Evaluation of recent combined global geopotential models in Brazil

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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On the advantage of normal heights

Geodesy and Cartography ◽

10.22389/0016-7126-2018-939-9-2-9 ◽

2018 ◽

Vol 939 (9) ◽

pp. 2-9

Author(s):

V.V. Popadyev

Keyword(s):

Gravitational Field ◽

Tide Gauge ◽

General Term ◽

Reference Ellipsoid ◽

Height Anomaly ◽

Normal Height ◽

Anomalous Field ◽

Normal Heights ◽

Basic Concepts ◽

Orthometric Heights

The author analyzes the arguments in the report by Robert Kingdon, Petr Vanicek and Marcelo Santos “The shape of the quasigeoid” (IX Hotin-Marussi Symposium on Theoretical Geodesy, Italy, Rome, June 18 June 22, 2018), which presents the criticisms for the basic concepts of Molodensky’s theory, the normal height and height anomaly of the point on the earth’s surface, plotted on the reference ellipsoid surface and forming the surface of a quasigeoid. The main advantages of the system of normal heights, closely related to the theory of determining the external gravitational field and the Earth’s surface, are presented. Despite the fact that the main advantage of Molodensky’s theory is the rigorous determining the anomalous potential on the Earth’s surface, the use of the system of normal heights can be shown and proved separately. To do this, a simple example is given, where the change of marks along the floor of a strictly horizontal tunnel in the mountain massif is a criterion for the convenience of the system. In this example, the orthometric heights show a change of 3 cm per 1.5 km, which will require corrections to the measured elevations due the transition to a system of orthometric heights. The knowledge of the inner structure of the rock mass is also necessary. It should be noted that the normal heights are constant along the tunnel and behave as dynamic ones and there is no need to introduce corrections. Neither the ellipsoid nor the quasi-geoid is a reference for normal heights, because so far the heights are referenced to initial tide gauge. The points of the earth’s surface are assigned a height value; this is similar to the ideas of prof. L. V. Ogorodova about the excessive emphasis on the concept of quasigeoid. A more general term is the height anomaly that exists both for points on the Earth’s surface and at a distance from it and decreases together with an attenuation of the anomalous field.

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Evaluation of the latest GOCE GGMs in support of regional geoid modeling over Greece

10.5194/egusphere-egu21-1648 ◽

2021 ◽

Author(s):

Georgios S. Vergos ◽

Ilias N. Tziavos ◽

Dimitrios A. Natsiopoulos ◽

Elisavet G. Mamagiannou ◽

Eleftherios A. Pitenis

Keyword(s):

Maximum Degree ◽

Gravity Data ◽

Ground Truth ◽

Satellite Gravity ◽

Disturbing Potential ◽

Geopotential Models ◽

Potential Functionals ◽

Geoid Computation ◽

Goce Satellite

<p>In the frame of the GeoGravGOCE project, funded by the Hellenic Foundation for Research Innovation, GOCE Satellite Gravity Gradiometry (SGG) data are to be used for regional geoid and gravity field refinement as well as for potential determination in the frame of the International Height Reference Frame (IHRF). An inherent step in the geoid computation with either stochastic or spectral methods is the reduction of the related disturbing potential functionals within the well-known Remove-Compute-Restore (RCR) procedure. In this work we evaluate the latest, Release 6 (R6), satellite only and combined Global Geopotential Models (GGMs) which rely solely on GOCE and on land gravity data. The evaluation is performed over the established network of 1542 GPS/Levelling benchmarks over Greece mainland (BMs), which have been used in the past for the evaluation of GOCE GGMs. We employ the spectral enhancement approach, during which the GOCE-based GGMs are evaluated every one degree to the maximum degree of expansion coupled by EGM2008 and high-frequency RTM effects. This synthesis resolves wavelengths corresponding to maximum degree 216,000, hence the omission error is at the few mm-level. TIM-R6, DIR-R6, GOCO06s and XGM2019e are evaluated using EGM2008 residuals to the GPS/Levelling as the ground truth. From the results achieved, the optimal combination degree of a GOCE-only GGM augmented with EGM2008 is selected to be used in the sequel as reference field for the practical determination of the gravimetric geoid over Greece.</p>

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Accuracy Assessment of Recent High-Degree Global Geopotential Models Using Geodetic Control Points and Terrestrial Gravity Data in Turkey

10.5194/egusphere-egu21-11929 ◽

2021 ◽

Author(s):

