geoid thus defined is significantly improved relative to EGM –08 geoid.
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ZABLOTSKYI, F., and B. DZHUMAN. "Construction of STHA-model of geometric geoid on the Lviv region area." Modern achievements of geodesic science and industry 42, no. II (September 1, 2021): 49–56. http://dx.doi.org/10.33841/1819-1339-2-42-49-56.
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Nowadays there is a need to modernize the high system of Ukraine, which requires its integration in the European Vertical Reference System EVRS. In this regard there is also a need to build a regional model of the geoid on the territory of our country, which would be well consistent with the model of the European geoid EGG2015. To obtain the optimal model, it is necessary to use both gravimetric and geometric data. In this case, the model is called gravimetric-geometric. This approach is used both when building a model of the European geoid and when building geoid models on the territory of different European countries. Aim. The purpose of this work is to build a regional geometric STHA-model of the geoid on the Lviv region area and assess its accuracy. In the future it is planned to build a gravimetric STHA-model of the geoid in the same area and compare the results. Methods. To build a geometric STHA-model of the geoid on the Lviv region area, the heights of the geometric geoid, obtained from GNSS-observations at the points of SGN of I, II and III classes, were used. RMS error of determination of geodetic heights , obtained from GNSS leveling in static mode, did not exceed 15 mm. 205 values of the calculated heights of the geoid were used to build the geoid model. 8 values were not involved in the construction of the model, because they were used for an independent assessment of model accuracy. Results. The regional model of geoid within the “Remove–Compute–Restore” procedure with introduction of regularization parameter is obteined. RMS error of the obtained model, calculated on the basis of the data used in its construction, is 12 mm, and on other independent data is 25 mm. Scientific novelty and practical significance. For the first time STHA-functions were tested to build a regional geoid model. The geometric model of the geoid on the Lviv region are is calculated and the accuracy of the obtained model is estimated on the basis of dependent and independent data. The RMS error of the obtained model was about 2 cm, which corresponds to the accuracy of GNSS-measurements. The obtained model can be used as a transformation field on the Lviv region area.
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Zhao, Ya Hong, Li Hua Zhang, and Jin Xing Wang. "Research and Application of the Refining Method of Region Quasi-Geoid." Applied Mechanics and Materials 170-173 (May 2012): 2935–39. http://dx.doi.org/10.4028/www.scientific.net/amm.170-173.2935.
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GPS technology has penetrated into all fields of surveying and mapping disciplines,and has been widely used in leveling measurement .By studying the feasibility of the refining of region quasi-geoid based on the existing quasi-geoid,this paper shows a new method which is a combination of the Earth's gravity field model and the GPS leveling fitting method to determine the region quasi-geoid and provide the specific ideas and calculation steps and do analysis and discussion about the feasibility and superiority of this method using actual data.This new method makes full use of the advantages of the high resolution of the gravity geoid and the high-precision of the GPS geoid to realize the complementary strengths.
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Lee, Suk Bae, Keun Sang Lee, and Min Kun Lee. "Analysis of the Feasibility of GNSS/Geoid Technology in Determining Orthometric Height in Mountain." Journal of Korean Society for Geospatial Information System 25, no. 2 (June 30, 2017): 57–65. http://dx.doi.org/10.7319/kogsis.2017.25.2.057.
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Buczyńska, Anna. "Precision study of satellite levelling with using various models of geoid." E3S Web of Conferences 71 (2018): 00015. http://dx.doi.org/10.1051/e3sconf/20187100015.
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The main purpose of this study is comparison of orthometric heights of measuring points and the accuracy of these heights depending on selected geoid model and measurement method. In addition, for better understanding of the essence of conducted research, paper provides information about: geoid and other surfaces used in geodesy to describe the terrestrial globe, modelling methods of equipotential surfaces and data that can be used to develop them, the most important geoid models developed for the area of Poland and the world, the technique of determining the orthometric heights using various measuring methods. Heights of two measuring points, located on the premises of Wrocław University of Science and Technology, were determined to achieve thesis statement. The scope of the study is limited to determining the orthometric heights of points for three global geoid models and four geoid models developed for the area of Poland. Among the selected equipotential surfaces were: geoida niwelacyjna 2000, GUGiK 2001, GEOIDPOL 2008A/C/CN, PL-GEOID-2011, OSU91, EGM96 and EGM2008.
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IBRAHIM YAHAYA, Salissou, El Hassan EL BRIRCHI, and Driss EL AZZAB. "IMPACT OF DATUM TRANSFORMATION ON LOCAL VARIATIONS OF GEOMETRIC GEOID IN NIGER." Geodesy and cartography 43, no. 4 (December 21, 2017): 147–57. http://dx.doi.org/10.3846/20296991.2017.1412615.
