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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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Marques, Éder Teixeira, William Rodrigo Dal Poz, and Gabriel Do Nascimento Guimarães. "GEOID MODELLING USING INTEGRATION AND FFT ASSOCIATED WITH DIFFERENT GRAVIMETRIC REDUCTION METHODS." Revista Brasileira de Geofísica 36, no. 1 (March 20, 2018): 81. http://dx.doi.org/10.22564/rbgf.v36i1.909.
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ABSTRACT. A vertical reference system is characterized by a vertical datum and a set of scientific altitudes. In the case of orthometric altitudes, the geoid is used as a reference surface, equipotential surface of the gravity field of the Earth that better fits, in the sense of the Least Square Method, to the mean sea level. This study aimed to determine the geoid by applying two processes for calculation of residual ondulation, the integration and the Fast Fourier Transform. These techniques were applied to the values of the residual anomalies obtained from different methods of gravimetric reduction, the Helmert’s Second Method of Condensation, Bouguer and Rudzki. Two test areas were used. For area 1, the best gravimetric geoid was obtained by applying 1D planar FFT with the Helmert’s SecondMethod of Condensation. For area 2, the best gravimetric geoid was obtained through the application of integration and the Rudzki’s reduction. It can be concluded that the physical characteristics of both areas are relevant in the determination of the geoid and that additional procedures must be applied to improve the geoid determination, mainly, in area 2 whose physical characteristics are more heterogeneous than in area 1.Keywords: Geoid, GeoFis 1.0, Gravimetric Reduction, FFT, Stokes Integral. RESUMO. Um sistema vertical de referência é caracterizado por um datum vertical e pelo conjunto de altitudes científicas. No caso das altitudes científicas adotadas serem as ortométricas utiliza-se como superfície de referência o geoide, superfície equipotencial do campo da gravidade da Terra que melhor se ajusta, no sentido do método dos mínimos quadrados, ao nível médio do mar. O objetivo desse trabalho foi determinar o geoide aplicando dois processos de cálculo da ondulação residual, a integração e a Transformada Rápida de Fourier. Essas técnicas foram empregadas aos valores de anomalias residuais obtidas a partir de diferentes métodos de redução gravimétrica, Segundo Método de Condensação de Helmert, Bouguer e Rudzki. Foram utilizadas duas áreas de teste. Verificou-se que para a área 1 o melhor geoide gravimétrico foi obtido pela aplicação da FFT planar 1D juntamente com o Segundo Método de Condensação de Helmert. Para a área 2 o melhor geoide gravimétrico foi obtido pela aplicação da integração e da redução de Rudzki. Conclui-se que as características físicas das duas áreas são relevantes na determinação do geoide e que procedimentos complementares devem ser aplicados para melhorar a determinação do geoide, principalmente, na área 2 cujas características físicas são mais heterogêneas do que da área 1. Palavras-chave: Geoide, GeoFis 1.0, Redução gravimétrica, FFT, Integral de Stokes.
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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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Udama, Zahroh Arsy, Ira Mutiara Anjasmara, Arisauna Maulidyan Pahlevi, and Anas Sharafeldin Mohamed Osman. "Geoid Modelling of Kalimantan Island using Airborne Gravity Data and Global Geoid Model (EGM2008)." IOP Conference Series: Earth and Environmental Science 936, no. 1 (December 1, 2021): 012029. http://dx.doi.org/10.1088/1755-1315/936/1/012029.
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Abstract The availability of geoids, especially in survey and mapping activities, is useful for transforming the geometric heights obtained from observations of the Global Navigation Satellite System (GNSS) into orthometric heights that have real physical meanings such as those obtained from waterpass measurements. If a geoid is available, the orthometric heights of points on earth can be determined using the GNSS heighting method. The use of modern survey and mapping instruments based on satellite observations such as GNSS is more efficient in terms of time, effort, and cost compared to the accurate waterpass method. According to the Indonesian Geospatial Information Agency (BIG) it is stated that the application of geoid as a national Vertical Geospatial Reference System has an adequate and ideal category if the accuracy is higher than 15 cm. Recent studies have shown that it is possible to generate local geoid models with centimetre accuracy by utilizing airborne gravity data. We calculate free-air gravity anomaly data is calculated by processing airborne gravity and GNSS data using the Stokes Integral method on AGR software. Next a geoid model is created by calculating the contribution of three components, namely the long wave component represented by the EGM2008 global geoid data model, the shortwave component represented by the Shuttle Radar Topography Mission (SRTM) data and the medium wave component represented by the free-air gravity anomaly data. The geoid model validation was carried out using the geoid fitting method for geoid accuracy by calculating the difference between the gravimetric geoid and the geometric geoid and comparing it with the global geoid model EGM2008 degrees 2190. As a result, the total geoid model accuracy value was determined to be 49.4 cm on gravimetric geoid undulations with a standard deviation of 7.1 cm. Meanwhile, the results of the EGM2008 geoid undulation accuracy test at 2190 degrees resulted in an accuracy of 51.9 cm with a standard deviation of 9.9 cm. These results indicate that the local geoid model from airborne gravity measurement data produces a geoid model with a higher accuracy than the global geoid model EGM2008 degrees 2190. However, the accuracy of the resulting data is still below the BIG standard of 15 cm, so further research is needed to produce a geoid model which conforms to the standard.