Muhammed Raşit Çevikalp ◽

Bihter Erol ◽

Bilal Mutlu ◽

Serdar Erol

Keyword(s):

Gravity Data ◽

Geopotential Model ◽

Geoid Model ◽

Terrestrial Gravity ◽

Practical Applications ◽

Geopotential Models ◽

Vertical Datum ◽

Height System ◽

Orthometric Heights ◽

Height System Unification

<p>The maintenance of leveling benchmark is both laborious and costly due to distortions caused by geodynamic activities and local deformations. It is necessary to realize geoid-based vertical datum, which also enables calculation from ellipsoidal heights obtained from GNSS to orthometric heights that have physical meaning. It can be considered as an important step for height system unification as it eliminates the problems stem from the conventional vertical datum. The ongoing height modernization efforts in Turkey focus to improve quality and coverage of the gravity data, eliminate errors in existing terrestrial gravity measurements in order to achieve a precise geoid model. Accuracy of the geopotential model is crucial while realizing a geoid model based vertical datum as well as unifying the regional height systems with the International Heights Reference System. In this point of view, we assessed the accuracies of recently released global geopotential models including XGM2019e_2159, GECO, EIGEN-6C4, EGM2008, SGG-UGM-1, EIGEN-6C3stat, and EIGEN-6C2 using high order GNSS/leveling control benchmarks and terrestrial gravity data in Turkey. The reason for choosing these models in the validations is their relatively higher spatial resolutions and improved accuracies compared to other GGMs in published validation results with globally distributed terrestrial data. The GNSS/leveling data used in validations include high accuracy GNSS coordinates in ITRF datum with co-located Helmert orthometric heights in regional vertical datum. 100 benchmarks are homogeneously distributed in the country with the benchmarks along the coastlines. In addition, the terrestrial gravity anomalies with 5 arc-minute resolution were also used in the tests. In order to have comparable results, residual terrain effect has been restored to the GGM derived parameters. Numerical tests revealed significant differences in accuracies of the tested GGMs. The most accurate GGM has the comparable performance with official regional geoid model solutions in Turkey. The drawn results in the study were interpreted and discussed from practical applications and height system unification points in conclusion.</p>

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Simplification of Geopotential Perturbing Force Acting on A Satellite

Artificial Satellites ◽

10.2478/v10018-009-0006-7 ◽

2008 ◽

Vol 43 (2) ◽

pp. 45-64 ◽

Cited By ~ 5

Author(s):

M. Eshagh ◽

M. Abdollahzadeh ◽

M. Najafi-Alamdari

Keyword(s):

Maximum Degree ◽

Legendre Functions ◽

Orbital Elements ◽

Associated Legendre Functions ◽

Geopotential Models ◽

Orbit Integration ◽

Vector Differential Equation ◽

Derivatives Of ◽

Geopotential Coefficients ◽

Short Arc

Simplification of Geopotential Perturbing Force Acting on A SatelliteOne of the aspects of geopotential models is orbit integration of satellites. The geopotential acceleration has the largest influence on a satellite with respect to the other perturbing forces. The equation of motion of satellites is a second-order vector differential equation. These equations are further simplified and developed in this study based on the geopotential force. This new expression is much simpler than the traditional one as it does not derivatives of the associated Legendre functions and the transformations are included in the equations. The maximum degree and order of the geopotential harmonic expansion must be selected prior to the orbit integration purposes. The values of the maximum degree and order of these coefficients depend directly on the satellite's altitude. In this article, behaviour of orbital elements of recent geopotential satellites, such as CHAMP, GRACE and GOCE is considered with respect to the different degree and order of geopotential coefficients. In this case, the maximum degree 116, 109 and 175 were derived for the Earth gravitational field in short arc orbit integration of the CHAMP, GRACE and GOCE, respectively considering millimeter level in perturbations.

