Normal-orthometric Heights Research Articles

Towards a new height datum for Uganda

A new height datum for Uganda is computed using the corrective surface principle. It is based on a combination of the Uganda Gravimetric Quasigeoid model (UGQ) 2014 and GNSS/levelling. UGQ2014 was derived from the Uganda Gravimetric Geoid model (UGG) 2014, which was computed from sparse terrestrial gravity data from the International Gravimetric Bureau, the 3 arc second Shuttle Radar Topography Mission digital elevation model and the GOCE – only global geopotential model GO_CONS_GCF_2_TIM_R5. The corrective surface was constructed based on 21 discrete GNSS/levelling points and then evaluated with 4 independent points. Three interpolation techniques were tested for the creation of the corrective surface with the Kriging method giving the lowest standard deviation and noise level suggesting that it is the best method for interpolation. In absolute terms, the Root Mean Square of the fit between the known and computed normal-orthometric heights based on the new height datum is 11cm, which is about 5cm (31%) better than using UGQ2014 alone. For relative heights an average precision of 29 ppm is computed for all baselines tested. Both the absolute and relative tests show that the new height datum satisfies the precision and accuracy requirements of third order precise levelling. Therefore, UGQ2014C represents a significant step towards the determination of a precise new height datum for Uganda.

A hybridized geoid model for Ashanti Region, Ghana

GNSS positioning techniques deliver accurate three dimensional coordinates in Easting, Northing and geometric heights. However, the use of the geometric heights for topographic mapping is limited due to the unavailability of accurate National geoid models for their conversion into used Normal-Orthometric height systems in Ghana. Though global gravimetric geoids such as EGM2008 are readily available, these are not suitable for direct conversion of geometric heights from GNSS into the useful normalorthometric height system used because local geoids are offset in an unpredictable way from such global geoids. In this investigation, a new hybrid geoid model for the Ashanti Region is developed and tested. The developed model incorporates the contribution of global geopotential models (GGMs) provided by EGM2008 together with GPS/Levelling using a remove and restore-like approach to develop a surface corrector model that separates the deterministic trend from the stochastic errors which then is separately modelled using the Gauss-Markov method. The main idea is thence to model the anomalies after comparing the gravimetric and quasi-geoid models from several collocated points. A Four-parameter Helmert transformation model have been applied to reduce data biases and provide a fitting quasi geoid heights obtained from the GGMs to those from GPS/levelling data. Whereas the gravimetric geoid alone has revealed that the vertical datum offset from the National height datum over Ashanti Region was at the level of 8cm up to 1.0m with a mean offset of 44cm. The Hybrid geoid model (ASHGeoid21) computed through the Remove-Compute-Restore (RCR) procedure resulted in geoid heights that are offset from Local geoid values at nineteen additional checkpoints for up to ± 50cm. with a standard deviation of ±10cm. It is recommended that, the hybrid residual height anomalies of a maximum of 50cm, could be further improved with the inclusion of more GPS/levelling points.

Strategy for Connecting to the IHRF: Case Study for the Tide Gauge of Cananeia-SP

In July 2018, IBGE launched the new heights of the Brazilian Geodetic System (BGS), the normal height, which has associated gravity. These new heights are replacing the old normal-orthometric ones, in which there was only the non-parallelism correction. The IBGE informs that the values farther from the origin, have less accuracy. This lower accuracy may interfere in the future, the connection of the local tide gauges to IHRF (International Reference Frame Height). Thus, this paper proposes the integration of the local tide gauge of Cananeia-SP to the IHRF. In order to validate the methodology, the normal, Helmert, and rigorous orthometric heights using two distinct references: the Imbituba-SC tide gauge, as the origin of the BGS and the Cananeia-SP tide gauge, as a local tide gauge to be integrated into the IHRF. Calculating the three heights through these two origins, we analyzed the discrepancies in comparison to the heights calculated by IBGE. Numerical tests indicate that there was an improvement in terms of a mean and standard deviation when using the Cananeia gauge as origin in the calculation of normal, Helmert, and rigorous heights. In the congruence analysis, the calculations indicate that the highest standard deviation is presented when using IBGE normal heights. Thus, we have a new origin that is reliable and functional, can be integrated with the IHRF, where the Helmert and rigorous orthometric heights have the best statistical results.