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In this study, we have conducted an investigation on the impact of the coordinates’ transformation on local variations of geometric geoid. The study area is limited by 1°43′12″ to 4°00′37″ East and 13°01′57″ to 14°31′20″ North in the southwest of the Niger Republic. We used 39 network GPS/levelling points established by the Japan International Cooperation Agency (JICA) and the National Geographic Institute of Niger (IGNN), including the DOPPLER point ANG302/no.65. Using other coordinates of point no. 65 provided by IGNN, we transformed the points into WGS84 and computed a new geometric geoid model. The comparison of the new model with EGM2008 geoid up to d/o 2160 gives the STD of 15 cm and the RMS of 16cm. Local variations of the geometric geoids, were compared to that of EGM2008 geoid. The comparison through basic statistics, trend lines and 3D overlaps, showed a similar trend between the geometric geoid from the transformed coordinates and that of EGM2008. On the contrary, the JICA-IGNN geometric geoid generated an opposite and exaggerated trend. The Jarque-Bera test confirms that the three samples follow a normal distribution at the significance level α = 5%. The equality of variances between EGM2008 and JICA-IGNN geoids has been rejected by the Fisher’s F-Test/two-tailed at α = 10%. However the test confirms the variances equality between EGM2008 and the transformed geometric geoid at α = 5% and α = 10%. The two-tailed Student’s T-Test at α = 5% also confirms the equality of means between EGM2008 geoid and transformed geometric geoid samples.
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Ismail, M. K., A. H. M. Din, M. N. Uti, and A. H. Omar. "ESTABLISHMENT OF NEW FITTED GEOID MODEL IN UNIVERSITI TEKNOLOGI MALAYSIA." ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences XLII-4/W9 (October 26, 2018): 27–33. http://dx.doi.org/10.5194/isprs-archives-xlii-4-w9-27-2018.
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<p><strong>Abstract.</strong> The purpose of this study is to produce fitted geoid for Universiti Teknologi Malaysia (UTM), Johor Bahru by using precise levelling and 3D GNSS control network technique. This study focuses on the theory, computation method and analysis of fitted geoid around Universiti Teknologi Malaysia. The computation of accuracy fitted geoid model is based on the GNSS levelling and Precise Levelling. The achieved accuracy of UTM Fitted Geoid Model is at 8<span class="thinspace"></span>mm. In conclusion, this research can contribute to Universiti Teknologi Malaysia by providing good UTM fitted geoid model that can give better accuracy for various purposes of work related to surveying and mapping.</p>
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Akcin, Hakan, and Cahit Tagi Celik. "Performance of artificial neural networks on kriging method in modeling local geoid." Boletim de Ciências Geodésicas 19, no. 1 (March 2013): 84–97. http://dx.doi.org/10.1590/s1982-21702013000100006.
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Transformation of ellipsoidal heights determined by satellite techniques into local leveling heights requires geoid heights at points of interest. However, the geoid heights at each point are not available. In order to determine them, the local geoid in the transformation area must be modeled or computed by an appropriate method, one way of doing it, is to use control points both of whose ellipsoidal and local leveling heights are available. In this study, performance of geoid by ANN compared to Kriging method in modeling local geoid was presented. Moreover, the transformation ability of the methods was investigated through a geodetic test network in Bursa Metropolitan Area of Turkey. The results suggest that the model by ANN exhibit better results than the one by Kriging Method.
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Sjöberg, L. "Comments to X. Li and Y. M. Wang (2011) Comparisons of geoid models over Alaska computed with different Stokes' kernel modifications, JGS 1(2): 136-142." Journal of Geodetic Science 2, no. 1 (January 1, 2012): 38–39. http://dx.doi.org/10.2478/v10156-011-0022-y.
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Comments to X. Li and Y. M. Wang (2011) Comparisons of geoid models over Alaska computed with different Stokes' kernel modifications, JGS 1(2): 136-142Li and Wang recently compared geoid determination by various gravimetric methods for modifying Stokes' formula vs. using GPS/levelling geoid heights as a reference model. Possible large systematic errors in the differences of gravimetric and GPS/levelling geoid models deteriorate the results and conclusions. Moreover, spectral combination, the only stochastic method in the study, was applied in an unrealistic way.
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Vega Fernádez, Alonso, Oscar Lücke Castro, and Jaime Garbanzo Leon. "Geoid heights in Costa Rica, Case of Study: Baseline Along the Central Pacific Zone." Revista Ingeniería 30, no. 1 (November 12, 2019): 1–20. http://dx.doi.org/10.15517/ri.v30i1.35839.
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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.
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VARBLA, Sander, Artu ELLMANN, Silja MÄRDLA, and Anti GRUNO. "ASSESSMENT OF MARINE GEOID MODELS BY SHIP-BORNE GNSS PROFILES." Geodesy and cartography 43, no. 2 (June 25, 2017): 41–49. http://dx.doi.org/10.3846/20296991.2017.1330771.
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Even though the entire Baltic Sea is included in previous geoid modelling projects such as the NKG2015 and EGG07, the accuracy of contemporary geoid models over marine areas remains unknown, presumably being offshore around 15–20 cm. An important part of the international cooperation project FAMOS (Finalising Surveys for the Baltic Motorways of the Sea) efforts is conducting new marine gravity observations for improving gravimetric quasigeoid modelling. New data is essential to the project as the existing gravimetric data over some regions of the Baltic Sea may be inaccurate and insufficiently scarce for the purpose of 5 cm accuracy geoid modelling. Therefore, it is important to evaluate geoid modelling outcome by independent data, for instance by shipborne GNSS measurements. Accordingly, this study presents results of the ship-borne marine gravity and GNSS campaign held on board the Estonian Maritime Administration survey vessel “Jakob Prei” in West-Estonian archipelago in June/July 2016. Emphasis of the study is on principles of using the GNSS profiles for validation of existing geoid models, post-processing of GNSS raw data and low-pass filtering of the GNSS results. Improvements in geoid modelling using new gravimetric data are also discussed. For example, accuracy of geoid models including the new marine gravity data increased 11 mm as assessed from GNSS profiles. It is concluded that the marine GNSS profiles have a potential in providing complementary constraints in problematic geoid modelling areas.
