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1
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 Previous geoid model LV98 which was developed for Baltic-1977 height system almost 20 years ago is outdated now.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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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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Sjöberg, Lars E. "On the topographic bias and density distribution in modelling the geoid and orthometric heights." Journal of Geodetic Science 8, no. 1 (February 1, 2018): 30–33. http://dx.doi.org/10.1515/jogs-2018-0004.
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Abstract It is well known that the success in precise determinations of the gravimetric geoid height (N) and the orthometric height (H) rely on the knowledge of the topographic mass distribution. We show that the residual topographic bias due to an imprecise information on the topographic density is practically the same for N and H, but with opposite signs. This result is demonstrated both for the Helmert orthometric height and for a more precise orthometric height derived by analytical continuation of the external geopotential to the geoid. This result leads to the conclusion that precise gravimetric geoid heights cannot be validated by GNSS-levelling geoid heights in mountainous regions for the errors caused by the incorrect modelling of the topographic mass distribution, because this uncertainty is hidden in the difference between the two geoid estimators.
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Sjöberg, Lars E. "On the geoid and orthometric height vs. quasigeoid and normal height." Journal of Geodetic Science 8, no. 1 (December 1, 2018): 115–20. http://dx.doi.org/10.1515/jogs-2018-0011.
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Abstract The geoid, but not the quasigeoid, is an equipotential surface in the Earth’s gravity field that can serve both as a geodetic datum and a reference surface in geophysics. It is also a natural zero-level surface, as it agrees with the undisturbed mean sea level. Orthometric heights are physical heights above the geoid,while normal heights are geometric heights (of the telluroid) above the reference ellipsoid. Normal heights and the quasigeoid can be determined without any information on the Earth’s topographic density distribution, which is not the case for orthometric heights and geoid. We show from various derivations that the difference between the geoid and the quasigeoid heights, being of the order of 5 m, can be expressed by the simple Bouguer gravity anomaly as the only term that includes the topographic density distribution. This implies that recent formulas, including the refined Bouguer anomaly and a difference between topographic gravity potentials, do not necessarily improve the result. Intuitively one may assume that the quasigeoid, closely related with the Earth’s surface, is rougher than the geoid. For numerical studies the topography is usually divided into blocks of mean elevations, excluding the problem with a non-star shaped Earth. In this case the smoothness of both types of geoid models are affected by the slope of the terrain,which shows that even at high resolutions with ultra-small blocks the geoid model is likely as rough as the quasigeoid model. In case of the real Earth there are areas where the quasigeoid, but not the geoid, is ambiguous, and this problem increases with the numerical resolution of the requested solution. These ambiguities affect also normal and orthometric heights. However, this problem can be solved by using the mean quasigeoid model defined by using average topographic heights at any requested resolution. An exact solution of the ambiguity for the normal height/quasigeoid can be provided by GNSS-levelling.
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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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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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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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Kearsley, A. W. H., and R. M. Eckels. "The determination of the geoid-spheroid separation for GPS levelling and applications." Exploration Geophysics 20, no. 2 (1989): 185. http://dx.doi.org/10.1071/eg989185.
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The heights which are obtained from global positioning system (GPS) satellite observations are measured with respect to an earth-centred ellipsoid and are not, as a result, generally useful for surveying and engineering. In order to become useful they must be transformed into orthometric heights, that is, heights which are measured with respect to the actual level reference surface termed the geoid. The parameter which enables this transformation is N, the geoid height or geoid-ellipsoid separation.This paper reviews the capabilities of the GPS system for height measurements, describes the various methods used to evaluate N from gravimetry, and explores the suitability of these methods in the various applications in which height measurements from the GPS may be used.
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ZABLOTSKYY, F., B. DZHUMAN, and I. BRUSAK. "On the accuracy of (quasi) geoid models relatively UELN/EVRS2000 height systems." Modern achievements of geodesic science and industry 41, no. I (April 1, 2021): 29–36. http://dx.doi.org/10.33841/1819-1339-1-41-29-36.
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Nowadays the Baltic Height System 1977 operates in Ukraine, the starting point of which is the zero of the Kronstadt banchmark. However, the current height system in Ukraine is morally obsolete primarily due to the great distance from the zero-point of height (about 2 thousand km) and the difficulty of adapting to the use of satellite surveying methods. Therefore, today it does not correspond to the level of development of modern geospatial technologies and it needs to be modernized. The most optimal way to modernize the height network of Ukraine is its integration into the United European Leveling Network UELN, the zero point of which is the Amsterdam banchmark. Within the framework of such integration it is necessary to create a high-precision geoid model for the territory of Ukraine, connected to the UELN/EVRS2000 height system. Aim. The purpose of the work is to compare the accuracy of different geoid/quasigeoid models and the global gravitational field of the Earth on the Western Ukraine area (border region) relative to the heights of points in the height system UELN/EVRS2000, where GNSSleveling is performed, and to determine the most optimal model in relation to which a high-precision geoid model can be created, consistent with the UELN/EVRS2000 height system.Method. To obtain the heights of leveling points on the Ukraine area in the UELN/EVRS2000 height system we performed I class leveling on two lines from the fundamental benchmarks on the territory of Ukraine (heights are known in the Baltic height system 1977) to I class benchmarks on the Poland area (UELN/EVRS2000 height system). GNSS-leveling in static mode (1-second sampling observations for more than 6 hours) was performed on all fundamental and ground benchmarks, as well as horizontal marks. Results. The heights of the quasigeoid at 26 points are obtained from the performed measurements. The heights are compared with three global models of the Earth’s gravitational field: EGM2008, EIGEN-6C4 and XGM2019e_2159 (the maximum order of all these models is 2190), as well as with the European geoid EGG2015. It is established that the best accuracy (≈ 7 cm) allows to obtain the European geoid EGG2015. Scientific novelty and practical significance. For the first time the accuracy of the Earth’s gravitational field models and geoid models on the Ukraine area is investigated at points where the height in the UELN/EVRS2000 height system is known. We established that when constructing a high-precision quasigeoid using the “Remove–Restore” procedure, it is best to use the European geoid EGG2015 as a systematic component.