Global gravity models and the Ghanaian Vertical Datum: challenges of a proper definition

This paper analyzes errors in satellite gravity and GPS/trigonometric benchmarks (BMs) in relation to defining the Ghanaian Vertical Datum (GhVD). Results indicate that synthesized gravity introduce approximately 5 mm of error to corrected heights. However, large errors in BMs render them unsuitable for applications, including properly defining the GhVD. Overall, normal-orthometric corrections were of the order of a few millimetres, with comparatively larger Helmert orthometric and normal corrections. Accordingly, the most suitable heights for the GhVD are the normal-orthometric heights, with the geopotential of the Helmert orthometric heights, m s, suggested as the potential of the GhVD.

Alternativa para determinação de altitudes normais-ortométricas na Amazônia Legal Brasileira

El presente trabajo tiene por objetivo desarrollar una metodología alternativa para predicciones de altitudes normales-ortométricas a lo largo de la Amazonia Legal Brasileña, región que impone dificultades logísticas-operacionales para trabajos de campo y en la que hay considerable precariedad en la Red Altimétrica Fundamental Brasileña (RAFB), evidenciando necesidades de mejora de las redes en cuestión para una completa alineación a las actuales recomendaciones y esfuerzos para la consecución de una Red Internacional de Referencia Altimétrica. Una estrategia alternativa se basa en observaciones GNSS y en la utilización de modelos globales y geopotenciales (MGGs); alternativamente se utiliza el modelo geoidal nacional MAPGEO2015. Para ello, se utiliza un enfoque de comparación de tres variantes distintas: a) utilización de métodos absolutos o relativos para determinación altimétrica, b) utilización de extractos de los MGGs obtenidos en diferentes grados de desarrollo y del MAPGEO2015, y c) utilización de las funcionalidades altitud geoidal y anomalía de altitud para modelado de altitud normal-geoidal. Datos referentes a observaciones GNSS son extraídos de las estaciones de la rede SAT-GPS en coincidencia con estaciones RAFB, dotadas de información de altitudes elipsoidal y normal-ortométricas; los extractos de los MGG se obtienen punto a punto para los principales MGG combinados de la actualidad. En vistas de la baja precisión media de datos en el área de estudio y su baja vinculación con la RAFB, se adopta un área de prueba—el estado de Paraná— que se comporta mejor para la elaboración y consolidación de estrategias para aplicar posteriormente en el área de estudio. De los estudios realizados en el área de estudio, se verifica una incuestionable ventaja de utilización del método relativo sobre el absoluto aliado a los MGG, siendo en promedio un 72% mejores para extractos desarrollados hasta grados 2190 y 720; o MAPGEO2015 como una excepción a los resultados, no habiendo

A NEW PERSPECTIVE FOR PHYSICAL HEIGHTS IN BRAZIL

Abstract The physical heights definition of heights, proposed by Helmert in 1890 is one of the commonly used heights systems in practice. In Helmert’s definition, the mean value of gravity along plumbline is computed by simplifying the topography with a Bouguer shell containing masses with mean density value. Although this approximation might be accurate enough many purposes, a more rigorous definition can be determined by considering the effects of terrain, topographic mass density variation, and masses contained in the geoid the mean gravity value along the plumbline. The purpose of this paper is to compute the corrections for the Helmert’s definition of the orthometric heights to obtain the rigorous orthometric heights in the state of São Paulo and adjacent states and to evaluate these corrections. The heights system used in Brazil (until July 2018) and some South American countries is normal-orthometric heights, therefore the corrections needs to be applied accordingly. Our numerical results show that there are significant differences between the normal-orthometric and rigorous orthometric heights, with maximum values of ~ 0.4 m, minimum of ~ -0.8 m and mean value of ~ -0.32 m. There are larger differences between normal-orthometric and normal height than the ones between normal and rigorous definition of orthometric heights.

Separação Entre Geoide e Quase-Geoide: Análise das Diferenças Entre as Altitudes Normal-Ortométrica e Ortométrica Rigorosa

The orthometric and normal heights are the two altitude systems most used in the practical realization of the local and national vertical geodesic data. The main difference between these two concepts is that the actual mean gravity along the plumb line between the geoid and the topographic surface theoretically defines the orthometric heights, as well as the normal mean gravity along the plumb line between the reference ellipsoid and teluroid is used in the definition of normal heights. In the Brazilian geodetic system, only a correction of non-parallelism is applied, resulting in the normal-orthometric heights. The objective of this work is to calculate the separation between geoid and quasi-geoid obtained through the systems of normal-orthometric and rigorous orthometric heights. By means of numerical tests, it was observed that the separation is greater when using the brazilian system with values between -0.5 and 0.5 meters. On the other hand, by using the new rigorous heights, the average gravity along the long plumb line is evaluated, taking into account the variations of topographic densities and masses above the geoid, the values are smaller, being in the range of -0.05 to 0.2 meters. It can be said that the rigorous orthometric heights system is more accurate, since it has the smallest difference between the geoid/quasi-geoid separation.