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THE GEOID AND QUASIGEOID OF SÃO PAULO STATE USING THE UPDATED GRAVIMETRIC DATA AND THE 2018 BVRF

Boletim de Ciências Geodésicas ◽

10.1590/1982-2170-2020-0061 ◽

2021 ◽

Vol 27 (2) ◽

Author(s):

Valéria Cristina Silva ◽

Flavio Guilherme Vaz de Almeida Filho ◽

Denizar Blitzkow ◽

Ana Cristina Oliveira Cancoro de Matos

Keyword(s):

Gravity Anomalies ◽

Geoid Height ◽

Sao Paulo ◽

Height Anomaly ◽

São Paulo ◽

Geoid Model ◽

Normal Height ◽

Paulo State ◽

Gravimetric Data ◽

São Paulo State

Abstract The combination of physical and geometric heights, required for geodetic purposes, uses Global Geopotential Models (GGMs), local geoid, or quasigeoid models. The geoid height and the height anomaly, provided by GGMs, are not accurate enough for most engineering applications. Considering the normal height system of Brazil and the physical concepts of the involved reference surfaces, a quasigeoid model is more appropriate than the current Brazilian geoid model MAPGEO2015. This paper shows the determination of the geoid and the quasigeoid models for São Paulo state using the updated gravimetric data and the new system of the normal height of the 2018 Brazilian Vertical Reference Frame (BVRF). The computation of the quasigeoid model was performed by numerical integration through the Fast Fourier Transform (FFT). The Molodensky gravity anomaly was determined in a 5’ grid and reduced and restored using the Residual Terrain Model (RTM) technique and the XGM2019e GGM truncated at degree and order 250 and 720. The geoid model was derived from the Bouguer gravity anomalies. The quasigeoid model validation has shown a Root Mean Square (RMS) difference of 18 cm compared with the Global Positioning System (GPS) measurements in the levelling network.

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ASSESSMENT OF RECENT GOCE-BASED GLOBAL GEOPOTENTIAL MODELS AND EGM2008 IN NIGER REPUBLIC

Geodesy and Cartography ◽

10.3846/gac.2019.8699 ◽

2019 ◽

Vol 45 (3) ◽

pp. 116-125

Author(s):

Salissou Ibrahim Yahaya ◽

Driss El Azzab

Keyword(s):

Gravity Data ◽

Geoid Height ◽

Terrestrial Gravity ◽

Terrain Model ◽

Spectral Bands ◽

Geopotential Models ◽

Before And After ◽

Gravity Database ◽

Enhancement Method ◽

The One

In this study, we assessed recent GOCE-based Global Geopotential Models (GGMs) and EGM2008 in Niger. The combined GGMs EIGEN_6C4, GECO and EGM2008 were evaluated up to their maximum degree and order (d/o) 2,190 to select the one for gravity database densification. The following pure satellite GGMs were assessed for the modelling of the long and medium wavelengths in geoid computation: GGM05G, ITU_GGC16, EIGEN_6S4v2 and the fifth releases from direct (DIR5), space-wise (SPW5) and time-wise (TIM5) approaches. The GGMs are compared to terrestrial gravity data and geoid heights from GNSS/Levelling points before and after applying spectral enhancement method (SEM) by residual terrain model (RTM) for combined models and by RTM and the coefficients of selected combined GGM for pure satellite models. The agreements of combined GGMs with terrestrial gravity data and GNSS/Levelling points, in terms of root mean square (RMS) are about 4.88 to 5.02 mGal and 0.14 to 0.16 m, respectively. EIGEN_6C4 was selected as it showed the best performance in terms of geoid height differences and the probability of 3-sigma rule for gravity anomaly differences. At d/o 200, DIR5 showed a good agreement with terrestrial gravity data (5.04 mGal) and GNSS/Levelling points (0.15 m) after applying SEM, it was then retained. All GOCE-based models exhibited a good performance in long and medium wavelengths confirming the good recovery of the gravity field by the spatial gravity mission in these spectral bands.

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ANALYSIS OF ISOSTATICALLY-BALANCED CORTICAL MODELS USING MODERN GLOBAL GEOPOTENTIAL MODELS

Boletim de Ciências Geodésicas ◽

10.1590/s1982-21702017000400041 ◽

2017 ◽

Vol 23 (4) ◽

pp. 623-635

Author(s):

Claudia Infante ◽

Claudia Tocho ◽

Daniel Del Cogliano

Keyword(s):

Gravity Field ◽

Temporal Variations ◽

Geoid Height ◽

Geological Structure ◽

Earth’S Gravity Field ◽

Isostatic Equilibrium ◽

Geopotential Models ◽

Show Evidence ◽

Residual Geoid ◽

Cortical Models

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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Quantitative analysis of Linum usitatissimum crosses for dual-purpose traits

The Journal of Agricultural Science ◽

10.1017/s0021859698005917 ◽

1998 ◽

Vol 131 (3) ◽

pp. 285-292 ◽

Cited By ~ 10

Author(s):

