Height Systems and Vertical Datums: a Review in the Australian Context

This paper reviews (without equations) the various definitions of height systems and vertical geodetic datum surfaces, together with their practical realisation for users in Australia. Excluding geopotential numbers, a height system is a one-dimensional coordinate system used to express the metric distance (height) of a point from some reference surface. Its definition varies according to the reference surface chosen and the path along which the height is measured. A vertical geodetic datum is the practical realisation of a height system and its reference surface for users, nominally tied to mean sea level. In Australia, the normal-orthometric height system is used, which is embedded in the Australian Height Datum (AHD). The AHD was realised by the adjustment of ~195,000 km of spirit-levelling observations fixed to limited-term observations of mean sea level at multiple tide-gauges. The paper ends by giving some explanation of the problems with the AHD and of the differences between the AHD and the national geoid model, pointing out that it is preferable to recompute the AHD

Ellipsoidal area mean gravity anomalies - precise computation of gravity anomaly reference fields for remove-compute-restore geoid determination

Gravity anomaly reference fields, required e.g. in remove-compute-restore (RCR) geoid computation, are obtained from global geopotential models (GGM) through harmonic synthesis. Usually, the gravity anomalies are computed as point values or area mean values in spherical approximation, or point values in ellipsoidal approximation. The present study proposes a method for computation of area mean gravity anomalies in ellipsoidal approximation ('ellipsoidal area means') by applying a simple ellipsoidal correction to area means in spherical approximation. Ellipsoidal area means offer better consistency with GGM quasi/geoid heights. The method is numerically validated with ellipsoidal area mean gravity derived from very fine grids of gravity point values in ellipsoidal approximation. Signal strengths of (i) the ellipsoidal effect (i.e., difference ellipsoidal vs. spherical approximation), (ii) the area mean effect (i.e., difference area mean vs. point gravity) and (iii) the ellipsoidal area mean effect (i.e., differences between ellipsoidal area means and point gravity in spherical approximation) are investigated in test areas in New Zealand and the Himalaya mountains. The impact of both the area mean and the ellipsoidal effect on quasigeoid heights is in the order of several centimetres. The proposed new gravity data type not only allows more accurate RCR-based geoid computation, but may also be of some value for the GGM validation using terrestrial gravity anomalies that are available as area mean values

Error sources and data limitations for the prediction ofsurface gravity: a case study using benchmarks

Gravity-based heights require gravity values at levelled benchmarks (BMs), whichsometimes have to be predicted from surrounding observations. We use EGM2008 andthe Australian National Gravity Database (ANGD) as examples of model and terrestrialobserved data respectively to predict gravity at Australian national levelling network(ANLN) BMs. The aim is to quantify errors that may propagate into the predicted BMgravity values and then into gravimetric height corrections (HCs). Our results indicatethat an approximate ±1 arc-minute horizontal position error of the BMs causesmaximum errors in EGM2008 BM gravity of ~ 22 mGal (~55 mm in the HC at ~2200 melevation) and ~18 mGal for ANGD BM gravity because the values are not computed atthe true location of the BM. We use RTM (residual terrain modelling) techniques toshow that ~50% of EGM2008 BM gravity error in a moderately mountainous regioncan be accounted for by signal omission. Non-representative sampling of ANGDgravity in this region may cause errors of up to 50 mGals (~120 mm for the Helmertorthometric correction at ~2200 m elevation). For modelled gravity at BMs to beviable, levelling networks need horizontal BM positions accurate to a few metres, whileRTM techniques can be used to reduce signal omission error. Unrepresentative gravitysampling in mountains can be remedied by denser and more representative re-surveys,and/or gravity can be forward modelled into regions of sparser gravity

Improving EGM2008 by GPS and leveling data at local scale

The development of the Earth Gravitational Model 2008 (EGM2008) model is a significant contribution for modeling the Earth's gravity and geoid. Recently, it can be confidently used versus geometric models following a simple refinement procedure. Several studies show that, EGM2008 can reach the accuracy of regional or local geoid models after modeling the differences between the GPS-leveling geoid heights and EGM2008 derived geoid heights at identified control points. The study focuses on a corrector surface fitting (CSF) approach based on radial basis functions (RBF) as improvement procedure for EGM2008. A detailed mathematical model and solution algorithm of the proposed model is given, and it has been applied in different test areas covering the city borders of Bursa, Konya, Denizli and Gaziantep in Turkey. Accuracy of the improved model was evaluated in scattered check points within test regions. The geoid heights of all check points obtained by GPS-leveling measurements were compared with the geoid heights obtained from improved model. The discrepancies between the calculated and measured geoid heights were analyzed and discussed

Indirect evaluation of Mars Gravity Model 2011 using a replication experiment on Earth