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Isik, Mustafa Serkan, Muhammed Raşit Çevikalp, Bihter Erol, and Serdar Erol. "Improvement of GOCE-Based Global Geopotential Models for Gravimetric Geoid Modeling in Turkey." Geosciences 12, no. 12 (November 23, 2022): 432. http://dx.doi.org/10.3390/geosciences12120432.
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This study investigates the contribution of global geopotential models which are calculated with GOCE satellite mission data to the improvement of gravimetric geoid models in Turkey. In this context, direct (DIR), time-wise (TIM), space-wise (SPW), and GOCO satellite-only model series were considered. The research was carried out in two parts. The first part includes the validation of models in each series at 100 homogeneously distributed GNSS/leveling stations over the country utilizing spectrally enhanced geoid heights to determine the best performing model and its optimal expansion degree. According to obtained statistics, the TIM-R6 model was selected as the best model with an optimal expansion degree of 204. In the second part, the TIM-R6 model up to 204 degree/order was linearly blended with EGM2008 to obtain an improved version up to 360 degree/order of expansion. To clarify the contribution of the linearly blended model to the improvement of the regional geoid model, the gravimetric geoid models were computed adopting TIM-R6 up to 204 degree/order and its improved version up to 360 degree/order as reference models. To further emphasize the contribution of the GOCE mission’s data, the gravimetric geoid computations were repeated relying on EGM2008 up to 204 and 360 degrees of expansions, since EGM2008 does not contain GOCE data. In addition, we computed gravimetric geoids based on another combined model that includes GOCE mission data, the EIGEN-6C4 model. The calculated regional geoids were compared to each other and validated using GNSS/leveling data set. The obtained results revealed a ∼23% improvement in regional geoid model accuracy when the blended GOCE-based geopotential model was used as a reference. In addition, the results of this study presented the significance of GOCE contribution to mapping the gravity field in Turkey. The best accuracy obtained from this study was 7.7 cm for the Turkey geoid.
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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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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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Doganalp, Serkan. "An Evaluation of Recent Global Geopotential Models for Strip Area Project in Turkey." Earth Sciences Research Journal 20, no. 3 (December 1, 2016): 1. http://dx.doi.org/10.15446/esrj.v20n3.55440.
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The aim of this study is to present the evaluations based on comparisons of geoid heights that are computed from several global geopotential models (GGMs) and the GNSS/levelling data. In this application framework, differences between geoid heights obtained by GGMs and GNSS/levelling were computed. Then, the availability of geoid heights calculated by GGMs for engineering applications were investigated. The Konya-Polatli (Ankara) Express Train Project as a strip area project was chosen as the study area. The length of the project is approximately 210 km and consists of 110 benchmarks that belong to the Turkish National Triangulation Network. In this study a total of 69 GGMs were compared. In order to examine more detail, these models were classified as three groups based on CHAMP, GRACE and GOCE. Each group was evaluated separately and the results were obtained. According to results, the best five models were detected for geoid height differences (NGNSS/lev-Nggm) in terms of standard deviation. These are EIGEN-6c4, EIGEN-GRACE01s, EGM2008, EIGEN-6c3stat and EIGEN-6c2, respectively. Also, geoid heights were obtained using different parametric models. These parametric models were used in order to minimize the impact of the terms of bias, tilt etc. Generally, three, four, five and seven parametric models are used for the least-squares adjustment of the geoid height differences in the literature. Therefore, in this study the geoid heights were calculated for such different parametric models. After the geoid height values were computed from the parametric models, the best global geopotential models in terms of standard deviation were obtained as EIGEN-6c2, EIGEN-6c3stat, EGM2008, EIGEN-6c4 and EIGEN-GRACE01s, respectively. Evaluación de modelos geopotenciales