A NEW ESTIMATE FOR BRAZILIAN VERTICAL DATA OFFSET BASED ON GLOBAL GEOPOTENTIAL MODELS AND HEIGHT DETERMINATIONS THROUGH RELATIVE APPROACH

Abstract This paper aims to present a new estimate for the vertical offset between both Brazilian vertical data: DVB-I, in Imbituba-SC, and DVB-S, in Santana-AP. Brazilian Fundamental Altimetric Network (BFAN) currently has over 69000 stations with known normal-orthometric heights; 472 of these stations are connected to a tide gauge located in Santana-AP, at the North portion of Brazil, and the other ones are connected to a tide gauge located in Imbituba-SC, at the South portion of Brazil and considered Brazilian's main vertical reference. The vertical offset estimate is based on comparisons between reference and calculated normal-orthometric heights from values obtained arising of discrete GNSS observations on BFAN benchmarks, normal-geoid heights calculated from GGM XGM2016, which has proven to better model this variable in the region, and through a relative approach for heights determination, which has also proven to be the best way to handling the appropriate variables. As a result, a vertical offset of 1.32 m ± 0.07 m was obtained, which is coherent to previous studies performed in the same intent. This study up-comes as a new validation of the employed methodology itself, by achieving satisfactory results through independent manipulation even with low quality of input data for the region.

Evaluation of recent combined global geopotential models in Brazil

AbstractThe 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.

Description and release of Australian gravity field model testing data

ABSTRACTGravimetric geoid and/or quasigeoid models are routinely evaluated using co-located GPS-levelling and/or astrogeodetic vertical deflections, globally and regionally. This short note describes these ground-truth data for Australia as of August 2017, which are provided as Electronic Supplementary Material. We provide ∼7500 GPS-derived ellipsoidal heights, normal-orthometric heights from the 1971 adjustment of the Australian Height Datum, normal heights from a readjustment of levelling constrained to a model of the ocean's mean dynamic topography, and ∼1000 historical astrogeodetic vertical deflections. Updates to these data will be posted on the Intergovernmental Committee on Surveying and Mapping GitHub repository (https://github.com/icsm-au), together with a readme.txt file describing them.

Evaluation of the various orthometric height systems and the Nigerian scenario – A case study of Lagos State

Though considered the easiest in 3-Dimensional Point Positioning, the choice of a height system especially in areas with spatially-vast land mass is rather a complicated choice. Orthometric heights are naturally and fully referenced to the actual earth gravity field but laborious to compute considering the required approximations of gravity variation along the plumb-line from the surface to the geoid. Normal heights on the other hand are less laborious to compute and do not require actual gravity observations. Unfortunately, natural height systems are the only systems that can efficiently predict fluid flows. This paper has therefore examined the theory and practical possibility of replacing the use of Helmert Orthometric Heights with Normal Orthometric heights within Lagos State. A maximum height discrepancy of 1mm was obtained in the comparison of both systems and thus their replaceability found suitable to within 3rd order geodetic accuracy.