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Bingham, Rory J., Keith Haines, and Chris W. Hughes. "Calculating the Ocean’s Mean Dynamic Topography from a Mean Sea Surface and a Geoid." Journal of Atmospheric and Oceanic Technology 25, no. 10 (October 1, 2008): 1808–22. http://dx.doi.org/10.1175/2008jtecho568.1.
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Abstract In principle the global mean geostrophic surface circulation of the ocean can be diagnosed by subtracting a geoid from a mean sea surface (MSS). However, because the resulting mean dynamic topography (MDT) is approximately two orders of magnitude smaller than either of the constituent surfaces, and because the geoid is most naturally expressed as a spectral model while the MSS is a gridded product, in practice complications arise. Two algorithms for combining MSS and satellite-derived geoid data to determine the ocean’s mean dynamic topography (MDT) are considered in this paper: a pointwise approach, whereby the gridded geoid height field is subtracted from the gridded MSS; and a spectral approach, whereby the spherical harmonic coefficients of the geoid are subtracted from an equivalent set of coefficients representing the MSS, from which the gridded MDT is then obtained. The essential difference is that with the latter approach the MSS is truncated, a form of filtering, just as with the geoid. This ensures that errors of omission resulting from the truncation of the geoid, which are small in comparison to the geoid but large in comparison to the MDT, are matched, and therefore negated, by similar errors of omission in the MSS. The MDTs produced by both methods require additional filtering. However, the spectral MDT requires less filtering to remove noise, and therefore it retains more oceanographic information than its pointwise equivalent. The spectral method also results in a more realistic MDT at coastlines.
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Yazid, N. M., A. H. M. Din, K. M. Omar, Z. A. M. Som, A. H. Omar, N. A. Z. Yahaya, and A. Tugi. "MARINE GEOID UNDULATION ASSESSMENT OVER SOUTH CHINA SEA USING GLOBAL GEOPOTENTIAL MODELS AND AIRBORNE GRAVITY DATA." ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences XLII-4/W1 (September 30, 2016): 253–63. http://dx.doi.org/10.5194/isprs-archives-xlii-4-w1-253-2016.
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Global geopotential models (GGMs) are vital in computing global geoid undulations heights. Based on the ellipsoidal height by Global Navigation Satellite System (GNSS) observations, the accurate orthometric height can be calculated by adding precise and accurate geoid undulations model information. However, GGMs also provide data from the satellite gravity missions such as GRACE, GOCE and CHAMP. Thus, this will assist to enhance the global geoid undulations data. A statistical assessment has been made between geoid undulations derived from 4 GGMs and the airborne gravity data provided by Department of Survey and Mapping Malaysia (DSMM). The goal of this study is the selection of the best possible GGM that best matches statistically with the geoid undulations of airborne gravity data under the Marine Geodetic Infrastructures in Malaysian Waters (MAGIC) Project over marine areas in Sabah. The correlation coefficients and the RMS value for the geoid undulations of GGM and airborne gravity data were computed. The correlation coefficients between EGM 2008 and airborne gravity data is 1 while RMS value is 0.1499.In this study, the RMS value of EGM 2008 is the lowest among the others. Regarding to the statistical analysis, it clearly represents that EGM 2008 is the best fit for marine geoid undulations throughout South China Sea.
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Sjöberg, Lars E. "On the topographic bias and density distribution in modelling the geoid and orthometric heights." Journal of Geodetic Science 8, no. 1 (February 1, 2018): 30–33. http://dx.doi.org/10.1515/jogs-2018-0004.
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Abstract It is well known that the success in precise determinations of the gravimetric geoid height (N) and the orthometric height (H) rely on the knowledge of the topographic mass distribution. We show that the residual topographic bias due to an imprecise information on the topographic density is practically the same for N and H, but with opposite signs. This result is demonstrated both for the Helmert orthometric height and for a more precise orthometric height derived by analytical continuation of the external geopotential to the geoid. This result leads to the conclusion that precise gravimetric geoid heights cannot be validated by GNSS-levelling geoid heights in mountainous regions for the errors caused by the incorrect modelling of the topographic mass distribution, because this uncertainty is hidden in the difference between the two geoid estimators.
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Gruber, T., and M. Willberg. "Signal and error assessment of GOCE-based high resolution gravity field models." Journal of Geodetic Science 9, no. 1 (January 1, 2019): 71–86. http://dx.doi.org/10.1515/jogs-2019-0008.
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Abstract The signal content and error level of recent GOCE-based high resolution gravity field models is assessed by means of signal degree variances and comparisons to independent GNSS-levelling geoid heights. The signal of the spherical harmonic series of these models is compared to the pre-GOCE EGM2008 model in order to identify the impact of GOCE data, of improved surface and altimetric gravity data and of modelling approaches. Results of the signal analysis show that in a global average roughly 80% of the differences are due to the inclusion of GOCE satellite information, while the remaining 20% are contributed by improved surface data. Comparisons of the global models to GNSS-levelling derived geoid heights demonstrate that a 1 cm geoid from the global model is feasible, if there is a high quality terrestrial gravity data set available. For areas with less good coverage an accuracy of several centimetres to a decimetre is feasible taking into account that GOCE provides now the geoid with a centimetre accuracy at spatial scales of 80 to 100 km. Comparisons with GNSS-levelling geoid heights also are a good tool to investigate possible systematic errors in the global models, in the spirit levelling and in the GNSS height observations. By means of geoid height differences and geoid slope differences one can draw conclusions for each regional data set separately. These conclusions need to be considered for a refined analysis e.g. to eliminate suspicious GNSS-levelling data, to improve the global modelling by using full variance-covariance matrices and by consistently weighting the various data sources used for high resolution gravity field models. The paper describes the applied procedures, shows results for these geoid height and geoid slope differences for some regional data sets and draws conclusions about possible error sources and future work to be done in this context.
