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Volume 2 Issue 4 - Special issue on Regional and Global Geoid-based Vertical Datums, Eds. Michael Sideris and Georgia Fotopoulos

December 2012

Issue of Journal of Geodetic Science

Contents
Journal Overview

Open Access January 29, 2013

Preface to the Special Issue of the Journal of Geodetic Sciences on Regional and Global Geoid-based Vertical Datums

Michael G. Sideris

Page range: 246-246

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Open Access January 29, 2013

Approximations of the GOCE error variance-covariance matrix for least-squares estimation of height datum offsets

Ch. Gerlach, Th. Fecher

Page range: 247-256

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Abstract

One 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 quantities H, h and N , 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.

Open Access January 29, 2013

Estimating Canadian vertical datum offsets using GNSS/levelling benchmark information and GOCE global geopotential models

T. Hayden, B. Amjadiparvar, E. Rangelova, M.G. Sideris

Page range: 257-269

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Abstract

The 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.

Open Access January 29, 2013

Intercontinental height datum connection with GOCE and GPS-levelling data

T. Gruber, C. Gerlach, R. Haagmans

Page range: 270-280

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Abstract

In 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.

Open Access January 29, 2013

How Significant is the Dynamic Component of the North American Vertical Datum?

E. Rangelova, W. Van Der Wal, M.G. Sideris

Page range: 281-289

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Abstract

One 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.

Open Access January 29, 2013

Evaluation of W₀ in Canada using tide gauges and GOCE gravity field models

T. Hayden, E. Rangelova, M. G. Sideris, M. Véronneau

Page range: 290-301

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Abstract

The existing Canadian Geodetic Vertical Datum of 1928 (CGVD28) does not meet the needs of the modern user in terms of accuracy and accessibility. As a result, Canada plans to implement a geoid-based and global navigation satellite system (GNSS)-accessible vertical datum by 2013. One of the primary concerns in realizing this new vertical datum is to determine a W0 value that will represent the potential of the zero height surface. The objective of this study is to evaluate W0 by averaging the potential of points on the mean sea water surface utilizing tide gauge recordings and gravity field and steady-state ocean circulation explorer (GOCE)-based global geopotential models. In order to assess the performance of the GOCE-based models for the computation of W0, the models are extended with the high resolution gravitational model EGM2008 . Regional gravimetric geoid models are also used for the estimation of W0. Additionally, local sea surface topography models are utilized in order to validate the W0 results at the tide gauges. Excluding the Arctic coast, the W0 values obtained from both tide gauges and oceanic sea surface topography models are not statistically different from the International Earth Rotation and Reference Systems Service (IERS) 2010 global conventional value 62636856.00 m 2 /s 2 .

Open Access January 29, 2013

Towards worldwide height system unification using ocean information

P.L. Woodworth, C.W. Hughes, R.J. Bingham, T. Gruber

Page range: 302-318

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Abstract

We 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.

Open Access January 29, 2013

A conventional approach for comparing vertical reference frames

C. Kotsakis

Page range: 319-324

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Abstract

A conventional transformation model between different realizations of a vertical reference system is an important tool for geodetic studies related to precise vertical positioning and physical height determination. Its fundamental role is the evaluation of the consistency for colocated vertical reference frames that are obtained from different observation techniques, data sources or optimal estimation strategies in terms of an appropriate set of “vertical datum perturbation” parameters. Our scope herein is to discuss a number of key issues related to the formulation of such a transformation model and to present some simple examples from its practical implementation in the comparison of existing vertical frames over Europe.

Open Access January 29, 2013

Towards a vertical datum standardisation under the umbrella of Global Geodetic Observing System