R. FOSTER ◽

H. S. POONI ◽

I. J. MACKAY

Keyword(s):

Quantitative Analysis ◽

Flowering Time ◽

Seed Yield ◽

Linum Usitatissimum ◽

Seed Weight ◽

Superior Performance ◽

Dual Purpose ◽

Good Potential ◽

Common Parent ◽

Number Of Branches

The commercial future of Linum usitatissimum is intrinsically linked to its cultivation as a dual-purpose crop for producing increased seed and fibre yields. The present study evaluates 36 F1 crosses derived from nine linseed/flax accessions for their potential as dual-purpose cultivars and/or their suitability for extracting new recombinants producing high seed yield as well as increased fibre output. The quantitative analysis indicated that variation between the F1 families is largely but not exclusively due to the additive and non-additive (dominance) effects of genes. Dominance is high for plant height (H1), height at maturity (HMT), number of branches (NBr) and seed weight (SdWt) while 100 seed weight (Wt100) displays no dominance at all. The repeatability estimates representing the heritability of each trait, vary from low (0·20) for number of branches (NBr) to high (0·71) for height at flowering time (HFT). The dual-purpose traits such as seed weight (SdWt) and straw weight (StWt) were only moderately inherited while flowering time (FT) and various heights were rather highly heritable. A moderate and positive correlation (r=0·57) between StWt and SdWt, and a completely independent inheritance of Wt100 suggested that there are good chances of combining these traits into a single genotype. The phenotypic performance of the crosses also confirmed this trend and at least four crosses showed superior performance for both SdWt and StWt compared to their parental lines. All these crosses involved a linseed line (B3) as a common parent and the second parent was either another linseed line (A1 and A3) or a flax accession (K3 and L2); none of the flax×flax crosses showed good potential for seed yield. While all four crosses possess the potential to become highly productive, dual-purpose, hybrid varieties, the extraction of desirable inbred lines from them, however, may prove difficult because the superior performance of the hybrids seems largely due to strong unidirectional dominance and high SCA effects.

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Determination of orthometric elevations using gnss-derived height with the egm2008 geoid height model

International Journal of Advanced Geosciences ◽

10.14419/ijag.v5i1.7190 ◽

2017 ◽

Vol 5 (1) ◽

pp. 13

Author(s):

Emmanuel Menegbo

Keyword(s):

Geoid Height ◽

Global Navigation Satellite Systems ◽

Satellite Systems ◽

Maximum Elevation ◽

Gis Data ◽

Gnss Receivers ◽

Orthometric Heights ◽

Global Navigation Satellite ◽

The Relationship

The Global navigation satellite systems (GNSS) has imparted positively on civilian positioning & surveying in the horizontal component in Nigeria for the past two decades. The GNSS receivers’ data are longitude, latitude & elevation. However, the vertical distance measurement have not been fully exploited by geodetic and land surveyors. The GNSS derived heights are ellipsoidal elevation. To convert the GNSS elevation to orthometric heights, a geoidal elevation models is needed. The Earth Gravitational Model, 2008 (EGM2008) is a global geoidal models that can be used to obtain GNSS orthometric heights by defining the relationship with the ellipsoid. This work determines GNSS-derived orthometric heights with ellipsoid-geoidal relationship using GPS ellipsoidal heights and EGM2008 geoidal model GIS data. The EGM2008 GIS data was downloaded and interpolated with GPS data to obtain geoidal heights using ArcGIS 10.1. GNSS-derived heights determined with geoid-ellipsoid relationship formula. The result shows minimum elevation of -2.37599m and maximum elevation of 53.8566m.The derived orthometric heights use to create a model in raster format. The orthometric elevation models created useful in all vertical surveying work, construction work and urban planning. The GNSS orthometric heights models need to be compare with spirit levelling and the local geoidal model determined for improve accuracy.

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

Boletim de Ciências Geodésicas ◽

10.1590/s1982-21702018000300022 ◽

2018 ◽

Vol 24 (3) ◽

pp. 335-350

Author(s):

Eurico Nicacio ◽

Regiane Dalazoana

Keyword(s):

Input Data ◽

Tide Gauge ◽

The Other ◽

The South ◽

The North ◽

Vertical Data ◽

Geopotential Models ◽

Orthometric Heights ◽

Gnss Observations

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.

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