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Oluyori, Paul Dare, and Sylvester Okiemute Eteje. "IMPROVING THE LOCAL GEOMETRIC GEOID MODEL OF FCT ABUJA ACCURACY BY FITTING A HIGHER ORDER/DEGREE POLYNOMIAL SURFACE." FUDMA JOURNAL OF SCIENCES 4, no. 3 (September 11, 2020): 114–20. http://dx.doi.org/10.33003/fjs-2020-0403-276.
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The improvement of the accuracy of a local geometric geoid model using the same data set (geoid heights) requires the fitting of a higher degree polynomial surface to the data set. Consequently, this paper presents improving the local geometric geoid model of FCT, Abuja accuracy by fitting a higher order polynomial surface. A fifth degree polynomial surface was fit to the existing geoid heights of 24 points used previously for the determination of the geometric geoid model of the study area to improve its accuracy. The least squares adjustment technique was applied to compute the model parameters, as well as the fit. The RMSE index was applied to compute the accuracy of the model. The computed accuracy (0.081m) of the model was compared with those of the previously determined geoid models (Multiquadratic, 0.110m and Bicubic, 0.136m models) of the study area to determine which of the models best fit the study area, as well as has the highest resolution. The comparison result shows that the fifth degree polynomial surface best fit the study area.
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Marotta, Giuliano Sant’Anna, and Roberta Mary Vidotti. "DEVELOPMENT OF A LOCAL GEOID MODEL AT THE FEDERAL DISTRICT, BRAZIL, PATCH BY THE REMOVE-COMPUTE-RESTORE TECHNIQUE, FOLLOWING HELMERT'S CONDENSATION METHOD." Boletim de Ciências Geodésicas 23, no. 3 (September 2017): 520–38. http://dx.doi.org/10.1590/s1982-21702017000300035.
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Abstract: There are several techniques for determining geoid heights using ground gravity data, the geopotential models, the astro-geodetic components or a combination of them. Among the techniques used, the Remove-Compute-Restore (RCR) technique has been widely applied for the accurate determination of the geoid heights. This technique takes into account short, medium and long wavelength components derived from the elevation data obtained from Digital Terrain Models (DTM), ground gravity data and global geopotential models, respectively. This technique can be applied after adopting the procedures to compute gravity anomalies and, then, the geoid model, considering the integration of different wavelengths mentioned, and their compatibility with the vertical datum adopted. Thus, this paper presents the procedures, involving the RCR technique, following Helmert's condensation method, and its application to compute one local geoid model for the Federal District, Brazil. As a result, the local geoid model computed for the studied area was consistent with the available values of geoid heights derived from geometrical levelling technique supported by GNSS positioning.
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Anonymous. "Geoid Commission." Eos, Transactions American Geophysical Union 70, no. 41 (1989): 891. http://dx.doi.org/10.1029/89eo00320.
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Wolf, Detlef. "On deglaciation-induced perturbations of the geoid." Canadian Journal of Earth Sciences 23, no. 2 (February 1, 1986): 269–72. http://dx.doi.org/10.1139/e86-030.
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The importance of geoid perturbations in interpreting tilts of glacial lake levels is investigated, using a representative theoretical model. It is shown that near the ice margin, the slope of the Earth's perturbed surface is everywhere large compared with the slope of the associated undulation of the geoid. Perturbations of the geoid may therefore be neglected in interpretations of glacial strandline tilt.
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Borghi, Alessandra, Riccardo Barzaghi, Omar Al-Bayari, and Suhail Al Madani. "Centimeter Precision Geoid Model for Jeddah Region (Saudi Arabia)." Remote Sensing 12, no. 12 (June 26, 2020): 2066. http://dx.doi.org/10.3390/rs12122066.
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In 2014, the Jeddah Municipality made a call for an estimate of a centimetric precision geoid model to be used for engineering and surveying applications, because the regional geoid model available at that time did not reach a sufficient precision. A project was set up to this end and dedicated sets of gravity and Global Positioning System (GPS)/levelling data were acquired in the framework of this project. In this paper, a thorough analysis of these newly acquired data and of the last available Global Gravity Field Models (GGMs) has been done in order to obtain a geoid undulation estimate with the prescribed precision. In the framework of the Remove–Compute–Restore (RCR) approach, the collocation method was used to obtain the height anomaly estimation that was then converted to geoid undulation. The remove and restore steps of the RCR approach were based on GGMs, derived from the Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) and Gravity Recovery and Climate Experiment (GRACE) dedicated gravity satellite missions, which were used to improve the long wavelength components of the Earth’s gravity field. Furthermore, two different quasi-geoid collocation estimates were computed, based on gravity data only and on gravity plus GPS/levelling data (the so-called hybrid estimate). The best solutions were obtained with the hybrid geoid estimate. This was tested by comparison with an independent set of GPS/levelling geoid undulations that were not included in the computed solutions. By these tests, the precision of the hybrid geoid is estimated to be 3.7 cm. This precision proved to be better, by a factor of two, than the corresponding one estimated from the pure gravimetric geoid. This project has been also useful to verify the importance and reliability of GGMs developed from the last satellite gravity missions (GOCE and GRACE) that have significantly improved our knowledge of the long wavelength components of the Earth’s gravity field, especially in areas with poor coverage of terrestrial gravity data. In fact, the geoid models based on satellite-only GGMs proved to have a better performance, despite the lower spatial resolution with respect to high-resolution models (i.e., Earth Gravitational Model 2008 (EGM2008)).