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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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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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Gruber, T., C. Gerlach, and R. Haagmans. "Intercontinental height datum connection with GOCE and GPS-levelling data." Journal of Geodetic Science 2, no. 4 (December 1, 2012): 270–80. http://dx.doi.org/10.2478/v10156-012-0001-y.
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AbstractIn this study an attempt is made to establish height system datum connections based upon a gravity field and steady-state ocean circulation explorer (GOCE) gravity field model and a set of global positioning system (GPS) and levelling data. The procedure applied in principle is straightforward. First local geoid heights are obtained point wise from GPS and levelling data. Then the mean of these geoid heights is computed for regions nominally referring to the same height datum. Subsequently, these local mean geoid heights are compared with a mean global geoid from GOCE for the same region. This way one can identify an offset of the local to the global geoid per region. This procedure is applied to a number of regions distributed worldwide. Results show that the vertical datum offset estimates strongly depend on the nature of the omission error, i.e. the signal not represented in the GOCE model. For a smooth gravity field the commission error of GOCE, the quality of the GPS and levelling data and the averaging control the accuracy of the vertical datum offset estimates. In case the omission error does not cancel out in the mean value computation, because of a sub-optimal point distribution or a characteristic behaviour of the omitted part of the geoid signal, one needs to estimate a correction for the omission error from other sources. For areas with dense and high quality ground observations the EGM2008 global model is a good choice to estimate the omission error correction in theses cases. Relative intercontinental height datum offsets are estimated by applying this procedure between the United State of America (USA), Australia and Germany. These are compared to historical values provided in the literature and computed with the same procedure. The results obtained in this study agree on a level of 10 cm to the historical results. The changes mainly can be attributed to the new global geoid information from GOCE, rather than to the ellipsoidal heights or the levelled heights. These historical levelling data are still in use in many countries. This conclusion is supported by other results on the validation of the GOCE models.
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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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Rummel, R. "Height unification using GOCE." Journal of Geodetic Science 2, no. 4 (December 1, 2012): 355–62. http://dx.doi.org/10.2478/v10156-011-0047-2.
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AbstractWith the gravity field and steady-state ocean circulation explorer (GOCE) (preferably combined with the gravity field and climate experiment (GRACE)) a new generation of geoid models will become available for use in height determination. These models will be globally consistent, accurate (<3 cm) and with a spatial resolution up to degree and order 200, when expressed in terms of a spherical harmonic expansion. GOCE is a mission of the European Space Agency (ESA). It is the first satellite equipped with a gravitational gradiometer, in the case of GOCE it measures the gradient components Vxx , Vyy, Vzzand Vxz. The GOCE gravitational sensor system comprises also a geodetic global positioning system (GPS)-receiver, three star sensors and ion-thrusters for drag compensation in flight direction. GOCE was launched in March 2009 and will fly till the end of 2013. Several gravity models have been derived from its data, their maximum degree is typically between 240 and 250. In summer 2012 a first re-processing of all level-1b data took place. One of the science objectives of GOCE is the unification of height systems. The existing height offsets among the datum zones can be determined by least-squares adjustment. This requires several precise geodetic reference points available in each height datum zone, physical heights from spirit levelling (plus gravimetry), the GOCE geoid and, in addition, short wavelength geoid refinement from terrestrial gravity anomalies. GOCE allows for important simplifications of the functional and stochastic part of the adjustment model. The future trend will be the direct determination of physical heights (orthometric as well as normal) from precise global navigation satellite system (GNSS)-positioning in combination with a next generation combined satellite-terrestrial high-resolution geoid model.
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Yazid, N. M., A. H. M. Din, K. M. Omar, Z. A. M. Som, A. H. Omar, N. A. Z. Yahaya, and A. Tugi. "MARINE GEOID UNDULATION ASSESSMENT OVER SOUTH CHINA SEA USING GLOBAL GEOPOTENTIAL MODELS AND AIRBORNE GRAVITY DATA." ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences XLII-4/W1 (September 30, 2016): 253–63. http://dx.doi.org/10.5194/isprs-archives-xlii-4-w1-253-2016.