Curtin University’s Mars Gravity Model 2011 (MGM2011) is a high-resolution composite set of gravity field functionals that uses topography-implied gravity effects at medium- and short-scales (~125 km to ~3 km) to augment the space-collected MRO110B2 gravity model. Ground-truth gravity observations that could be used for direct validation of MGM2011 are not available on Mars’s surface. To indirectly evaluate MGM2011 and its modelling principles, an as-close-as-possible replication of the MGM2011 modelling approach was performed on Earth as the planetary body with most detailed gravity field knowledge available. Comparisons among six ground-truth data sets (gravity disturbances, quasigeoid undulations and vertical deflections) and the MGM2011-replication over Europe and North America show unanimously that topography-implied gravity information improves upon space-collected gravity models over areas with rugged terrain. The improvements are ~55% and ~67% for gravity disturbances, ~12% and ~47% for quasigeoid undulations, and ~30% to ~50% for vertical deflections. Given that the correlation between space-collected gravity and topography is higher for Mars than Earth at spatial scales of a few 100 km, topography-implied gravity effects are more dominant on Mars. It is therefore reasonable to infer that the MGM2011 modelling approach is suitable, offering an improvement over space-collected Martian gravity field models

Rede geodésica para o monitoramento costeiro do litoral setentrional do estado do Rio Grande do Norte

Este trabalho apresenta os procedimentos técnicos envolvidos na implantação da Rede GPS do Litoral Setentrional do Rio Grande do Norte (RGLS), onde o objetivo é fornecer subsídios fundamentais aos levantamentos geodésicos destinados ao monitoramento de áreas costeiras, submetidas à intensa dinâmica e de grande importância socioeconômica e ecológica para o Estado do Rio Grande do Norte. A metodologia permitiu a determinação das coordenadas geodésicas e altitudes ortométricas das estações com precisão decimétrica em relação ao Sistema Geodésico Brasileiro (SGB), a partir do método de posicionamento relativo e da altimetria por GPS. Ainda, foi possível o estudo de aspectos geodésicos envolvidos na altimetria por GPS, tais como avaliação da situação física e da densidade das Referências de Nível (RRNN) disponíveis, avaliação absoluta e relativa do modelo geoidal, proposição de metodologia para a altimetria por GPS de precisão e desenvolvimento de software para essa finalidade, que contribuíram para o conhecimento geodésico na área de estudo

Closed-Form transformation between geodetic and ellipsoidal coordinates

We present formulas for direct closed-form transformation between geodetic coordinates(Φ, λ, h) and ellipsoidal coordinates (β, λ, u) for any oblate ellipsoid of revolution.These will be useful for those dealing with ellipsoidal representations of the Earth's gravityfield or other oblate ellipsoidal figures. The numerical stability of the transformations for nearpolarand near-equatorial regions is also considered

DETERMINISTICALLY-MODIFIED INTEGRAL ESTIMATORS OF GRAVITATIONAL TENSOR

The Earth's global gravity field modelling is an important subject in Physical Geodesy. For this purpose different satellite gravimetry missions have been designed and launched. Satellite gravity gradiometry (SGG) is a technique to measure the second-order derivatives of the gravity field. The gravity field and steady state ocean circulation explorer (GOCE) is the first satellite mission which uses this technique and is dedicated to recover Earth's gravity models (EGMs) up to medium wavelengths. The existing terrestrial gravimetric data and EGM scan be used for validation of the GOCE data prior to their use. In this research, the tensor of gravitation in the local north-oriented frame is generated using deterministically-modified integral estimators involving terrestrial data and EGMs. The paper presents that the SGG data is assessable with an accuracy of 1-2 mE in Fennoscandia using a modified integral estimatorby the Molodensky method. A degree of modification of 100 and an integration cap size of for integrating terrestrial data are proper parameters for the estimator

The computation of the geoid model in the state of São Paulo using two methodologies and GOCE models

The purpose of this manuscript is to compute and to evaluate the geoid model in the State of São Paulo from two methodologies (Stokes' integral through the Fast Fourier Transform - FFT and Least Squares Collocation - LSC). Another objective of this study is to verify the potentiality of GOCE-based. A special attention is given to GOCE mission. The theory related to Stokes' integral and Least Squares Collocation is also discussed in this work. The spectral decomposition was employed in the geoid models computation and the long wavelength component was represented by EGM2008 up to degree and order 150 and 360 and GOCE-based models up to 150. The models were compared in terms of geoid height residual and absolute and relative comparisons from GPS/leveling and the results show consistency between them. In addition, a comparison in the mountain regions was carried out to verify the methodologies behavior in this area; the results showed that LSC is less consistent than FFT