globales recientes para un proyecto de área lineal en Turquía ResumenEl propósito de este estudio es presentar las evaluaciones comparativas de alturas geoidales que fueron computadas a partir de varios Modelos Geopotenciales Globales (GGM, del inglés Global Geopotential Models) y la nivelación de información del Sistema Global de Navegación por Satélite. Luego se investigó la disposición para aplicaciones de ingeniería de las alturas geoidales calculadas por los modelos GGM. Se seleccionó el proyecto del Tren Expreso Konya-Polatli (Ankara) como el área de estudio por ser un terreno lineal. La longitud del proyecto es de 210 kilómetros y consiste de 110 puntos de referencia que pertenecen a la Red de Triangulación Nacional de Turquía. En este estudio se compararon 69 modelos GGM. Para un mejor examen, estos modelos se clasificaron en tres grupos basados en CHAMP (CHAllenging Minisatellite Payload), GRACE (Gravity Recovery and Climate Experiment) y GOCE (Gravity field and steady-state Ocean Circulation Explorer). Cada grupo se evaluó por separado. De acuerdo con los resultados, se detectaron los cinco modelos mejores para las diferencias de alturas geoidales (NGNSS/LEV-NGGM) en términos de desviación estándar. Estos son EIGEN-6c4, EIGENGRACE01s, EGM2008, EIGEN-6c3stat, y EIGEN-6c2. También se obtuvieron las alturas geoide a través de diferentes modelos paramétricos. Este mecanismo se utilizo para minimizar el impacto en términos de inclinación y declive. Generalmente, se utilizan tres, cuatro, cinco, y siete modelos paramétricos para el ajuste por mínimos cuadrados de las diferencias de alturas geoide, según la literatura. Por lo tanto, en este estudio se calcularon las alturas geoide con estos modelos paramétricos. Después de que se computaron los valores de altura geoide desde los modelos paramétricos, se obtuvieron los mejores modelos geopotenciales globales en términos de desviación estándar, estos son el EIGEN-6c2, EIGEN-6c3stat, EGM2008, EIGEN-6c4 y EIGEN-GRACE01s, respectivamente.
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Osman, Anas Sharafeldin Mohamed, and Ira Mutiara Anjasmara. "Determination of a new gravimetric geoid modelling for Sudan using the least-squares collocation technique." IOP Conference Series: Earth and Environmental Science 1127, no. 1 (January 1, 2023): 012014. http://dx.doi.org/10.1088/1755-1315/1127/1/012014.
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Abstract The main purpose of this study is to compute a new gravimetric geoid model for Sudan by using the least-square collocation technique (LSC method) and applying the remove-compute-restore (RCR) technique. The computation of the model contains different datasets which are the gravity contribution of the model GO_CONS_GCF_2_TIM_R6e degree/order 300, BGI free-air gravity dataset in Sudan, GPS/levelling data, and high-resolution topographic information from ASTER digital elevation model. The “residual gravity anomalies” were run through the GEOCOL program using the GRAVSOFT software package, and the effects were restored to calculate the quasi-geoid surface (height anomalies). The gravimetric geoid was computed by adding the (N − 𝜁 h ) separation term to the quasi-geoid and was fitted to the GPS and levelling data provided by Sudan. The accuracy of our gravimetric geoid model SDN-LSC-G22 of the area of Sudan and some areas of bordering countries has been investigated by using geoid undulations computed from GPS and levelling data and by investigating the differences between the geoids of the GGM models which are EGM2008 and SGG-UGM-2. Our gravimetric geoid model (SDN-LSC-G22) has indicated an accuracy of 17.4 cm, in terms of a standard deviation compared with 66 GPS and Leveling data distributed in the area of Khartoum (most of these points are control points and benchmarks). Also, we evaluated our gravimetric geoid model by using 19 points distributed in the area of Sudan, and they indicated a standard deviation of 51.3 cm. The overall accuracy of SDN-LSC-G22 compared with the geoid undulation of all GPS and levelling has indicated an STD of 34.1 cm. The model SDN-LSC-G22 has shown better accuracy and significant differences compared with the GGM models EGM2008 and SGG-UGM-2 in terms of the differences with the available GPS and levelling data which have shown ~17 cm differences using (Abdalla, 2009) GPS and levelling data. It has demonstrated STD of ~17 cm differences by using 66 GPS and levelling data. Therefore, the model SDN-LSC-G22 provided better improvements and reliable geoid heights over Sudan compared to EGM2008 and SGG-UGM-2 gravity field models.