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Global geopotential models (GGMs) are vital in computing global geoid undulations heights. Based on the ellipsoidal height by Global Navigation Satellite System (GNSS) observations, the accurate orthometric height can be calculated by adding precise and accurate geoid undulations model information. However, GGMs also provide data from the satellite gravity missions such as GRACE, GOCE and CHAMP. Thus, this will assist to enhance the global geoid undulations data. A statistical assessment has been made between geoid undulations derived from 4 GGMs and the airborne gravity data provided by Department of Survey and Mapping Malaysia (DSMM). The goal of this study is the selection of the best possible GGM that best matches statistically with the geoid undulations of airborne gravity data under the Marine Geodetic Infrastructures in Malaysian Waters (MAGIC) Project over marine areas in Sabah. The correlation coefficients and the RMS value for the geoid undulations of GGM and airborne gravity data were computed. The correlation coefficients between EGM 2008 and airborne gravity data is 1 while RMS value is 0.1499.In this study, the RMS value of EGM 2008 is the lowest among the others. Regarding to the statistical analysis, it clearly represents that EGM 2008 is the best fit for marine geoid undulations throughout South China Sea.
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Sjöberg, L. E. "The geoid or quasigeoid – which reference surface should be preferred for a national height system?" Journal of Geodetic Science 3, no. 2 (September 1, 2013): 103–9. http://dx.doi.org/10.2478/jogs-2013-0013.
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Abstract Most European states use M. S. Molodensky’s concept of normal heights for their height systems with a quasigeoid model as the reference surface, while the rest of the world rely on orthometric heights with the geoid as the zero-level. Considering the advances in data caption and theory for geoid and quasigeoid determinations, the question is which system is the best choice for the future. It is reasonable to assume that the latter concept, in contrast to the former, will always suffer from some uncertainty in the topographic density distribution, while Molodensky’s approach to quasigeoid determination has a convergence problem. On the contrary, geoid and quasigeoid models computed by analytical continuation (e.g., rcr technique or KTH method) have no integration problem, and the quasigeoid can always be determined at least as accurate as the geoid. As the numerical instability of the analytical continuation is better controlled in the KTH method vs. the rcr method, we propose that any future height system be based on normal heights with a quasigeoid model computed similar to or directly based on the KTH method (Least squares modification of Stokes formula with additive corrections).
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Yu, Daocheng, Cheinway Hwang, Ole Baltazar Andersen, Emmy T. Y. Chang, and Lucile Gaultier. "Gravity recovery from SWOT altimetry using geoid height and geoid gradient." Remote Sensing of Environment 265 (November 2021): 112650. http://dx.doi.org/10.1016/j.rse.2021.112650.
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Petrovskaya, Margarita. "Simplified formulas for geoid height evaluation." Bulletin Géodésique 62, no. 2 (June 1988): 161–70. http://dx.doi.org/10.1007/bf02519223.
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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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Nguyen, Van Sang, and V. V. Popadyev. "Development of the mean sea dynamic topography on the Vietnam water area based on TOPEX/POSEIDON, ENVISAT and JASON-2 DATA." Geodesy and Cartography 925, no. 7 (August 20, 2017): 9–14. http://dx.doi.org/10.22389/0016-7126-2017-925-7-9-14.
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Mean Dynamic Topography (MDT) is the difference between mean sea surface height and geoid. Satellite altimetry data are known as sea surface height (ellipsoidal height), including geoid height, Mean Dynamic Topography and dynamic sea surface topography ht. To determine Mean Dynamic Topography from satellite altimetry data, the geoid height and dynamic sea surface topography should be removed from sea surface height. In this study, geoid height was computed from spherical harmonic coefficients of global Earth Gravity Model (EGM-2008). ht was determined using technique of tracks crossover adjustment. Finally, gridded model of Mean Dynamic Topography was established by using mean-squares prediction technique. By experimental processing and analysis, the gridded model of Mean Dynamic Topography had successfully built 5′ × 5′, named HUMG16MDT, for East Sea, using data of three altimetric satellites, namely TOPEX/POSEIDON, ENVISAT and JASON-2. For control purposes, this model was compared with the measurements on nine tidal stations, the computed estimation of standard deviation 15,5 cm.
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Morales Maqueda, M. A., N. T. Penna, S. D. P. Williams, P. R. Foden, I. Martin, and J. Pugh. "Water Surface Height Determination with a GPS Wave Glider: A Demonstration in Loch Ness, Scotland." Journal of Atmospheric and Oceanic Technology 33, no. 6 (June 2016): 1159–68. http://dx.doi.org/10.1175/jtech-d-15-0162.1.
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AbstractA geodetic GPS receiver has been installed on a Wave Glider, an unmanned water surface vehicle. Using kinematic precise point positioning (PPP) GPS, which operates globally without directly requiring reference stations, surface heights are measured with ~0.05-m precision. The GPS Wave Glider was tested in Loch Ness, Scotland, by measuring the gradient of the loch’s surface height. The experiment took place under mild weather, with virtually no wind setup along the loch and a wave field made mostly of ripples and wavelets. Under these conditions, the loch’s surface height gradient should be approximately equal to the geoid slope. The PPP surface height gradient and that of the Earth Gravitational Model 2008 geoid heights do indeed agree on average along the loch (0.03 m km−1). Also detected are 1) ~0.05-m-sized height changes due to daily water pumping for hydroelectricity generation and 2) high-frequency (0.25–0.5 Hz) oscillations caused by surface waves. The PPP heights compare favorably (~0.02-m standard deviation) with relative carrier phase–based GPS processing. This suggests that GPS Wave Gliders have the potential to autonomously determine centimeter-precise water surface heights globally for lake modeling, and also for applications such as ocean modeling and geoid/mean dynamic topography determination, at least for benign surface states such as those encountered during the reported experiment.