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Stammer, Detlef, Armin Köhl, and Carl Wunsch. "Impact of Accurate Geoid Fields on Estimates of the Ocean Circulation." Journal of Atmospheric and Oceanic Technology 24, no. 8 (August 1, 2007): 1464–78. http://dx.doi.org/10.1175/jtech2044.1.
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Abstract The impact of new geoid height models on estimates of the ocean circulation, now available from the Gravity Recovery and Climate Experiment (GRACE) spacecraft, is assessed, and the implications of far more accurate geoids, anticipated from the European Space Agency’s (ESA) Gravity and Ocean Circulation Explorer (GOCE) mission, are explored. The study is based on several circulation estimates obtained over the period 1992–2002 by combining most of the available ocean datasets with a global general circulation model on a 1° horizontal grid and by exchanging only the EGM96 geoid model with two different geoid models available from GRACE. As compared to the EGM96-based solution, the GRACE geoid leads to an estimate of the ocean circulation that is more consistent with the Levitus temperature and salinity climatology. While not a formal proof, this finding supports the inference of a substantially improved GRACE geoid skill. However, oceanographic implications of the GRACE model are only modest compared to what can be obtained from ocean observations alone. To understand the extent to which this is merely a consequence of a not-optimally converged solution or if a much more accurate geoid field could in principle play a profound role in the ocean estimation procedure, an additional experiment was performed in which the geoid error was artificially reduced relative to all other datasets. Adjustments occur then in all elements of the ocean circulation, including 10% changes in the meridional overturning circulation and the corresponding meridional heat transport in the Atlantic. For an optimal use of new geoid fields, improved error information is required. The error budget of existing time-mean dynamic topography estimates may now be dominated by residual errors in time-mean altimetric corrections. Both these and the model errors need to be better understood before improved geoid estimates can be fully exploited. As is commonly found, the Southern Ocean is of particular concern.
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Saari, Timo, and Mirjam Bilker-Koivula. "Applying the GOCE-based GGMs for the quasi-geoid modelling of Finland." Journal of Applied Geodesy 12, no. 1 (January 26, 2018): 15–27. http://dx.doi.org/10.1515/jag-2017-0020.
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AbstractThe gravity satellite mission GOCE made its final observations in the fall of 2013. Since the re-entry to the Earth’s atmosphere, the full cycle of the GOCE data has been published by ESA. At first, we evaluated all the GOCE-based global geoid models over Finland using terrestrial gravity and GNSS-levelling data. The most suitable model was selected as a global background model for the Finnish quasi-geoid calculations.Next, we combined the chosen model with terrestrial gravity data of Finland and surrounding areas. Quasi-geoid models with different modifications were calculated using the GOCE DIR5 model up to spherical harmonic degree and order (d/o) 240 and 300, and the high resolution EIGEN-6C4 (includes the complete GOCE data) model up to degree and order 1000 and 2190.The calculated quasi-geoid models were validated to the measurements on site with two independent GPS-levelling datasets. The best quasi-geoid models with GOCE gave standard deviations of 2.6 cm (FIN_DIR5 d/o 240) and 2.3 cm (FIN_DIR5 d/o 300) in Finland. For the high resolution model FIN_EIGEN-6C4, the results were 1.8 cm (d/o 1000) and 1.7 cm (d/o 2190). In addition, the results were compared with the latest geoid models available in Finland (FIN2005N00, NKG2004, NKG2015, EGG2008). The sub-2-centimetre (and near 2 cm, when using the GOCE-based models) accuracy is an improvement over the previous and current Finnish geoid models.
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Kim, Su-Kyung, Jihye Park, Daniel Gillins, and Michael Dennis. "On determining orthometric heights from a corrector surface model based on leveling observations, GNSS, and a geoid model." Journal of Applied Geodesy 12, no. 4 (October 25, 2018): 323–33. http://dx.doi.org/10.1515/jag-2018-0014.