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Oltean, Marius, Richard J. Epp, Paul L. McGrath, and Robert B. Mann. "Geoids in general relativity: geoid quasilocal frames." Classical and Quantum Gravity 33, no. 10 (April 15, 2016): 105001. http://dx.doi.org/10.1088/0264-9381/33/10/105001.
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Jürgenson, Harli, Kristina Türk, and Jüri Randjärv. "DETERMINATION AND EVALUATION OF THE ESTONIAN FITTED GEOID MODEL EST-GEOID 2003 / ESTIJOS GEOIDO MODELIO EST-GEOID 2003 SUDARYMAS IR VERTINIMAS / СОЗДАНИЕ И ОЦЕНКА МОДЕЛИ ГЕОИДА ЭСТОНИИ EST-GEOID2003." Geodesy and Cartography 37, no. 1 (April 15, 2011): 15–21. http://dx.doi.org/10.3846/13921541.2011.558339.
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This paper focuses on issues related to the calculation of a high-precision fitted geoid model on Estonian territory. Model Est-Geoid2003 have been used in Estonia several years in geodesy and other applications. New data from precise levelling, new global models and terrestrial gravity data give plenty of possibilities for updates and accuracy evaluation. The model is based on a gravimetric geoid. From the gravimetric data gathered, a gravimetric geoid for Estonia was calculated as an approximately 3-km net using the FFT method. After including the new gravimetric data gathered, the gravimetric geoid no longer had any significant tilt relative to the height anomalies derived from GPS-levelling points. The standard deviation between the points was 2.7 cm. The surface of the calculated gravimetric geoid was fitted by high-precision GPS-levelling points. As a result, a height transformation model was determined to reflect the differences between the normal heights of BK77 and the ellipsoidal heights of EUREF-EST97 on Estonian territory. The model was originally called Est-Geoid2003 and is part of the official national geodetic system in Estonia. The model is updated and evaluated here using precise GPS-levelling points obtained from different measurement campaigns. In 2008–2010 the preliminary results from the latest precise levelling sessions became available, leading to a significant increase in the number of precise GPS-levelling points. Both networks are part of the Estonian integrated geodetic network. Using very precise levelling connections from new levelling lines, normal heights of several RGP points were calculated additionally. Misclosure of 300 km polygons are less than 2–3 mm normally. Ealier all precisely levelled RGP points were included into fitting points. Now many new points are available for fitting and independent evaluation. However, the use of several benchmarks for the same RGP point sometimes results in a 1–2 cm difference in normal height. This reveals problems with the stability of older wall benchmarks, which are widely used in Estonia. Even we recognized, that 0.5 cm fitted geoid model is not achievable using wall benchmarks. New evaluation of the model Est-Geoid2003 is introduced in the light of preliminary data from new precise levelling. Model accuracy is recognised about 1.2 cm as rms. Santrauka Akcentuojami klausimai, susiję su tiksliausio Estijos geoido modelio skaičiavimu. Šis modelis Estijoje geodezijoje ir kitose mokslo bei technikos šakose taikomas nuo 2003 metų. Nauji precizinės niveliacijos duomenys, nauji globalieji geopotencialo modeliai ir žemyno gravimetriniai duomenys – prielaidos geoido modeliui atnaujinti ir jo tikslumui įvertinti. Modelio pagrindas – gravimetrinis geoidas. Pagal surinktus gravimetrinius duomenis Estijos geoidas buvo apskaičiuotas greitųjų Furjė tranformacijų (FFT) metodu, sukuriant apie 3 km akių tinklą. Įtraukus naujuosius gravimetrinius duomenis, gravimetrinis geoidas daugiau nebeturi aukščių anomalijų. Vidutinė kvadratinė paklaida – 2,7 cm. Apskaičiuoto gravimetrinio geoido paviršius susietas su aukščių sistema pagal GPS niveliacijos taškus. 2008–2010 m. gavus precizinės niveliacijos duomenis, žymiai padidėjo GPS niveliacijos taškų skaičius bei jų tikslumas, nes precizinės niveliacijos poligonų iki 300 km nesąryšiai gauti mažesni nei 2–3 mm. Įvertinus naujo Estijos geoido modelio tikslumą nustatyta 1,2 cm vidutinė kvadratinė paklaida. Резюме Акцентируются вопросы, касающиеся вычисления точной модели геоида Эстонии. Эта модель применяется в Эстонии с 2003 г. в геодезии и других отраслях науки и техники. Новые данные высокоточной нивеляции, новые глобальные модели геопотенциала, а также гравиметрические данные создают предпосылки для обновления модели геоида и оценки его точности. Модель основана на гравиметрическом геоиде. Модель геоида Эстонии была вычислена быстрым методом Фурье с использованием всех гравиметрических данных и созданием сети 3×3 км. После использования новых гравиметрических данных в геоиде не оказалось значительного превышения высот по сравнению с точками, измеренными методом GPS. Среднеквадратическая погрешность составила 2,7 см. Вычисленная модель геоида была соединена с системой высот по точкам GPSнивелирования. Благодаря новым данным по высокоточной нивеляции, полученным в 2008–2010 гг., значительно увеличилось количество точек GPSнивелирования и тем самым увеличилась точность геоида, так как невязки полигонов нивелирования составляют всего 2–3 мм. Оценив точность нового геоида Эстонии, выявлено среднеквадратическое отклонение в 1,2 см.