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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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Hoa, Ha Minh. "ESTIMATING THE GEOPOTENTIAL VALUE W0 OF THE LOCAL GEOID BASED ON DATA FROM LOCAL AND GLOBAL NORMAL HEIGHTS OF GPS/LEVELING POINTS IN VIETNAM." Geodesy and Cartography 39, no. 3 (September 26, 2013): 99–105. http://dx.doi.org/10.3846/20296991.2013.823705.
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Currently, the determination of geopotential value W0 of local geoid that best fits local mean sea level at the Zero Tide Gauge Station is getting important in building the National Geoid-Based Vertical System. Ha Minh Hoa (2007) and Kotsakis et al. (2012) recommended a method, which estimates the geopotential value W0 of local geoid at the Zero Tide Gauge Station based on equations of relation between the local and global normal heights or between the local and global height anomalies at GPS/leveling points regularly located on the whole territory. The objective of this paper is to determine conditions for estimating the geopotential value W0 of local geoid at the Zero Tide Gauge Station accomplished for whole territory of Vietnam.
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Fanos, Ali, Rusul Tahir, Suad Mohammed, and May Mahmood. "Calculating of adjusted geoid undulation based on EGM08 and mean sea level for different regions in Iraq." MATEC Web of Conferences 162 (2018): 03028. http://dx.doi.org/10.1051/matecconf/201816203028.
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In last decades Global Navigation Satellite System (GNSS) or as known Global Positioning System (GPS) technique is considered a revolutionary technique in the field of geodetic survey in comparison with traditional techniques (level, theodolite and total station). The height obtained from GNSS technique is ellipsoid height and to have a physical meaning in a surveying or engineering application it must be transformed to orthometric height. Therefore, a geoid model has to be used to do this transformation process. In Iraq there is no specific geoid that can be used in order to get proper orthometric height. This research aims to calculate adjusted geoid undulation based on Earth Gravitational Model 2008 (EGM08) through observation of Iraqi official vertical network using GNSS technique. Different regions in Iraq have been chosen to perform this research. The result of this research can assist a lot to enhance the accuracy of elevations obtained from GNSS and support the establishment of Iraq geoid.
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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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Dangol, Susheel, Prakash Joshi, Suraj KC, Mahesh Thapa, Mahesh Thapa, Bigyan Banjara, Shanker KC, and Stallin Bhandari. "Measurement of Height of Mt. Sagarmatha." Journal on Geoinformatics, Nepal 20, no. 1 (December 1, 2020): 59–66. http://dx.doi.org/10.3126/njg.v20i1.39479.
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The height measurement of the highest peak of the world “Sagarmatha” was conducted by Nepal for the first time. The methodology for the measurement was finalized from the workshop held in Kathmandu with the constructive comments from national and international experts. Trignometrical levelling, precise levelling, GNSS survey and gravity survey was conducted. Previous air borne gravity data and present surface gravity data was used to determine the precise regional geoid for this program. Thus orthometric height was determined as 8848.86 m from the ellipsoid height observed at the top of Sagarmatha and precise geoid determined. The height was determined on the base of International Height Reference System (IHRS) and final height was announced jointly from Nepal and China on 8th of December 2020 from Kathmandu and Beijing through virtual media.
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Nicacio, E., R. Dalazoana, and S. R. C. de Freitas. "Evaluation of recent combined global geopotential models in Brazil." Journal of Geodetic Science 8, no. 1 (July 1, 2018): 72–82. http://dx.doi.org/10.1515/jogs-2018-0008.
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Abstract The aim of this paper is to present a quantitative analysis of the adequacy of the main currently existing combined Global Geopotential Models (GGMs) for modeling normal-geoid heights throughout Brazil. As major advances have been reached since mid-2016 in the combined GGMs elaboration and development, the main objective of this analysis is to verify if, in fact, the most recent models present superior or equivalent performance to the most performant previous models. The analysis was based on comparisons between normal-geoid height values obtained fromGNSS/leveling solutions and values calculated from GGMs XGM2016, GOCO05C, EIGEN-6C4 and EGM2008, according to different geopotential functionals - geoid height and height anomaly - and in different degrees of development, always through the relative method. This procedure was applied to 997 stations which carry information of both ellipsoidal and normal-orthometric heights, located all over Brazil. As a main result, it was observed the superior performance of the recent combined GGMs, GOCO05C and XGM2016, when compared to the older models, EIGEN-6C4 and EGM2008, when all of them are developed up to degree 720, the maximum degree of the recent models; and a approximate equality of results when all of the models are used in their individual maximum degrees.
