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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 Previous geoid model LV98 which was developed for Baltic-1977 height system almost 20 years ago is outdated now.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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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Guo, Jin Yun, Shu Yang Wang, Guo Wei Li, Wei Hua Mao, and Yuan Ming Ji. "Local Quasi-Geoid Refinement Based on Spherical Cap Harmonic Model." Applied Mechanics and Materials 226-228 (November 2012): 1947–50. http://dx.doi.org/10.4028/www.scientific.net/amm.226-228.1947.
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The local quasi-geoid model up to centimeter precision has became the basic requirement for the development of modern surveying and mapping science. There are a variety of models can be used for the quasi-geoid refinement, including the spherical cap harmonic model (SCH). This paper studies the theory of SCH to get the spherical cap harmonic expression to fit the height anomaly in the least squares sense, which is to achieve the transformation between the geodetic height and the normal height. We also discuss the selection of the maximum model degree in local region. The practical case is studied to refine the local quasi-geoid model with SCH using GPS/leveling data at 85 points. The results indicate that the local quasi-geoid model can reach 3 centimeter-level at the internal and external fitting precision.
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Mishra, Upendra Nath, and Jayanta Kumar Ghosh. "DEVELOPMENT OF A GRAVIMETRIC GEOID MODEL AND A COMPARATIVE STUDY." Geodesy and cartography 42, no. 3 (September 22, 2016): 75–84. http://dx.doi.org/10.3846/20296991.2016.1226368.
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Site specific geoid model is prerequisite for accurate determination of orthometric heights. No geoid model has been developed so far for India or any of its part. So, development of a geoid model for India or its part is of utmost need to make use of GNSS data towards determination of orthometric heights. In this research work, an attempt has been made to develop geoid undulation models by gravimetric method using Molodensky’s concept. Component parameters in line with the Remove – Compute – Restore (RCR) technique have been used recursively. Models have been developed for two study areas: one of these lies in and around Dehradun (30° 19′ N, 75° 04′E) in Uttarakhand state, India in lower Himalayan region having highly undulating topography and the other near Hyderabad (17° 30′N, 78°30′E) in Telengana state of India having gentle topography. The model has been tested for 7 stations in the first study area and accuracy has been found to be 17.5 cm; whereas, for the second area accuracy has been found to be 7.0 cm for 24 test stations. Further, the performances of the developed models have been evaluated with those from three global geoid models namely EIGEN6C4, EIGEN6C3stat and EGM2008; and have been found to be similar or better in case of first study and for second study area far more superior. Thus, local/regional geoid undulation model requiring accuracy better than 20 cm for any study area may be developed adopting the method. However, the optimality in the number and density of gravity stations may be considered as a future scope of work.
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Huang, Jianliang, and Marc Véronneau. "Canadian gravimetric geoid model 2010." Journal of Geodesy 87, no. 8 (June 12, 2013): 771–90. http://dx.doi.org/10.1007/s00190-013-0645-0.
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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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Kyamulesire, Bruno, Paul Dare Oluyori, and Sylvester Okiemute Eteje. "COMPARATIVE ANALYSIS OF THREE PLANE GEOMETRIC GEOID SURFACES FOR ORTHOMETRIC HEIGHT MODELLING IN KAMPALA, UGANDA." FUDMA JOURNAL OF SCIENCES 4, no. 3 (September 11, 2020): 48–51. http://dx.doi.org/10.33003/fjs-2020-0403-255.
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The conversion of theoretical, as well as geometric heights to practical heights requires the application of geoidal undulations from a geoid model. The various global geopotential models that are readily available for application in any part of the world do not best-fit regions, as well as countries. As a result, there is a need to determine the local geoid models of local areas, regions and countries. This study determines the local geoid model of Kampala in Uganda for orthometric heights computation by comparing three plane geometric geoid surfaces. A total of 19 points were used in the study. The least squares adjustment technique was applied to compute the models’ parameters. Microsoft Excel programs were developed for the application of the models in the study area. The Root Mean Square Index was applied to compute the accuracy of the models. The three geometric geoid models were compared using their accuracy to determine which of them is most suitable for application in the study area. The comparison results show that the three models can be applied in the study area with more reliability, with greater confidence in model 2.
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Elshambaky, Hossam Talaat. "Application of neural network technique to determine a corrector surface for global geopotential model using GPS/levelling measurements in Egypt." Journal of Applied Geodesy 12, no. 1 (January 26, 2018): 29–43. http://dx.doi.org/10.1515/jag-2017-0017.