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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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Oduyebo, O. F., M. N. Ono, and S. O. Eteje. "FITTING OF A TRANSFORMATION GEOID MODEL TO THE GRAVIMETRIC-GEOMETRIC GEOID MODEL OF BENIN CITY." FUDMA JOURNAL OF SCIENCES 5, no. 4 (January 17, 2022): 56–62. http://dx.doi.org/10.33003/fjs-2021-0504-781.
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The application of the transformation geoid model in Benin City has necessitated its fitting to the existing gravimetric-geometric geoid model of the study area. The transformation geoid model was determined using the Kotsakis (2008) model for the transformation of global geoid heights to local geoidal undulations. To obtain its accuracy, the root mean square error (RMSE) index was applied. The computed accuracy is 2.0172 m. To apply the determined geoid model in the study area, as well as improving on the computed accuracy, the model was fitted to the gravimetric-geometric geoid model of the study area. The fitting result shows that geoid heights can be computed using the determined geoid model with an accuracy of 1.1041 m in the study area.
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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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Oduyebo, O. F., M. N. Ono, and S. O. Eteje. "VERIFICATION OF THE CONSISTENCY OF THE PROPOSED TRANSFORMATION OF GLOBAL GEOID METHOD ACCURACY FOR LOCAL GEOID MODEL OF NIGERIA DETERMINATION." FUDMA JOURNAL OF SCIENCES 5, no. 4 (January 17, 2022): 49–55. http://dx.doi.org/10.33003/fjs-2021-0504-780.
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The proposed transformation of the global geoid model method for the determination of the local geoid model of Nigeria has only been applied in part of the Federal Capital Territory, Abuja. To determine the consistency of the accuracy of the method for the intended purpose, there is a need to apply it in some other parts of the country. As a result, this study presents the verification of the consistency of the proposed transformation of global geoid method accuracy for local geoid model of Nigeria determination. DGNSS observations were carried out to obtain the coordinates of the used points. The processed global geographic coordinates were used with online software (GeoidEval) to obtain the EGM 08 geoid heights of the points. The global geographic coordinates, the global geoid heights of the points and the transformation parameters from WGS 84 to Minna datum were applied to obtain the transformed (local) geoid heights of the points using a Microsoft Excel program. The transformed geoid heights were compared with their corresponding geoid heights from the gravimetric-geometric local geoid model of the study area to obtain the model RMSE (accuracy). The obtained accuracy (2.0172 m) was compared with those of the gravimetric-geometric geoid model of the study area (0.675 m) and the transformation of global geoid heights when the method was applied in part of Abuja (0.0014 m). The comparison results showed the inconsistency of the accuracy of the proposed method. It is recommended that the method should not be applied for the intended purpose.
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Dawod, Gomaa, and Hoda Mohamed. "Fitting Gravimetric Local and Global Quasi-Geoids to GPS/Levelling Data: The Role of Geoid/Quasi-Geoid Variations." Journal of King Abdulaziz University-Engineering Sciences 20, no. 1 (2009): 47–59. http://dx.doi.org/10.4197/eng.20-1.3.
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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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Anonymous. "Geoid Commission." Eos, Transactions American Geophysical Union 70, no. 41 (1989): 891. http://dx.doi.org/10.1029/89eo00320.
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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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Trojanowicz, Marek, Magdalena Owczarek-Wesołowska, Yan Ming Wang, and Olgierd Jamroz. "Quasi Geoid and Geoid Modeling with the Use of Terrestrial and Airborne Gravity Data by the GGI Method—A Case Study in the Mountainous Area of Colorado." Remote Sensing 13, no. 21 (October 21, 2021): 4217. http://dx.doi.org/10.3390/rs13214217.