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Rangelova, E., W. Van Der Wal, and M. G. Sideris. "How Significant is the Dynamic Component of the North American Vertical Datum?" Journal of Geodetic Science 2, no. 4 (December 1, 2012): 281–89. http://dx.doi.org/10.2478/v10156-012-0005-7.
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AbstractOne of the main current geodetic activities in North America is the definition and establishment of a geoid-based vertical datum that will replace the official CGVD28 and NAVD88 datums in Canada and the USA, respectively. The new datum will also have a time-dependent (dynamic) component required by the targeted one-centimetre accuracy of the datum. Heights of the levelling benchmarks are subject to temporal changes, which contribute to the degradation of the accuracy of the datum and increase the misfit of the geoid heights determined gravimetrically and by GNSS/levelling. The zero level surface, i.e., the geoid, also changes with time, most significantly due to postglacial rebound, climate-induced loss of polar ice masses and mountain glaciers, and hydrology variations. In this study, we examine the possible changes of the datum due to the aforementioned factors. We are mostly concerned with postglacial rebound as it can contribute more than 1 mm per year and more than 1 cm per decade to the geoid change. We also assess the significance of the temporal geoid and benchmark height changes and show that, compared to its current accuracy, the geoid change is only significant after a decade mostly in the flat areas of central Canada.
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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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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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Li, Xiong, and Hans‐Jürgen Götze. "Ellipsoid, geoid, gravity, geodesy, and geophysics." GEOPHYSICS 66, no. 6 (November 2001): 1660–68. http://dx.doi.org/10.1190/1.1487109.
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Geophysics uses gravity to learn about the density variations of the Earth’s interior, whereas classical geodesy uses gravity to define the geoid. This difference in purpose has led to some confusion among geophysicists, and this tutorial attempts to clarify two points of the confusion. First, it is well known now that gravity anomalies after the “free‐air” correction are still located at their original positions. However, the “free‐air” reduction was thought historically to relocate gravity from its observation position to the geoid (mean sea level). Such an understanding is a geodetic fiction, invalid and unacceptable in geophysics. Second, in gravity corrections and gravity anomalies, the elevation has been used routinely. The main reason is that, before the emergence and widespread use of the Global Positioning System (GPS), height above the geoid was the only height measurement we could make accurately (i.e., by leveling). The GPS delivers a measurement of height above the ellipsoid. In principle, in the geophysical use of gravity, the ellipsoid height rather than the elevation should be used throughout because a combination of the latitude correction estimated by the International Gravity Formula and the height correction is designed to remove the gravity effects due to an ellipsoid of revolution. In practice, for minerals and petroleum exploration, use of the elevation rather than the ellipsoid height hardly introduces significant errors across the region of investigation because the geoid is very smooth. Furthermore, the gravity effects due to an ellipsoid actually can be calculated by a closed‐form expression. However, its approximation, by the International Gravity Formula and the height correction including the second‐order terms, is typically accurate enough worldwide.
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Hejrati, S., and M. Najafi-Alamdari. "ON THE COMPUTATION OF A PRECISE GEOID – TO – QUASIGEOID SEPARATION." ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences XLII-4/W4 (September 27, 2017): 489–96. http://dx.doi.org/10.5194/isprs-archives-xlii-4-w4-489-2017.
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In geodesy, orthometric and normal heights are considered as basic height systems on the earth. The reference surfaces for these heights are the geoid and quasigeoid respectively. Taking advantage of GNSS measurements, one can achieve a precise solution for the geoid and for the quasigeoid. Two methods, called direct and indirect, are worked out in this research for the computation of separation between geoid and quasigeoid in a mountainous region in the USA. The area selected for this purpose is mountainous and rough enough in order to be able to show the effect of roughness of topography in the sought quantity. The results of the two methods and testing them against GNSS-Levelling on 445 known points indicates an accuracy of 1.3 cm in RMS scale with the direct method, where there is 7 cm as an average difference between the observed geoid and quasigeoid separation and the same quantity derived from the direct method. Using Chi-squared goodness of fit test showed that the distribution of the residual quantities are normally distributed in the test area.
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Gerlach, Ch, and Th Fecher. "Approximations of the GOCE error variance-covariance matrix for least-squares estimation of height datum offsets." Journal of Geodetic Science 2, no. 4 (December 1, 2012): 247–56. http://dx.doi.org/10.2478/v10156-011-0049-0.
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AbstractOne main geodetic objective of the European Space Agency’s satellite mission GOCE (gravity field and steady-state ocean circulation explorer) is the contribution to global height system unification. This can be achieved by applying the Geodetic Boundary Value Problem (GBVP) approach. Thereby one estimates the unknown datum offsets between different height networks (datum zones) by comparing the physical (e.g. orthometric) height values H of benchmarks in different datum zones to the corresponding values derived from the difference between ellipsoidal heights h (e.g. determined by means of global navigation satellite systems) and geoid heights N. In the ideal case, i.e. neglecting data errors, the misfit between H and (h − N) is constant inside one datum zone and represents the datum offset. In practise, the accuracy of the offset estimation depends on the accuracy of the three quantitiesH, h andN, where the latter can be computed from the combination of a GOCE-derived Global Potential Model (GPM) for the long to medium wavelength and terrestrial data for the short wavelength content. Providing an optimum estimation of the datum offsets along with realistic error estimates, theoretically, requires propagation of the full error variance and covariance information of the GOCE spherical harmonic coefficients to geoid heights, respectively geoid height differences. From a numerical point of view, this is a very demanding task which cannot simply be run on a single PC. Therefore it is worthwhile to investigate on different levels of approximation of the full variance-covariance matrix (VCM) with the aim of minimizing the numerical effort. In this paper, we compare the estimation error based on three levels of approximation, namely (1) using the full VCM, (2) using only elements of the dominant m-block structure of the VCM and (3) using only the main diagonal of the VCM, i.e. neglecting all error covariances between the spherical harmonic coefficients. We show that the m-block approximation gives almost the same result as provided by the full VCM. The diagonal approximation however over- or underestimates the geoid height error, depending on the geographic location and therefore is not regarded to be a suitable approximation.