우리나라 수준노선에서 실측중력에 의한 정사보정량 계산

우리나라의 수준점은 성과계산에 있어서 실측중력에 의한 정사보정량 계산을 실시하지 않고 정규중력을 이용한 정사보정량 계산을 함으로써 정확한 정표고가 아닌 정규정표고를 사용하여 왔다. 본 연구에서는 우리나라 1,2등 수준노선을 대상으로 직접 중력을 관측하고 정사보정량을 계산하였으며, 그 결과에 따라 우리나라 수준점 체계개선방안을 제시하고자 하였다. 연구를 위하여 강원도 지역의 속초~강를구간의 1등수준 노선과 속사~인제구간의 2등 수준노선을 대상으로 CG5 디지털중력계를 이용하여 직접 중력관측을 실시하고 상대중력성과를 계산하였으며, 중력성과에 기초하여 정사보정량을 계산한 결과 1등 수준노선에서 최대 -0.349mm, 최대 -44.060mm의 값을 보였다. 따라서 우리나라에서 보다 정확한 수준점 체계로 개선하기 위해서는 실측중력에 의한 정사보정량의 계산과 정사보정량을 고려한 정표고 산정이 필요한 것으로 확인되었다. It has been used not orthometric height but normal orthometric height for the official height in Korean benchmark because it has been used not observed gravity but normal gravity for the computation of orthometric correction. The purpose of this study is to propose height renewal method of Korean benchmark. For this purpose, we observed gravity by CG5 digital gravimeter in both the first benchmark line between Sokcho and Gangneung area and the second benchmark line between Soksa and Inje area. We calculated relative gravity value and orthometric correction in all benchmarks. So, the maximum orthometric correction shows -0.349mm in the first benchmark line, and the maximum orthometric correction shows -44.060mm in the second benchmark line. In conclusion, we can confirm that the orthometric correction based on observed gravity is necessary for more accurate official height computation in the Korean benchmark.

Error propagation for three common height-system corrections to differential levelling

This paper investigates the propagation of input data errors through the application of Helmert orthometric, normal and normal-orthometric height corrections to differential levelling observations, these being the three principal height systems in practical use around the world. Height corrections are required to remove the systematic error resulting from the geometric non-parallelism of the Earth's equipotential surfaces, but different height systems propagate errors differently. These systematic errors are thus present within levelling networks and subsequently in local vertical datums. Here, we show that the Helmert orthometric correction is sensitive to errors in the mean value of gravity along the plumbline, particularly for heights above 1000 m. The normal correction is much less sensitive due to the use of normal gravity along the normal plumbline. The normal-orthometric correction of Rapp (1961) is largely insensitive to such errors, but it does not properly correct for the non-parallelism of the Earth's equipotential surfaces. Information showing the circumstances under which survey practitioners should apply height corrections to levelling lines is provided, demonstrating that normal-orthometric corrections only need be applied to class LC levelling lines that are to be used for large levelling networks extending in the north-south direction, particularly at high elevations.

Combined approach for the unification of levelling networks in New Zealand

Combined approach for the unification of levelling networks in New ZealandThe unification of levelling networks in New Zealand is done using a combined approach. It utilises the joint levelling network adjustment and the geopotential-value approach. The levelling and normal gravity data are used for a joint adjustment of the levelling networks at the South and North Islands of New Zealand while fixing the heights of tide gauges in Dunedin and Wellington. The results reveal a good quality of levelling data; the STD of residuals is 2 mm for the whole country. The comparison of the newly determined and original normal-orthometric heights confirms the presence of large local vertical datum offsets and systematic levelling errors. Since the geopotential-value approach is based on the Molodensky's theory, the newly adjusted normal-orthometric heights are converted to the normal heights. This conversion is based on applying the cumulative normal to normal-orthometric height correction computed from levelling and gravity anomaly data. In the absence of the observed gravity data the gravity anomalies along levelling lines are generated fromEGM2008. The GPS-levelling data and EGM2008 are used to estimate the average offsets of the jointly adjusted levelling networks at the North and South Islands with respect to World Height System defined by the adopted geoidal geopotential value of W0 = 62636856 ± 0.5 m2s-2; the estimated offsets are 10.6 cm and 27.5 cm.

Assessment of the LVD offsets for the normal-orthometric heights and different permanent tide systems—a case study of New Zealand

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

Evaluation of the NZGeoid05 using GPS levelling in rural and elevated locations, South Island, New Zealand

To facilitate day to day surveying and mapping activities, Land Information New Zealand (LINZ) has developed a regional quasigeoid (NZGeoid05) by enhancing a global geopotential model with satellite, terrestrial and sea gravity data over the continental shelf of New Zealand (NZ). The overall national precision of NZGeoid05 was estimated by LINZ to be ±0.08 m (1σ). Six regions, distributed throughout the South Island of NZ, have been used to provide further independent verification of the precision of the NZGeoid05 by determining the geometric geoid-ellipsoid separation. In each region, several benchmarks with first-order normal-orthometric heights were selected and ellipsoidal heights measured independently using geodetic position techniques. A comparison has also been made with the global geopotential model, EGM2008. For NZGeoid05, four of the six regions tested have a RMS fit better than ±0.05 m, while for the EGM2008 this is only achieved in two regions. The estimated geoid slopes for both the NZGeoid05 and EGM2008 models agree with the geometric data to better than 1 cm/km in five of the six regions tested.