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AbstractOwing to the appearance of many global geopotential models, it is necessary to determine the most appropriate model for use in Egyptian territory. In this study, we aim to investigate three global models, namely EGM2008, EIGEN-6c4, and GECO. We use five mathematical transformation techniques, i.e., polynomial expression, exponential regression, least-squares collocation, multilayer feed forward neural network, and radial basis neural networks to make the conversion from regional geometrical geoid to global geoid models and vice versa. From a statistical comparison study based on quality indexes between previous transformation techniques, we confirm that the multilayer feed forward neural network with two neurons is the most accurate of the examined transformation technique, and based on the mean tide condition, EGM2008 represents the most suitable global geopotential model for use in Egyptian territory to date. The final product gained from this study was the corrector surface that was used to facilitate the transformation process between regional geometrical geoid model and the global geoid model.
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Eshagh, Mehdi, and Jenny Berntsson. "On quality of NKG2015 geoid model over the Nordic countries." Journal of Geodetic Science 9, no. 1 (January 1, 2019): 97–110. http://dx.doi.org/10.1515/jogs-2019-0010.
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Abstract The NKG2015 geoid model covers the Nordic and Baltic countries and has been computed based on the least-squares modification of Stokes’ formula with additive corrections method. New and precise terrestrial, airborne and shipborne gravimetric measurements, the recent global gravity model of the gravity field and steady-state ocean circulation explorer (GOCE) and detailed digital terrain models over each territory have been used for computing this new geoid model. Some estimates for the error of this model have been roughly presented by comparing it with the global navigation satellite system (GNSS) data over each country. In this paper, our goal is to have a closer look at the relative error of this model by performing some statistical tests and finding the proper corrective surface for absorbing the systematic errors over each country. Our main assumption is realisticity of the errors of GNSS/levelling data and we will investigate its consequences in estimating the error of the geoid model. Our results show that the 4-parameter corrective surface is suitable for modelling the systematic trends of the differences between the gravimetric and GNSS geoid heights in Sweden, Denmark and Finland, but a filtered discrepancies by a confidence interval of 95% should be used for Sweden. A 7-aparameter model is suitable for the filtered discrepancies with the confidence interval of 95% in Norway. Based on the selected corrective surface and our newly developed regional iterative variance estimator, the confidence interval for the error of NKG2015 geoid model in Sweden, Denmark and Norway yielded 0-6.5 mm, 1.8-5.2 mm, 14.8-17.7 mm, respectively with a confidence level of 95%. We could not estimate the geoid error in Finland because the given error of the GNSS/levelling heights is significantly larger than the size of residuals. Based on the selected corrective surfaces and our presented local variance estimator, the average error of geoid becomes 3.6, 2.4, 8.8 and 5.8 mm with a confidence interval of 68%, respectively, over Sweden, Denmark, Norway and Finland.
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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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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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Kuhar, Miran. "Towards a new geoid model of Slovenia." Geodetski vestnik 61, no. 02 (2017): 187–200. http://dx.doi.org/10.15292//geodetski-vestnik.2017.02.187-200.
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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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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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JÚNIOR, C. A. C. C., G. N. GUIMARÃES, and N. C. FERREIRA. "The Geoid Model of Goiás - MODGEO-GO." Anuário do Instituto de Geociências - UFRJ 41, no. 3 (December 4, 2018): 460–69. http://dx.doi.org/10.11137/2018_3_460_469.
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Janák, Juraj, Petr Vańiček, Ismael Foroughi, Robert Kingdon, Michael B. Sheng, and Marcelo C. Santos. "Computation of precise geoid model of Auvergne using current UNB Stokes-Helmert’s approach." Contributions to Geophysics and Geodesy 47, no. 3 (September 1, 2017): 201–29. http://dx.doi.org/10.1515/congeo-2017-0011.
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AbstractThe aim of this paper is to show a present state-of-the-art precise gravimetric geoid determination using the UNB Stokes-Helmert’s technique in a simple schematic way. A detailed description of a practical application of this technique in the Auvergne test area is also provided. In this paper, we discuss the most problematic parts of the solution: correct application of topographic and atmospheric effects including the lateral topographical density variations, downward continuation of gravity anomalies from the Earth surface to the geoid, and the optimal incorporation of the global gravity field into the final geoid model. The final model is tested on 75 GNSS/levelling points supplied with normal Molodenskij heights, which for this investigation are transformed to rigorous orthometric heights. The standard deviation of the computed geoid model is 3.3 cm without applying any artificial improvement which is the same as that of the most accurate quasigeoid.