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This article concerns the development of gravimetric quasigeoid and geoid models using the geophysical gravity data inversion technique (the GGI method). This research work was carried out on the basis of the data used in the Colorado geoid experiment, and the mean quasigeoid (ζm) and mean geoid (Nm) heights, determined by the approaches used in the Colorado geoid experiment, were used as a reference. Three versions of the quasigeoid GGI models depending on gravity data were analyzed: terrestrial-only, airborne-only, and combined (using airborne and terrestrial datasets). For the combined version, which was the most accurate, a model in the form of a 1′×1′ grid was calculated in the same area as the models determined in the Colorado geoid experiment. For the same grid, the geoid–quasigeoid separation was determined, which was used to build the geoid model. The agreement (in terms of the standard deviation of the differences) of the determined models, with ζm and Nm values for the GSVS17 profile points, was ±0.9 cm for the quasigeoid and ±1.2 cm for the geoid model. The analogous values, determined on the basis of all 1′×1′ grid points, were ±2.3 cm and ±2.6 cm for the quasigeoid and geoid models, respectively.
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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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Osman, Anas Sharafeldin Mohamed, Ira Mutiara Anjasmara, Abdelrahim Ruby, and Zahroh Arsy Udama. "Assessment of high-degree reference models and Recent Goce/Grace Global Geopotential Models over Sudan based on the GPS/Leveling data." IOP Conference Series: Earth and Environmental Science 936, no. 1 (December 1, 2021): 012035. http://dx.doi.org/10.1088/1755-1315/936/1/012035.
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Abstract Nowadays, Global Geopotential Models (GGMs) can be used as a reference to develop more detailed regional/local geoids, or they can be used to provide geoid heights on their own. Since 2000, several GGMs have been released, and they are mainly derived from satellite gravity measurements, satellite-only models, terrestrial gravimetry, altimeter-derived gravity data in marine areas, and airborne gravity data. With a precise geoid model, ellipsoidal heights obtained from GPS can be converted to orthometric heights, which is reasonably quite needed in Geodesy, Civil Engineering, etc. These heights reflect changes in topography as well as local variations in gravity. This paper evaluates some of the latest releases of high degree reference models and the satellite-only global gravity field model over Sudan using 19 GPS/Leveling stations. We have been selected 6 GGMs based on Gravity field Goce and Grace, and they released in 2020, 2019, 2014, 2008, and 1996 as shown in the International Centre for Global Earth Models website (ICGEM). The accuracy evaluation of the GGM models have been discussed, the accurate GGMs over Sudan are XGM2019e_2159 and GOCO05s, which have indicated -0.019 and 0.046 meters, respectively. The evaluation results produce valuable information to academia and geoid modeling research topics in Sudan, which shows the precise model from the selected GGMs in Sudan by using the available GPS/Leveling data.
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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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Mahin Hosseini-Asl, Alireza Amiri-Simkooei, and Abdolreza Safari. "Combination of regional and global geoid models at continental scale: application to Iranian geoid." Annals of Geophysics 64, no. 4 (November 16, 2021): GD434. http://dx.doi.org/10.4401/ag-8643.
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High precision geoid determination is a challenging task at the national scale. Many efforts have been conducted to determine precise geoid, locally or globally. Geoid models have different precision depending on the type of information and the strategy employed when calculating the models. This contribution addresses the challenging problem of combining different regional and global geoid models, possibly combined with the geometric geoid derived from GNSS/leveling observations. The ultimate goal of this combination is to improve the precision of the combined model. We employ fitting an appropriate geometric surface to the geoid heights and estimating its (co)variance components. The proposed functional model uses the least squares 2D bi-cubic spline approximation (LS-BICSA) theory, which approximates the geoid model using a 2D spline surface fitted to an arbitrary set of data points in the region. The spline surface consists of third- order polynomial pieces that are smoothly connected together, imposing some continuity conditions at their boundaries. In addition, the least-squares variance component estimation (LS- VCE) is used to estimate precise weights and correlation among different models. We apply this strategy to the combined adjustment of the high-degree global gravitational model EIGEN-6C4, the regional geoid model IRG2016, and the Iranian geometric geoid derived from GNSS/leveling data. The accuracy of the constructed surface is investigated with five randomly selected subsamples of check points. The optimal combination of the two geoid models along with the GNSS/leveling data shows a reduction of 21 mm (~20%) in the RMSE values of discrepancies at the check points.