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Abstract Leveling is a traditional geodetic surveying technique that has been used to realize a vertical datum. However, this technique is time consuming and prone to accumulate errors, where it relies on starting from one station with a known orthometric height. Establishing orthometric heights using Global Navigation Satellite Systems (GNSS) and a geoid model has been suggested [14], but this approach may involve less precisions than the direct measurements from leveling. In this study, an experimental study is presented to adjust the highly accurate leveling observations along with orthometric heights derived from GNSS observations and a geoid model. For the geoid model, the National Geodetic Survey’s gravimetric geoid model (TxGEOID16B) and hybrid geoid model (GEOID12B) were applied. Uncertainties in the leveled height differences, GNSS derived heights, and the geoid models were modeled, and a combined adjustment was implemented to construct the optimal combination of orthometric, ellipsoidal, and geoid height at each mark. As a result, the discrepancy from the published orthometric heights and the CSM (Corrector Surface Model) based adjusted orthometric heights with GEOID12B showed a mean and RMS of -8.5 mm and 16.6 mm, respectively, while TxGEOID16B had a mean and RMS of 28.9 mm and 34.6 mm, respectively. It should be emphasized that this approach was not influenced by the geodetic distribution of the stations where the correlation coefficients between the distance from the center of the surveying network and the discrepancy from the published heights using TxGEOID16B and GEOID12B are 0.03 and 0.36, respectively.
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Bruno Kyamulesire, Sylvester Okiemute Eteje, and Paul Dare Oluyori. "Establishment of local geometric geoid model for Busoga, Uganda." World Journal of Advanced Research and Reviews 8, no. 3 (December 30, 2020): 139–48. http://dx.doi.org/10.30574/wjarr.2020.8.3.0468.
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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.
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Rangelova, E., W. Van Der Wal, and M. G. Sideris. "How Significant is the Dynamic Component of the North American Vertical Datum?" Journal of Geodetic Science 2, no. 4 (December 1, 2012): 281–89. http://dx.doi.org/10.2478/v10156-012-0005-7.
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AbstractOne of the main current geodetic activities in North America is the definition and establishment of a geoid-based vertical datum that will replace the official CGVD28 and NAVD88 datums in Canada and the USA, respectively. The new datum will also have a time-dependent (dynamic) component required by the targeted one-centimetre accuracy of the datum. Heights of the levelling benchmarks are subject to temporal changes, which contribute to the degradation of the accuracy of the datum and increase the misfit of the geoid heights determined gravimetrically and by GNSS/levelling. The zero level surface, i.e., the geoid, also changes with time, most significantly due to postglacial rebound, climate-induced loss of polar ice masses and mountain glaciers, and hydrology variations. In this study, we examine the possible changes of the datum due to the aforementioned factors. We are mostly concerned with postglacial rebound as it can contribute more than 1 mm per year and more than 1 cm per decade to the geoid change. We also assess the significance of the temporal geoid and benchmark height changes and show that, compared to its current accuracy, the geoid change is only significant after a decade mostly in the flat areas of central Canada.
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Hoa, Ha Minh. "ESTIMATING THE GEOPOTENTIAL VALUE W0 OF THE LOCAL GEOID BASED ON DATA FROM LOCAL AND GLOBAL NORMAL HEIGHTS OF GPS/LEVELING POINTS IN VIETNAM." Geodesy and Cartography 39, no. 3 (September 26, 2013): 99–105. http://dx.doi.org/10.3846/20296991.2013.823705.
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Currently, the determination of geopotential value W0 of local geoid that best fits local mean sea level at the Zero Tide Gauge Station is getting important in building the National Geoid-Based Vertical System. Ha Minh Hoa (2007) and Kotsakis et al. (2012) recommended a method, which estimates the geopotential value W0 of local geoid at the Zero Tide Gauge Station based on equations of relation between the local and global normal heights or between the local and global height anomalies at GPS/leveling points regularly located on the whole territory. The objective of this paper is to determine conditions for estimating the geopotential value W0 of local geoid at the Zero Tide Gauge Station accomplished for whole territory of Vietnam.
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Arana, Daniel, Fabricio dos Santos Prol, Paulo de Oliveira Camargo, and Gabriel do Nascimento Guimarães. "ERRORS MEASUREMENT OF INTERPOLATION METHODS FOR GEOID MODELS: STUDY CASE IN THE BRAZILIAN REGION." Boletim de Ciências Geodésicas 24, no. 1 (March 2018): 44–57. http://dx.doi.org/10.1590/s1982-21702018000100004.
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Abstract: The geoid is an equipotential surface regarded as the altimetric reference for geodetic surveys and it therefore, has several practical applications for engineers. In recent decades the geodetic community has concentrated efforts on the development of highly accurate geoid models through modern techniques. These models are supplied through regular grids which users need to make interpolations. Yet, little information can be obtained regarding the most appropriate interpolation method to extract information from the regular grid of geoidal models. The use of an interpolator that does not represent the geoid surface appropriately can impair the quality of geoid undulations and consequently the height transformation. This work aims to quantify the magnitude of error that comes from a regular mesh of geoid models. The analysis consisted of performing a comparison between the interpolation of the MAPGEO2015 program and three interpolation methods: bilinear, cubic spline and neural networks Radial Basis Function. As a result of the experiments, it was concluded that 2.5 cm of the 18 cm error of the MAPGEO2015 validation is caused by the use of interpolations in the 5'x5' grid.
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Sjüberg, L. "Quality Estimates in Geoid Computation by EGM08." Journal of Geodetic Science 1, no. 4 (January 1, 2011): 361–66. http://dx.doi.org/10.2478/v10156-011-0014-y.