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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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Tenzer, Robert. "Global spectral model of the geoid." Geodesy and Geodynamics 8, no. 1 (January 2017): 24–33. http://dx.doi.org/10.1016/j.geog.2016.12.001.
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Lopes, Alexandre Bernardino, and Joseph Harari. "Use of recent geoid models to estimate mean dynamic topography and geostrophic currents in South Atlantic and Brazil Malvinas confluence." Brazilian Journal of Oceanography 60, no. 1 (March 2012): 41–48. http://dx.doi.org/10.1590/s1679-87592012000100005.
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The use of geoid models to estimate the Mean Dynamic Topography was stimulated with the launching of the GRACE satellite system, since its models present unprecedented precision and space-time resolution. In the present study, besides the DNSC08 mean sea level model, the following geoid models were used with the objective of computing the MDTs: EGM96, EIGEN-5C and EGM2008. In the method adopted, geostrophic currents for the South Atlantic were computed based on the MDTs. In this study it was found that the degree and order of the geoid models affect the determination of TDM and currents directly. The presence of noise in the MDT requires the use of efficient filtering techniques, such as the filter based on Singular Spectrum Analysis, which presents significant advantages in relation to conventional filters. Geostrophic currents resulting from geoid models were compared with the HYCOM hydrodynamic numerical model. In conclusion, results show that MDTs and respective geostrophic currents calculated with EIGEN-5C and EGM2008 models are similar to the results of the numerical model, especially regarding the main large scale features such as boundary currents and the retroflection at the Brazil-Malvinas Confluence.
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Falchi, Ugo, Claudio Parente, and Giuseppina Prezioso. "GLOBAL GEOID ADJUSTMENT ON LOCAL AREA FOR GIS APPLICATIONS USING GNSS PERMANENT STATION COORDINATES." Geodesy and cartography 44, no. 3 (October 16, 2018): 80–88. http://dx.doi.org/10.3846/gac.2018.4356.
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Orthometric heights, useful for many engineering and geoscience applications, can be obtained by GPS (Global Positioning System) surveys only when an accurate geoid undulation model (that supplies the vertical separation between the geoid and WGS84 ellipsoid) is available for the considered topic area. Global geoid height models (i.e., EGM2008), deriving from satellite gravity measurements suitably integrated with other data are free available on web, but their accuracy is often not sufficient for the user’s purposes. More accurate local models can nevertheless be acquired, but often only for a fee. GPS/levelling surveys are suitable for determining a local, accurate geoid model, but may be too expensive. This paper aims to demonstrate that GNSS (Global Navigation Satellite System) Permanent Station documents (monographs), freely available on the web and supplying orthometric and ellipsoidal heights, permit to calculate precise geoidal undulations useful to perform global geoid modelling on a local area. In fact, in this study 25 GNSS Permanent Stations (GNSS PS), located in North-Western Italy are considered: the differences between GNSS PS geoidal heights and the corresponding EGM2008 1′ × 1′ ones are used as a starting dataset for Ordinary Kriging applications. The resulting model is summed to the EGM2008 1′ × 1′, obtaining a better-performed model of the interest area. The accuracy tests demonstrate that the resulting model is better than EGM2008 grids to produce contours from a GPS dataset for large-scale mapping.
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Hartanto, Prayudha, and Febrylian Fahmi Chabibi. "UJI KETELITIAN MODEL GEOPOTENSIAL GLOBAL DI PULAU JAWA DAN MADURA." Seminar Nasional Geomatika 3 (February 15, 2019): 827. http://dx.doi.org/10.24895/sng.2018.3-0.1071.