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Dimitrova, Alexandra, Maxim Nikolenko, and Natalia Samsonova. "Problems of the evolution of the figure and the earth's gravitational field." E3S Web of Conferences 363 (2022): 04020. http://dx.doi.org/10.1051/e3sconf/202236304020.
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The relevance of geoid research involves examining a number of problems, the consideration of which reveals the evolution of the geoid. Measurements of the geoid help to understand the internal structure of our planet.
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Liu, Li Long, Teng Xu Zhang, Miao Zhou, Lin He, and Liang Ke Huang. "The Research of GPS Elevation Fitting Considering the Influence of Covariance Function." Applied Mechanics and Materials 568-570 (June 2014): 114–20. http://dx.doi.org/10.4028/www.scientific.net/amm.568-570.114.
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The common method to determine Quasi-Geoids is GPS leveling however the Quasi-Geoid of this method determined is a kind of trend surface which not take the physical property of geoid into consideration, and the fitting method is surface fitting which only consider the surveying error, lead to inaccurate fitting result. In allusion to these problems, Remove-restore method is used to remove the long wave information of earth gravity field model to get more smooth residual gravity height anomaly, then compared the influence of different covariance function to the fitting result of least square collocation which take surveying error and model error into account. The results show that Gaussian and resemble Gaussian function can achieve higher fitting precision to the large area with height anomaly value changes significance; the Remove-restore method can effectively improve the fitting precision to least square collocation method which depend on the covariance value of each points.
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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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Nguyễn, Duy Đô, and Insisiengmay Sisomphone. "Đánh giá độ chính xác mô hình Geoid." Tạp chí Khoa học Đo đạc và Bản đồ, no. 9 (September 1, 2011): 25. http://dx.doi.org/10.54491/jgac.2011.9.461.
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Trong đo cao gps, mô hình geoid được sử dụng để chuyển độ cao trắc địa về độ cao thủy chuẩn. Độ chính xác của mô hình geoid đóng vai trò quyết định đến độ chính xác đo cao bằng GPS. Dựa trên mối quan hệ giữa hiệu độ cao trắc địa, hiệu độ cao thủy chuẩn và hiệu độ cao Geoid giữa các điểm song trùng có thể đánh giá được độ chính xác của mô hình Geoid. Trong bài báo này trình biafy kết quả đánh giá độ chính xác mô hình Geoid EGM96 và EGM2008 trên khu vực miền bắc Việt Nam
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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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Liu, Yusheng, and Lizhi Lou. "Unified Land–Ocean Quasi-Geoid Computation from Heterogeneous Data Sets Based on Radial Basis Functions." Remote Sensing 14, no. 13 (June 23, 2022): 3015. http://dx.doi.org/10.3390/rs14133015.
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The determination of the land geoid and the marine geoid involves different data sets and calculation strategies. It is a hot issue at present to construct the unified land–ocean quasi-geoid by fusing multi-source data in coastal areas, which is of great significance to the construction of land–ocean integration. Classical geoid integral algorithms such as the Stokes theory find it difficult to deal with heterogeneous gravity signals, so scholars have gradually begun using radial basis functions (RBFs) to fuse multi-source data. This article designs a multi-layer RBF network to construct the unified land–ocean quasi-geoid fusing measured terrestrial, shipborne, satellite altimetry and airborne gravity data based on the Remove–Compute–Restore (RCR) technique. EIGEN-6C4 of degree 2190 is used as a reference gravity field. Several core problems in the process of RBF modeling are studied in depth: (1) the behavior of RBFs in the spatial domain; (2) the locations of RBFs; (3) ill-conditioned problems of the design matrix; (4) the effect of terrain masses. The local quasi-geoid with a 1′ resolution is calculated, respectively, on the flat east coast and the rugged west coast of the United States. The results show that the accuracy of the quasi-geoid computed by fusing four types of gravity data in the east coast experimental area is 1.9 cm inland and 1.3 cm on coast after internal verification (the standard deviation of the quasi-geoid w.r.t GPS/leveling data). The accuracy of the quasi-geoid calculated in the west coast experimental area is 2.2 cm inland and 2.1 cm on coast. The results indicate that using RBFs to calculate the unified land–ocean quasi-geoid from heterogeneous data sets has important application value.
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Sjöberg, Lars E. "Geoid model validation and topographic bias." Journal of Geodetic Science 12, no. 1 (January 1, 2022): 38–41. http://dx.doi.org/10.1515/jogs-2022-0133.