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GARBANZO-LEÓN, Jaime, Alonso VEGA FERNÁNDEZ, Mauricio VARELA SÁNCHEZ, Juan Picado SALVATIERRA, Robert W. KINGDON, and Oscar H. LÜCKE. "A regional Stokes-Helmert geoid determination for Costa Rica (GCR-RSH-2020): computation and evaluation." Contributions to Geophysics and Geodesy 50, no. 2 (July 29, 2020): 223–47. http://dx.doi.org/10.31577/congeo.2020.50.2.3.
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GNSS observations are a common solution for outdoor positioning around the world for coarse and precise applications. However, GNSS produces geodetic heights, which are not physically meaningful, limiting their functionality in many engineering applications. In Costa Rica, there is no regional model of the geoid, so geodetic heights (h) cannot be converted to physically meaningful orthometric heights (H). This paper describes the computation of a geoid model using the Stokes-Helmert approach developed by the University of New Brunswick. We combined available land, marine and satellite gravity data to accurately represent Earth's high frequency gravity field over Costa Rica. We chose the GOCO05s satellite-only global geopotential model as a reference field for our computation. With this combination of input data, we computed the 2020 Regional Stokes-Helmert Costa Rican Geoid (GCR-RSH-2020). To validate this model, we compared it with 4 global combined geopotential models (GCGM): EGM2008, Eigen6C-4, GECO and SGG-UM-1 finding an average difference of 5 cm. GECO and SGG-UM-1 are more similar to the GCR-RSH-2020 based on the statistics of the difference between models and the shape of the histogram of differences. The computed geoid also showed a shift of 7 cm when compared to the old Costa Rican height system but presented a slightly better fit with that system than the other models when looking at the residuals. In conclusion, GCR-RSH-2020 presents a consistent behaviour with the global models and the Costa Rican height systems. Also, the lowest variance suggests a more accurate determination when the bias is removed.
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Nahavandchi, H., and A. Soltanpour. "Improved determination of heights using a conversion surface by combining gravimetric quasi-geoid/geoid and GPS-levelling height differences." Studia Geophysica et Geodaetica 50, no. 2 (April 2006): 165–80. http://dx.doi.org/10.1007/s11200-006-0010-3.
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Barzaghi, Riccardo, Carlo Iapige De Gaetani, and Barbara Betti. "The worldwide physical height datum project." Rendiconti Lincei. Scienze Fisiche e Naturali 31, S1 (August 27, 2020): 27–34. http://dx.doi.org/10.1007/s12210-020-00948-0.
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Abstract The definition of a common global vertical coordinate system is nowadays one of the key points in Geodesy. With the advent of GNSS, a coherent global height has been made available to users. The ellipsoidal height can be obtained with respect to a given geocentric ellipsoid in a fast and precise way using GNSS techniques. On the other hand, the traditional orthometric height is not coherent at global scale. Spirit levelling allows the estimation of height increments so that orthometric heights of surveyed points can be obtained starting from a benchmark of known orthometric heights. As it is well known, this vertical coordinate refers to the geoid, which is assumed to be coincident to the mean sea level. By means of a tide gauge, the mean sea level is estimated and thus a point of known orthometric height is defined. This assumption, which was acceptable in the past, became obsolete given the level of precision which is now required. Based on the altimetry observation, one can precisely quantify the existing discrepancy between geoid and mean sea level that can amount to 1 ÷ 2 m at global scale. Therefore, different tide gauges provide biased estimates of the geoid, given the discrepancy between this equipotential surface and the mean sea level. Also, in the last years, another vertical coordinate was used, the normal height that was introduced in the context of the Molodensky theory. In this paper, a review of the existing different height systems is given and the relationships among them are revised. Furthermore, an approach for unifying normal height referring to different tide gauges is presented and applied to the Italian test case. Finally, a method for defining a physical height system that is globally coherent is discussed in the context of the definition of the International Height Reference System/Frame, a project supported by the Global Geodetic Observing System of the International Association of Geodesy (IAG). This project was established in 2015 during the XXVI IAG General Assembly in Prague as described in IAG Resolution no. 1 that was presented and adopted there.
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Zlinszky, A., G. Timár, R. Weber, B. Székely, C. Briese, C. Ressl, and N. Pfeifer. "Observation of a local gravity isosurface by airborne LIDAR of Lake Balaton, Hungary." Solid Earth Discussions 6, no. 1 (January 14, 2014): 119–44. http://dx.doi.org/10.5194/sed-6-119-2014.