The effect of EGM2008-based normal, normal-orthometric and Helmert orthometric height systems on the Australian levelling network

This paper investigates the normal-orthometric correction used in the definition of the Australian Height Datum, and also computes and evaluates normal and Helmert orthometric corrections for the Australian National Levelling Network (ANLN). Testing these corrections in Australia is important to establish which height system is most appropriate for any new Australian vertical datum. An approximate approach to assigning gravity values to ANLN benchmarks (BMs) is used, where the EGM2008-modelled gravity field is used to ‘re-construct’ observed gravity at the BMs. Network loop closures (for first- and second-order levelling) indicate reduced misclosures for all height corrections considered, particularly in the mountainous regions of south eastern Australia. Differences between Helmert orthometric and normal-orthometric heights reach 44 cm in the Australian Alps, and differences between Helmert orthometric and normal heights are about 26 cm in the same region. Normal-orthometric heights differ from normal heights by up to 18 cm in mountainous regions >2,000 m. This indicates that the quasigeoid is not compatible with normal-orthometric heights in Australia.

Height transformation models from ellipsoidal into the normal orthometric height system for the territory of the City of Zagreb

The paper presents the testing of the possibility of determining the heights of GPS points in the homogeneous field in the new Croatian Height Reference System (HVRS71) by using the method of height transformation. The testing was made in the area of Zagreb. As part of the field works, normal orthometric heights of 27 GPS points were determined according to the new height system, by transferring the benchmark heights using the geometric levelling method, thus obtaining GPS/levelling points of known ellipsoidal and normal orthometric heights. The GPS/levelling points served as the basis for determining the transformation models that enabled the computation of normal orthometric heights from ellipsoidal heights of any GPS point in the observed area. The empirical data used for modelling were reduced undulation dN values of GPS/levelling points. As part of the dN modelling with parametric functions, the approximation surfaces were obtained on the basis of three polynomials: FN310, FN312 and FN318. The transformation models were also tested using non-parametric Watson and Loess algorithms. The FN318 and Loess models yielded the best results.

Analysis of different height systems along the sava river

The paper presents a project of renovating a levelling line from Hydroelectric Power Plant Medvode to Hydroelectric Power Plant Vrhovo. The levelling line is situated along the Sava River. A new height of benchmark was needed as a vertical reference system for the project building up a new HPP between the previously mentioned HPP. Further, the paper presents processing data on measurements (scale and temperature corrections). Gravimetric measurement was performed due to the determination of the geopotencial number and dynamic and normal heights. Slovenian official vertical system contains normal orthometric heights so we also calculated normal orthometric heights. Moreover, the article discusses the accuracy of measurements (levelling and gravimetric) and analyses height calculated in different vertical systems and vertical movements along the levelling line. Įvairių aukščių sistemų prie sava upės analizė Santrauka. Pateikiamos niveliavimo renovacijos projektas nuo Medvode iki Vrhovo hidroelektrinių. Niveliaciniai ėjimai projektuojami išilgai Savos upės. Nauja niveliavimo markių sistema tarnaus kaip referencinis vertikalus tinklas tarp minėtų hidroelektrinių. Toliau numatomas matavimo duomenų apdorojimas (mastelio ir temperatūros pataisos). Numatomi gravimetriniai matavimai, reikalingi nustatant geopotencialą ir dinaminius bei normalinius aukščius. Slovėnijoje naudojama normalinė ortometrinė aukščių sistema, todėl mes skaičiuojame normalinius ortometrinius aukščius. Pateikiami matavimų tikslumo skaičiavimai (niveliavimo ir gravimetriniai), apskaičiuotų aukščių analizė skirtingose aukščių sistemose ir niveliavimo ėjimo vertikalūs judesiai. First published online: 03 Aug 2012

正標高の導入―もう一つの測地成果２０００―

The vertical datum of Japan, which is realized with official heights at the benchmarks, had been updated for the first time in about 30 years and the new heights were put in force in April 2002. The heights were computed from the latest leveling data throughout Japan and detailed land gravity data were taken into account, for the first time in Japan, for yielding Helmert orthomeitric heights. On this occasion, the paper tries to give readers a brief description of the height systems, their relationship with gravity and the computation method employed, and the current, more precise vertical datum of Japan updated from the previously-employed normal orthometric heights.