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Badan Informasi Geospasial (BIG) sebagai penyelenggara Informasi Geospasial Dasar (IGD) di Indonesia hingga saat ini baru menyelesaikan pembuatan Geoid untuk sebagian wilayah Indonesia. Wilayah-wilayah tersebut yakni Pulau Kalimantan, Sulawesi dan Papua. Dalam pembuatan geoid tersebut dibutuhkan kombinasi data Model Geopotensial Global (GGM) dan data ukuran gayaberat (terestris maupun airborne ). GGM yang diyakini memiliki ketelitian tertinggi di wilayah Indonesia adalah EGM2008, dan menjadi pilihan utama sebagai dasar pembentukan geoid nasional Indonesia. Tujuan penelitian ini adalah menguji apakah EGM 2008 masih menjadi GGM terbaik sebagai dasar pembuatan Geoid Indonesia jika dibandingkan dengan GGM lain yang tersedia di portal ICGEM. GGM yang akan diuji ketelitiannya terhadap Jaring Kontrol Vertikal (JKV) adalah EGM 2008, GECO dan EIGEN-6C4. Ketiga model tersebut dipilih karena memiliki orde dan derajat maksimal 2190, yang merupakan orde terbesar yang dimiliki oleh sebuah GGM hingga saat ini. Selain menguji ketiga model tersebut pada orde dan derajat 2190, akan diuji juga pada orde dan derajat 360 dan 720 beserta trunkasi
yang diterapkan pada ketiga model tersebut. Berdasarkan hasil pengujian, EGM 2008 pada orde dan derajat 2190 (EGM08_2190), EIGEN-6C4 pada orde dan derajat 2190 (EIGEN-6C4_2190), dan GECO pada orde dan derajat 2190 memiliki root mean square kesalahan (RMSe) masing-masing 0,891 m, 0,898 m dan 0,877 m. Hasil ini menunjukkan bahwa model geoid GECO menjadi yang paling akurat di antara GGM resolusi sangat tinggi. Selain itu, dapat disimpulkan bahwa penerapan trunkasi pada ketiga model di orde dan derajat 360 dan 720 mampu meningkatkan ketelitian GGM sebesar 5 – 20 mm.
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Margaryan, Venera. "Analysis of Quasi-Geoid Model Created for Territory of the Republic of Armenia." Advanced Materials Research 1020 (October 2014): 484–87. http://dx.doi.org/10.4028/www.scientific.net/amr.1020.484.
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Abstract: National Geodesic Network of WGS-84 system was founded in the territory of the Republic of Armenia from 2002 to 2007, which includes zero, first, and second class 1115 stations and there were other 229 State Geodesic Triangular Network stations. The observation at these stations has been done by GPS system. Each of the above mentioned stations covers on the average 27 square kilometers of the territory of Armenia. The data obtained during GPS observations have become the foundation for creating local quasi-geoid models and obtaining differences of heights (geoid wave value) of normal and WGS-84 ellipsoid surfaces. On the basis of gravimetric data a quasi-geoid model has been computed and developed. To creat the model coordinates of four geodetic satations encompassing the area of the Republic of Armenia have been used. To get the digital model of the selected area was diveded into five-minute sections by latitude and longitude and then coordinates of geodetic points have been taken. The above mentioned points were recalculated from the local system to WGS-84 system. The creation of the local elippsoid quasi-model is conditioned by the difference of 3D coordinates difference of three-dimensional of each point’s position. The values of the geoid wave vary within the range of 17.4547 meters, the average difference being almost in the centre of the area and is 21.2522 meters. To obtain the digital model of the quasi-geoid at the given local ellipsoid at each 100m a square matrix (of the network) was made by coordinates of recomputed points.
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Featherstone, W. E., M. S. Filmer, S. J. Claessens, M. Kuhn, C. Hirt, and J. F. Kirby. "Regional geoid-model-based vertical datums – some Australian perspectives." Journal of Geodetic Science 2, no. 4 (December 1, 2012): 370–76. http://dx.doi.org/10.2478/v10156-012-0006-6.
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AbstractThis article summarises some considerations surrounding a geoid-model-based vertical datum that have to be thought through before its implementation and adoption. Our examples are based on many Australian and some South-East Asian experiences, but these probably also apply elsewhere. The key considerations comprise data quality and availability, politics, and difficulties that users may encounter when adopting quite a different approach to height determination. We advocate some form of new vertical datum to replace the Australian Height Datum, but the exact type (whether using levelling or geoid, or some combination of both) still needs to be decided. We are not specifically opposed to the adoption of a geoid model as the vertical datum, but it is possibly more challenging than appears initially, and may even deter some users that are already well served by levelling-based vertical datums.
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Oduyebo, O. F., M. N. Ono, and S. O. Eteje. "Comparison of Three Gravimetric-Geometric Geoid Models for Best Local Geoid Model of Benin City, Nigeria." International Journal of Advanced Engineering Research and Science 6, no. 12 (2019): 261–72. http://dx.doi.org/10.22161/ijaers.612.23.