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Abstract. Airborne LIDAR (Light Detection and Ranging) is a remote sensing method commonly used for mapping surface topography in high resolution. A water surface in hydrostatic equilibrium theoretically represents a gravity isosurface. Here we compare LIDAR-based ellipsoidal water surface height measurements all around the shore of a major lake with a local high resolution geoid model. The ellipsoidal heights of the 87 km2 we sampled all around the shore of the 597 km2 lake surface vary by 0.8 m and strong spatial correlation with the geoid undulation was calculated (R2=0.91). After subtraction of the local geoid undulation from the measured ellipsoidal water surface heights, their variation was considerably reduced. This demonstrates that the water surface heights of the lake were truly determined by the local gravity potential. We conclude that the accuracy of airborne LIDAR is sufficient for identifying the spatial variations of gravity potential over large inland water surfaces.
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Woodworth, P. L., and C. W. Hughes. "Towards worldwide height unification using ocean information." Proceedings of the International Association of Hydrological Sciences 365 (March 2, 2015): 11–15. http://dx.doi.org/10.5194/piahs-365-11-2015.
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Abstract. This paper describes how we are contributing to worldwide height system unification (WHSU) by using ocean models together with sea level (tide gauge and altimeter) information, geodetic (GPS and levelling) data, and new geoid models based on information from the GRACE and GOCE gravity missions, to understand how mean sea level (MSL) varies from place to place along the coast. For the last two centuries, MSL has been used to define datums for national levelling systems. However, there are many problems with this. One consequence of WHSU will be the substitution of conventional datums as a reference for heights with the use of geoid, as the only true "level" or datum. This work is within a number of GOCE-related activities funded by the European Space Agency. The study is focused on the coastlines of North America and Europe where the various datasets are most copious.
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Muhammad, Sher, and Lide Tian. "Assessment of ArcGIS based extraction of geoidal undulation compared to National Geospatial Intelligence Agency (NGA) model – A case study." Journal of Applied Geodesy 14, no. 1 (January 28, 2020): 77–81. http://dx.doi.org/10.1515/jag-2019-0030.
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AbstractGlobal Navigation Satellite System (GNSS) and remote sensing Digital Elevation Models (DEMs) represent earth’s surface elevation with reference to ellipsoid and orthometric heights. Proper estimation of the geoid (difference of ellipsoid and orthometric heights) is necessary before comparing data referenced to the different vertical datum. In this paper, an error in estimating EGM96 orthometric height is highlighted, verified by NGA/NASA developed model and MATLAB®. A significant error was found in the ArcGIS derived EGM96 orthometric heights range between ±6.9 meters. In addition, interpolation of low-resolution geoid data also produces significant biases depending on geographic location and the number of the interpolation data point. The bias was maximum negative in the central part of Tibetan Plateau and Himalaya. Therefore, estimation of orthometric height similar to NGA/NASA model precision is necessary for comparison of DEMs for natural resources management, 3D modelling and glaciers mass balance mainly in the mountainous regions.
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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
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Zlinszky, A., G. Timár, R. Weber, B. Székely, C. Briese, C. Ressl, and N. Pfeifer. "Observation of a local gravity potential isosurface by airborne lidar of Lake Balaton, Hungary." Solid Earth 5, no. 1 (May 22, 2014): 355–69. http://dx.doi.org/10.5194/se-5-355-2014.
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Abstract. Airborne lidar is a remote sensing method commonly used for mapping surface topography in high resolution. A water surface in hydrostatic equilibrium theoretically represents a gravity potential isosurface. Here we compare lidar-based ellipsoidal water surface height measurements all around the shore of a major lake with a local high-resolution quasi-geoid model. The ellipsoidal heights of the 87 km2 we sampled all around the shore of the 597 km2 lake surface vary by 0.8 m and strong spatial correlation with the quasi-geoid undulation was calculated (R2 = 0.91). After subtraction of the local geoid undulation from the measured ellipsoidal water surface heights, their variation was considerably reduced. Based on a network of water gauge measurements, dynamic water surface heights were also successfully corrected for. This demonstrates that the water surface heights of the lake were truly determined by the local gravity potential. We conclude that both the level of hydrostatic equilibrium of the lake and the accuracy of airborne lidar were sufficient for identifying the spatial variations of gravity potential.
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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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Dare, Oluyori P., and Eteje S. Okiemute. "Impact of different centroid means on the accuracy of orthometric height modelling by geometric geoid method." International Journal of Scientific Reports 6, no. 4 (March 24, 2020): 124. http://dx.doi.org/10.18203/issn.2454-2156.intjscirep20201267.