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Quality Estimates in Geoid Computation by EGM08The high-degree Earth Gravitational Model EGM08 allows for geoid determination with a resolution of the order of 5'. Using this model for estimating the quasigeoid height, we estimate the global root mean square (rms) commission error to 5 and 11 cm, based on the assumptions that terrestrial gravity contributes to the model with an rms standard error of 5 mGal and correlation length 0:01° and 0:1°, respectively. The omission error is estimated to—0:7Δg [mm], where Δg is the regional mean gravity anomaly in units of mGal.In case of geoid determination by EGM08, the topographic bias must also be considered. This is because the Earth's gravitational potential, in contrast to its spherical harmonic representation by EGM08, is not a harmonic function at the geoid inside the topography. If a correction is applied for the bias, the main uncertainty that remains is that from the uncertainty in the topographic density, which will still contribute to the overall geoid error.
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Abdalla, A., H. Fashir, A. Ali, and D. Fairhead. "Validation of recent GOCE/GRACE geopotential models over Khartoum state - Sudan." Journal of Geodetic Science 2, no. 2 (January 1, 2012): 88–97. http://dx.doi.org/10.2478/v10156-011-0035-6.
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Validation of recent GOCE/GRACE geopotential models over Khartoum state - SudanThis paper evaluates a number of latest releases of GOCE/GRACE global geopotential models (GGMs) using the GPS-levelling geometric geoid heights, terrestrial gravity data and existing local gravimetric models. We investigate each global model at every 5 degree of spherical harmonics. Our analysis shows that the satellite-only models derived by space-wise and time-wise approaches (SPW_R1, SPW_R2 TIM_R1 and TIM_R2), GOCO01S together with EGM08 (combined model) are very distinct and consistent to the local data, which guarantees one of them to be selected as the best of candidate models and then to be utilized in our further geoid studies. One of Satellite-only models will be employed for acquiring the long wavelength geoid component which is one of major steps in the geoid determination. EGM08 will be used to compensate and restore the missing gravity data points in the un-surveyed parts within the target area. We expect further improvements in geoid studies in Sudan due to the improved medium wavelength part of the gravity field from GOCE mission.
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Kaminskis, J., A. Vallis, I. Stamure, M. Reiniks, I. Geipele, and N. Zeltins. "Evaluation of Transition to Updated Regional Q-Geoid Model." Latvian Journal of Physics and Technical Sciences 55, no. 5 (October 1, 2018): 65–75. http://dx.doi.org/10.2478/lpts-2018-0037.
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Abstract During the last years, the European and the Nordic quasi-geoid models and existing national q-geoid models covered the territory of Latvia. There are many ways for comparison and tests of results achieved. Scientists and professionals can compare models directly at some special geodetic co-location stations or use GNSS/levelling sites. The results of this research can be used by scientists and specialists in the fundamental geodetic observations for independent monitoring of existing q-geoid models and evaluation of accuracy. The research aims at evaluating the transition to the best updated regional q-geoid model. The research objectives are the following: 1) to investigate and analyse the development of q-geoid model LV14; 2) to conduct precision research; 3) to assess the challenges of the European Vertical Reference System; 4) to draw conclusions that allow for further research in this area for development and improvement. Within the framework of the research, the authors have used a variety of research methods. Historical and logical approaches, comparative analysis and synthesis methods, as well as inductive – deductive data analysis methods have been selected for the research. A conclusion for such kind of studies is to implement the most appropriate q-geoid solution and to develop new astrogeodetic methods for unification, monitoring and for reliability of a geodetic reference network.
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Tenzer, R., R. Čunderlík, N. Dayoub, and A. Abdalla. "Application of the BEM approach for a determination of the regional marine geoid model and the mean dynamic topography in the Southwest Pacific Ocean and Tasman Sea." Journal of Geodetic Science 2, no. 1 (January 1, 2012): 8–14. http://dx.doi.org/10.2478/v10156-011-0019-6.
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Application of the BEM approach for a determination of the regional marine geoid model and the mean dynamic topography in the Southwest Pacific Ocean and Tasman SeaWe apply a novel approach for the gravimetric marine geoid modelling which utilise the boundary element method (BEM). The direct BEM formulation for the Laplace equation is applied to obtain a numerical solution to the linearised fixed gravimetric boundary-value problem in points at the Earth's surface. The numerical scheme uses the collocation method with linear basis functions. It involves a discretisation of the Earth's surface which is considered as a fixed boundary. The surface gravity disturbances represent the oblique derivative boundary condition. The BEM approach is applied to determine the marine geoid model over the study area of the Southwest Pacific Ocean and Tasman Sea using DNSC08 marine gravity data. The comparison of the BEM-derived and EGM2008 geoid models reveals that the geoid height differences vary within -25 and 18 cm with the standard deviation of 6 cm. The DNSC08 sea surface topography data and the new marine geoid are then used for modelling of the mean dynamic topography (MDT) over the study area. The local vertical datum (LVD) offsets estimated at 15 tide-gauge stations in New Zealand are finally used for testing the coastal MDT. The average value of differences between the MDT and LVD offsets is 1 cm.
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Balodis, Janis, Katerina Morozova, Gunars Silabriedis, Maris Kalinka, Kriss Balodis, Ingus Mitrofanovs, Irina Baltmane, and Izolde Jumare. "CHANGING THE NATIONAL HEIGHT SYSTEM AND GEOID MODEL IN LATVIA." Geodesy and cartography 42, no. 1 (April 8, 2016): 20–24. http://dx.doi.org/10.3846/20296991.2016.1168009.