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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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Guimarães, Gabriel do Nascimento, Denizar Blitzkow, Riccardo Barzaghi, and Ana Cristina Oliveira Cancoro de Matos. "The computation of the geoid model in the state of São Paulo using two methodologies and GOCE models." Boletim de Ciências Geodésicas 20, no. 1 (March 2014): 183–203. http://dx.doi.org/10.1590/s1982-21702014000100012.
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The purpose of this manuscript is to compute and to evaluate the geoid model in the State of São Paulo from two methodologies (Stokes' integral through the Fast Fourier Transform - FFT and Least Squares Collocation - LSC). Another objective of this study is to verify the potentiality of GOCE-based. A special attention is given to GOCE mission. The theory related to Stokes' integral and Least Squares Collocation is also discussed in this work. The spectral decomposition was employed in the geoid models computation and the long wavelength component was represented by EGM2008 up to degree and order 150 and 360 and GOCE-based models up to 150. The models were compared in terms of geoid height residual and absolute and relative comparisons from GPS/leveling and the results show consistency between them. In addition, a comparison in the mountain regions was carried out to verify the methodologies behavior in this area; the results showed that LSC is less consistent than FFT.
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Abdalla, Ahmed, and Saad Mogren. "Implementation of a rigorous least-squares modification of Stokes’ formula to compute a gravimetric geoid model over Saudi Arabia (SAGEO13)." Canadian Journal of Earth Sciences 52, no. 10 (October 2015): 823–32. http://dx.doi.org/10.1139/cjes-2014-0192.
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A gravimetric geoid model (SAGEO13) is computed for the Kingdom of Saudi Arabia using a rigorous stochastic computational method. The computational methodology is based on a combination of least-squares (LS) modification of Stokes’ formula and the additive corrections for topographic, ellipsoidal, atmospheric, and downward continuation effects on the geoid solution. In this study, we used terrestrial gravity data, a digital elevation model (SRTM3), and seven global geopotential models (GGMs) to compute a new geoid model for Saudi Arabia. The least-squares coefficients are derived based on the optimisation of the input modification parameters. The gravimetric solution and its additive corrections are computed based on the optimum LS coefficients. Compared to GPS-levelling data, SAGEO13 shows a fit of 18 cm (RMS) after using a 4-parameter fitting model.
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Abdalla, Ahmed, and Robert Tenzer. "THE EVALUATION OF THE NEW ZEALAND'S GEOID MODEL USING THE KTH METHOD / NAUJOSIOS ZELANDIJOS GEOIDO MODELIO VERTINIMAS KTH METODU / ОЦЕНКА МОДЕЛИ ГЕОИДА НОВОЙ ЗЕЛАНДИИ С ПРИМЕНЕНИЕМ МЕТОДА КТН." Geodesy and Cartography 37, no. 1 (April 15, 2011): 5–14. http://dx.doi.org/10.3846/13921541.2011.558326.
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We compile a new geoid model at the computation area of New Zealand and its continental shelf using the method developed at the Royal Institute of Technology (KTH) in Stockholm. This method utilizes the least-squares modification of the Stokes integral for the biased, unbiased, and optimum stochastic solutions. The modified Bruns-Stokes integral combines the regional terrestrial gravity data with a global geopotential model (GGM). Four additive corrections are calculated and applied to the approximate geoid heights in order to obtain the gravimetric geoid. These four additive corrections account for the combined direct and indirect effects of topography and atmosphere, the contribution of the downward continuation reduction, and the formulation of the Stokes problem in the spherical approximation. The gravimetric geoid model is computed using two heterogonous gravity data sets: the altimetry-derived gravity anomalies from the DNSC08 marine gravity database (offshore) and the ground gravity measurements from the GNS Science gravity database (onshore). The GGM coefficients are taken from EIGEN-GRACE02S complete to degree 65 of spherical harmonics. The topographic heights are generated from the 1×1 arc-sec detailed digital terrain model (DTM) of