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<p class="abstract"><strong>Background:</strong> Orthometric height, as well as geoid modelling using the geometric method, requires centroid computation. And this can be obtained using various models, as well as methods. These methods of centroid mean computation have impacts on the accuracy of the geoid model since the basis of the development of the theory of each centroid mean type is different. This paper presents the impact of different centroid means on the accuracy of orthometric height modelling by geometric geoid method.</p><p class="abstract"><strong>Methods:</strong> DGPS observation was carried out to obtain the coordinates and ellipsoidal heights of selected points. The centroid means were computed with the coordinates using three different centroid means models (arithmetic mean, root mean square and harmonic mean). The computed centroid means were entered accordingly into a Microsoft Excel program developed using the Multiquadratic surface to obtain the model orthometric heights at various centroid means. The root means square error (RMSE) index was applied to obtain the accuracy of the model using the known and the model orthometric heights obtained at various centroid means. </p><p class="abstract"><strong>Results:</strong> The computed accuracy shows that the arithmetic mean method is the best among the three centroid means types.</p><p class="abstract"><strong>Conclusions:</strong> It is concluded that the arithmetic mean method should be adopted for centroid computation, as well as orthometric height modelling using the geometric method.</p>
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Luong, Bao-Binh. "Computing height anomalies using spherical harmonic coefficients at certain degrees and orders in long-wavelength components." Science and Technology Development Journal 19, no. 2 (June 30, 2016): 11–18. http://dx.doi.org/10.32508/stdj.v19i2.662.
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Height anomaly / geoid undulation) is a basic quantity in geodesy. It can be directly measured from GPS and leveling or computed from gravitational models. This paper introduces program GeoH to compute height anomalies using spherical harmonic coefficients at certain degrees and orders in longwavelength components. By reasonably comparing with official values of EGM96, the reliability of results from GeoH is proved for the long-wavelength components, and then can be applied in the “remove-restore” technique for determining Vietnamese quasi-geoid in near future.
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Hayden, T., B. Amjadiparvar, E. Rangelova, and M. G. Sideris. "Estimating Canadian vertical datum offsets using GNSS/levelling benchmark information and GOCE global geopotential models." Journal of Geodetic Science 2, no. 4 (December 1, 2012): 257–69. http://dx.doi.org/10.2478/v10156-012-0008-4.
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AbstractThe performance of GOCE-based geopotential models is assessed for the estimation of offsets for three regional vertical datums in Canada with respect to a global equipotential surface using the GNSS benchmarks from the first-order vertical control network. Factors that affect the computed value of the local vertical datum offset include the GOCE commission and omission errors, measurement errors, the configuration of the network of GNSS/levelling benchmarks, and systematic levelling errors and distortions propagated through the vertical control network. Among these various factors, the effect of the GOCE omission error on the datum offsets is investigated by extending the models with the high resolution gravity field model EGM2008 and by means of Canada’s official high resolution geoid model CGG2010. The effect of the GOCE commission error in combination with errors from the GNSS/levelling data is also examined, in addition to the effect of systematic levelling errors. In Canada, the effect of the GOCE omission error is at the dm-level when computing local vertical datum offsets. The effect of including accuracy information for the GNSS/levelling data and the GOCE geoid heights can be up to 4 cm over the Canadian mainland and at the dm-level for island regions. Lastly, the spatial tilts found in the levelling network can be modelled with a 2-parameter bias corrector model, which reduces the RMS of the adjusted geoid height differences by 4 cm when compared to the RMS of adjusted geoid height differences computed without the use of a bias corrector model. Thus, when computing local vertical datum offsets in Canada, it is imperative to account for GOCE commission and omission errors, ellipsoidal and levelling height errors, as well as the systematic levelling errors of the vertical control network.
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Woodworth, P. L., C. W. Hughes, R. J. Bingham, and T. Gruber. "Towards worldwide height system unification using ocean information." Journal of Geodetic Science 2, no. 4 (December 1, 2012): 302–18. http://dx.doi.org/10.2478/v10156-012-0004-8.
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AbstractWe describe the application of ocean levelling to worldwide height system unification. The study involves a comparison of ‘geodetic’ and ‘ocean’ approaches to determination of the mean dynamic topography (MDT) at the coast, from which confidence in the accuracy of stateof- the-art ocean and geoid models can be obtained. We conclude that models are consistent at the sub-decimetre level for the regions that we have studied (North Atlantic coastlines and islands, North American Pacific coast and Mediterranean). That level of consistency provides an estimate of the accuracy of using the ocean models to provide an MDT correction to the national datums of countries with coastlines, and thereby of achieving unification. It also provides a validation of geoid model accuracy for application to height system unification in general. We show how our methods can be applied worldwide, as long as the necessary data sets are available, and explain why such an extension of the present study is necessary if worldwide height system unification is to be realised.
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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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Lee, Suk Bae, Keun Sang Lee, and Min Kun Lee. "Analysis of the Feasibility of GNSS/Geoid Technology in Determining Orthometric Height in Mountain." Journal of Korean Society for Geospatial Information System 25, no. 2 (June 30, 2017): 57–65. http://dx.doi.org/10.7319/kogsis.2017.25.2.057.
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Sandwell, David T., and Kevin R. MacKenzie. "Geoid height versus topography for oceanic plateaus and swells." Journal of Geophysical Research 94, B6 (1989): 7403. http://dx.doi.org/10.1029/jb094ib06p07403.
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Shibuya, K., Y. Fukuda, and Y. Michida. "Determination of geoid height at Breid Bay, east Antarctica." Journal of Geophysical Research 96, B11 (1991): 18285. http://dx.doi.org/10.1029/91jb01810.
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