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Abstract Recently a number of geoid campaigns were performed to verify different types of geoid and quasigeoid modeling techniques. Typically, GNSS-leveling was employed as an independent method, but in some cases zenith camera astronomic deflection data were also used in astrogeodetic determinations of the geoid and/or quasigeoid. However, due to the uncertainty in the topographic density distribution data (and thereby in orthometric heights), we conclude that neither GNSS-leveling nor astrogeodetic techniques can reliably verify differences between gravimetric geoid models at several centimeter levels in rough mountainous regions. This is because much the same topographic data are used both in the gravimetric geoid models and in their verifications by geometric and/or astrogeodetic geoid models. On the contrary, this is not a problem in verifying gravimetric quasigeoid models, as they are independent of the topographic density distribution, and so is the related normal height used in GNSS-leveling.
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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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Tocho, Claudia N., Ezequiel D. Antokoletz, Agustín R. Gómez, Hernán Guagni, and Diego A. Piñon. "Analysis of high-resolution global gravity field models for the estimation of International Height Reference System (IHRS) coordinates in Argentina." Journal of Geodetic Science 12, no. 1 (January 1, 2022): 131–40. http://dx.doi.org/10.1515/jogs-2022-0139.
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Abstract Following the definition and realization of the International Height Reference System (IHRS), the vertical coordinate of a given point at the Earth’s surface can be obtained from the computation of the geopotential value from a harmonic expansion of a Global Gravity Model of High-Resolution (GGM-HR) or based on the computation of a local or regional pure gravimetric geoid or quasigeoid. Therefore, an evaluation of the accuracy of GGMs-HR and the geoid model available is needed in order to assess its capability to infer IHRS coordinates. In this study, different GGMs-HR are evaluated against 2287 benchmarks in Argentina. Moreover, the most recent geoid model of Argentina is also evaluated. Geoid undulations at these benchmarks are obtained based on ellipsoidal and orthometric heights in the local vertical datum. Results suggest that among the evaluated GGMs-HR, XGM2019e provides the best agreement with the observed geoid heights, but none of them is accurate enough in order to infer vertical coordinates in the IHRS. Similar conclusions are obtained for the local geoid model for Argentina demonstrating the necessity for a more precise geoid model, following the standards and recommendations given for the IHRS.
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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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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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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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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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Varbla, Sander. "The Influence of Bathymetry on Regional Marine Geoid Modeling in Northern Europe." Journal of Marine Science and Engineering 10, no. 6 (June 9, 2022): 793. http://dx.doi.org/10.3390/jmse10060793.
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Although Northern Europe has been the target area in many regionwide geoid determination studies, the research has been land-focused, neglecting bathymetry information. With new projects, such as the Baltic Sea Chart Datum 2000, the attention is shifting toward the marine geoid. Hence, consideration for bathymetry has become relevant, the influence of which is studied. In the relatively shallow Baltic Sea, accounting for bathymetry-based residual terrain model reduction during gravity data processing induces marine geoid modeling differences (relative to neglecting bathymetry) mainly within 2 cm. However, the models can deviate up to 3–4 cm in some regions. Rugged Norwegian coastal areas, on the other hand, had modeling improvements around a decimeter. Considering bathymetry may thus help improve geoid modeling outcomes in future Northern Europe geoid determination projects. Besides using the conventional precise GNSS-leveling control points, the paper also demonstrates the usefulness of shipborne GNSS and airborne laser scanning-derived geoidal heights in validating geoid modeling results. A total of 70 gravimetric geoid solutions are presented, for instance, by varying the used reference global geopotential models. According to the comparisons, GOCO05c-based solutions generally perform the best, where modeling agreement with GNSS-leveling control points reached 2.9 cm (standard deviation) from a one-dimensional fit.
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Nguyễn, Tuấn Anh. "Nghiên cứu chi tiết độ cao của mặt Geoid cục bộ Hòn Dấu so với mặt Geoid toàn cầu trên lãnh thổ Việt Nam." Tạp chí Khoa học Đo đạc và Bản đồ, no. 25 (September 1, 2015): 33–38. http://dx.doi.org/10.54491/jgac.2015.25.152.
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Bài báo đề cập đến việc đánh giá chi tiết độ cao của mặt Geoid cục bộ Hòn Dấu sát nhất với mặt biển trung bình nhiều năm tại trạm nghiệm triều Hòn Dấu so với mặt Geoid toàn cầu dựa trên các điểm trọng lực chi tiết trên lãnh thổ Việt Nam. Các kết quả tính toán cho thấy độ cao của mặt Geoid cục bộ Hòn Dấu so với mặt Geoid toàn cầu bằng 0.890 m và không đổi trên toàn bộ lãnh thổ Việt Nam.