New Zealand and from the 30×30 arc-sec global elevation data of SRTM30_PLUS V5.0. The least-squares analysis is applied to combine the gravity and GPS-levelling data using a 7-parameter model. The fit of the KTH geoid model with GPS-levelling data in New Zealand is 7 cm in terms of the standard deviation (STD) of differences. This STD fit is the same as the STD fit of the NZGeoid2009, which is the currently adopted official quasigeoid model for New Zealand. Santrauka Stokholmo Karališkajame technologijos institute (KTH) sukurtu metodu apskaičiuotas naujas Naujosios Zelandijos ir kontinentinio šelfo geoido modelis. Taikoma Stokso integralo mažiausiųjų kvadratų modifikacija, įvertinant paklaidas ir jų nevertinant bei ieškant optimalių stochastinių sprendinių. Modifikuotas Bruno ir Stokso integralas sieja regioninius žemyninius gravimetrinius duomenis su globaliuoju geopotencialo modeliu (GGM). Gravimetriniam geoidui gauti skaičiuojamos keturios papildomos pataisos: topografinės situacijos ir atmosferos tiesioginės ir netiesioginės įtakos, redukcijos įtakos ir Stokso integralo taikymo sferiniam paviršiui. Gravimetrinis geoido modelis apskaičiuotas pagal du duomenų rinkinius: DNSC08 jūrinių gravimetrinių duomenų bazėje (šelfas) esančias altimetriniu metodu nustatytas sunkio pagreičio anomalijas ir žemyninės dalies gravimetrinių matavimų duomenis iš GNS gravimetrinės duomenų bazės (pakrantė). GGM koeficientai imti iš EIGEN-GRACE02S modelio sferinių iki 65 laipsnio harmonikų. Topografiniai aukščiai sugeneruoti iš Naujosios Zelandijos 1×1 sekundės detaliojo skaitmeninio reljefo modelio ir iš 30×30 sekundžių globaliojo aukščių modelio SRTM30_PLUS V5.0. Gravimetriniams ir GPS niveliacijos duomenims sujungti taikytas mažiausiųjų kvadratų 7 parametrų metodas. KTH metodu sudaryto geoido modelio vidutinė kvadratinė paklaida 7 cm. Tai sutampa su NZGeoid 2009 geoido modelio, taikomo Naujoje Zelandijoje, tikslumu. Резюме Модель геоида континентального шельфа Новой Зеландии построена с применением метода, созданного в Королевском технологическом институте Стокгольма. Данный метод основан на модификации решения интеграла Стокса методом наименьших квадратов с оценкой или без оценки погрешностей и поиском оптимальных статистических решений. Модифицированный интеграл БрунаСтокса объединяет региональные надземные гравиметрические данные с глобальной геопотенциальной моделью (GGM). Для определения гравиметрического геоида вычисляются дополнительные поправки прямого и косвенного влияния топографии и атмосферы, редукции и применения проблемы Стокса для сферической поверхности. Гравиметрическая модель геоида вычисляется на основе двух баз данных: альтиметрическим методом определенных аномалий силы тяжести в базе морских гравиметрических данных DNSC08 (шельф) и надземной части гравиметрических измерений из базы данных GNS. Коэффициенты GGM взяты из сферических гармоник до 65 степени модели EIGENGRACEO2S. Топографические высоты сгенерированы из детальной цифровой модели рельефа Новой Зеландии с сеткой 1×1 секунду и из глобальной модели высот SRTM30_PLUSv5.0 с сеткой 30×30 секунд. Для объединения гравиметрических и GPSнивелирных данных применялся метод наименьших квадратов с 7 параметрами. Среднеквадратическая погрешность модели геоида, созданной по методу КТН, равна 7 см. Точность аналогична точности применяемой в Новой Зеландии модели геоида NZGeoid2009.
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NING, FANG-SHII. "USING SURFACE FITTING AND BUFFER ANALYSIS TO ESTIMATE REGIONAL GEOIDAL UNDULATION." Boletim de Ciências Geodésicas 21, no. 3 (September 2015): 624–36. http://dx.doi.org/10.1590/s1982-21702015000300035.
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Abstract:Geoidal undulation is the distance from the surface of an ellipsoid to the surface of a geoid measured along a line that is perpendicular to the ellipsoid. This paper describes how the geoidal undulation can be derived from the orthometric height, Global Navigation Satellite System geodetic height, and a surface model. Various surfaces fitting using the plane coordinates of the reference points and analysis with different buffers were used to determine the geoid undulation Taiwan. The results show that the quadratic surface model outperformed other surface models, yielding a buffer radius ranging from 15 to 25 km. According to the results, the accuracy of regional geoid undulation (city or state) can be improved through this process of surface fitting