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According to the decision of IAG Reference Frame Sub-commission for Europe (EUREF) the EVRF2007 solution as the vertical reference has to be deployed in EU countries.The new height system LAS-2000,5 had been enacted as the European Vertical Reference System‘s EVRF2007 realization in Latvia and the new geoid model LV‘14 had been introduced by Latvian authority Latvian Geospatial Information Agency. However, the appreciation of the quality of quasi-geoid model LV‘14 is rather contradictious among the users in Latvia. The independent estimate and comparison of the two Latvian geoid models developed till now has been performed by the Institute of Geodesy and Geoinformatics. Previous geoid model LV98 which was developed for Baltic-1977 height system almost 20 years ago is outdated now. Preparatory actions described in order to fulfil the task of comparison the geoids in two different height systems. The equations and transformation parameters are presented in this article for the normal height conversion from Baltic-1977 height system to the Latvian realization named LAS-2000,5. The comparison is performed of both Latvian quasigeoid models – the new one LV‘14 and previous LV98. The quality of both models estimated by controlling the geoid heights at the properly densified GNSS/levelling network sites. The distribution of discrepancies in comparison with normal distribution N(x,μ,s) is depicted in corresponding figures. For LV‘14 quasi-geoid model the standard deviation of discrepancies is 3.2 cm, 75% of discrepancies x ≤ 3.2 cm. For LV98 quasigeoid model the standard deviation of discrepancies is 4.7 cm, 80% of discrepancies x ≤ 6 cm. Without doubt, the newly developed LV‘14 quasi-geoid model is of higher quality.
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Ince, E. Sinem, Michael G. Sideris, Jianliang Huang, and Marc Véronneau. "Assessment of the GOCE-Based Global Gravity Models in Canada." GEOMATICA 66, no. 2 (June 2012): 125–40. http://dx.doi.org/10.5623/cig2012-025.
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The aim of this study is to test the first, second and third generation GOCE geoid solutions, obtained from the first 2, 8 and 18-month observations, respectively. These solutions are assessed over Canada and for two sub-regions (the Great Lakes and Rocky Mountains). The Canadian GPS/leveling-derived geoid heights are used as independent control values in the assessment of the GOCE geoid models. The study is conducted in two steps. First, the geoid models are computed from satellite-only models and truncated to different spherical harmonic degrees. These models are compared with the GPS/leveling geoid heights which are reduced to the same spectral band as the satellite models by EGM2008 predicted frequency components higher than the truncation degrees. The results suggest that the GOCE models show a full power of signal up to about spherical harmonic degree 180. Moreover, the second and third generation GOCE models (with the exception of the direct approach models) provide better agreement with the GPS/leveling-derived geoid undulations than the first generation models due to the longer observation period. The second step involves the combination of the two third generation GOCE models with terrestrial data. These models are tested against to the GPS/leveling-derived geoid undulations in full spectrum. EGM2008 global geopotential model and Canadian gravimetric geoid model CGG2005 are also included in the comparisons to measure improvement provided by the GOCE models. The GOCE-combined models yielded GPS/leveling results that are comparable with those obtained from EGM2008 and CGG2005 models. The best comparative results with the combined models give standard deviations of 4.8 cm, 6.0 cm and 12.2 cm for the Great Lakes, Rocky Mountains and Canada, respectively. These results indicate that the third generation GOCE models conform to the Canadian terrestrial gravity data from degrees 90 to 180. The new generation models show evident improvement over the first and second generation models.
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Sjöberg, Lars E. "On the geoid and orthometric height vs. quasigeoid and normal height." Journal of Geodetic Science 8, no. 1 (December 1, 2018): 115–20. http://dx.doi.org/10.1515/jogs-2018-0011.
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Abstract The geoid, but not the quasigeoid, is an equipotential surface in the Earth’s gravity field that can serve both as a geodetic datum and a reference surface in geophysics. It is also a natural zero-level surface, as it agrees with the undisturbed mean sea level. Orthometric heights are physical heights above the geoid,while normal heights are geometric heights (of the telluroid) above the reference ellipsoid. Normal heights and the quasigeoid can be determined without any information on the Earth’s topographic density distribution, which is not the case for orthometric heights and geoid. We show from various derivations that the difference between the geoid and the quasigeoid heights, being of the order of 5 m, can be expressed by the simple Bouguer gravity anomaly as the only term that includes the topographic density distribution. This implies that recent formulas, including the refined Bouguer anomaly and a difference between topographic gravity potentials, do not necessarily improve the result. Intuitively one may assume that the quasigeoid, closely related with the Earth’s surface, is rougher than the geoid. For numerical studies the topography is usually divided into blocks of mean elevations, excluding the problem with a non-star shaped Earth. In this case the smoothness of both types of geoid models are affected by the slope of the terrain,which shows that even at high resolutions with ultra-small blocks the geoid model is likely as rough as the quasigeoid model. In case of the real Earth there are areas where the quasigeoid, but not the geoid, is ambiguous, and this problem increases with the numerical resolution of the requested solution. These ambiguities affect also normal and orthometric heights. However, this problem can be solved by using the mean quasigeoid model defined by using average topographic heights at any requested resolution. An exact solution of the ambiguity for the normal height/quasigeoid can be provided by GNSS-levelling.
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Gad, Moamen Awad Habib, Oleg Odalović, and Sofija Naod. "Possibility to determine highly precise geoid for Egypt territory." Geodetski vestnik 64, no. 04 (2020): 578–93. http://dx.doi.org/10.15292/geodetski-vestnik.2020.04.578-593.
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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.