L. Sánchez

Page range: 325-342

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Abstract

Most of the existing height systems refer to local sea surface levels, are stationary (do not consider variations in time), and realise different physical height types (orthometric, normal, normal-orthometric, etc.). In general, their accuracy is about two orders of magnitude less than that of the realisation of geometric reference systems (sub millimetre level). The Global Geodetic Observing System (GGOS) of the International Association of Geodesy (IAG), taking care of providing a precise geodetic infrastructure for monitoring the system Earth, promotes the standardisation of height systems worldwide. The main objectives are: (1) to provide a reliable frame for consistent analysis and modelling of global phenomena and processes affecting the Earth’s gravity field and the Earth’s surface geometry; and (2) to support the precise combination of physical and geometric heights in order to exploit at a maximum the advantages of satellite geodesy (e.g. combination of satellite positioning and gravity field models for worldwide unified precise height determination). According to this, the GGOS Theme 1 ”Unified Height System” was established in February 2010 with the purpose to bring together existing initiatives and to address the activities to be faced. Starting point are the results delivered by the IAG Inter-Commission Project 1.2 ”Vertical Reference Frames” during the period 2003-2011. The present actions related to the vertical datum homogenisation are being coordinated by the working group ”Vertical Datum Standardisation”, which directly depends on the GGOS Theme 1 and is supported by the IAG Commissions 1 (Reference Frames) and 2 (Gravity Field), as well as by the International Gravity Field Service (IGFS). This paper discusses some aspects to take into consideration for the realisation of a standardised globally unified vertical reference system.

Open Access January 29, 2013

Unification of European height system realizations

A. Rülke, G. Liebsch, M. Sacher, U. Schäfer, U. Schirmer, J. Ihde

Page range: 343-354

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Abstract

A suitable representation of the regional gravity field is used to estimate relative offsets between national height system realizations in Europe. The method used is based on a gravimetric approach and benefits from the significant improvements in the determination of the global gravity field by the recent satellite gravity missions the Gravity Recovery and Climate Experiment (GRACE) and the Gravity field and steady-state Ocean Circulation Explorerr (GOCE). The potential of these missions for the unification of height reference frames is analyzed in terms of accuracy and spatial resolution. The results of the gravimetric approach are compared to the independent results of the geodetic leveling approach. Advantages and drawbacks of both methods are discussed.

Open Access January 29, 2013

Height unification using GOCE

R. Rummel

Page range: 355-362

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Abstract

With 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 V xx , V yy , V zz and V xz . 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.

Open Access January 29, 2013

Referencing regional geoid-based vertical datums to national tide gauge networks

D. Bolkas, G. Fotopoulos, M. G. Sideris

Page range: 363-369

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Abstract

The 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.

Open Access January 29, 2013

Regional geoid-model-based vertical datums – some Australian perspectives

W. E. Featherstone, M. S. Filmer, S. J. Claessens, M. Kuhn, C. Hirt, J. F. Kirby

Page range: 370-376

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Abstract

This 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.

About this journal

Journal of Geodetic Science is a peer-reviewed, electronic-only journal that publishes original, high-quality research on topics broadly related to Geodesy. The journal focuses on theoretical and application papers. The aim of the Journal is to become a premier source of knowledge and a worldwide-recognized platform of exchange for scientists of different disciplinary origins and backgrounds (e.g., Surveyors, Geodesists and Geophysicists). The journal publishes geodetic research from a broad range of topics and approaches including Geodetic Networks, Deformation analysis, Adjustment theory and application of mathematical statistics, Satellite Geodesy, Physical Geodesy, Geodynamics, Geometric Geodesy, (see the scope listed below for more). However, we will accept both theoretical and empirical contributions in all subfields of Geodesy as long as they contribute in a broad sense to the core theme.

The scope includes, but is not restricted to:

Surveying Engineering
Geodetic Networks
Deformation Analysis
Adjustment Theory and Mathematical Geodesy
Global Navigation Satellite Systems (GNSS)
Inertial Geodesy
Geoid determination and height systems
Marine Geodesy and Satellite Altimetry
Satellite Gravimetry
Geometric Geodesy
Numerical methods and software developments in Geodesy
Geodynamics
Geophysical Geodesy

Journal Partners

Volume 2 Issue 4 - Special issue on Regional and Global Geoid-based Vertical Datums, Eds. Michael Sideris and Georgia Fotopoulos

Issue of Journal of Geodetic Science

Preface to the Special Issue of the Journal of Geodetic Sciences on Regional and Global Geoid-based Vertical Datums

Approximations of the GOCE error variance-covariance matrix for least-squares estimation of height datum offsets

Abstract

Estimating Canadian vertical datum offsets using GNSS/levelling benchmark information and GOCE global geopotential models

Abstract

Intercontinental height datum connection with GOCE and GPS-levelling data

Abstract

How Significant is the Dynamic Component of the North American Vertical Datum?

Abstract

Evaluation of W0 in Canada using tide gauges and GOCE gravity field models

Abstract

Towards worldwide height system unification using ocean information

Abstract

A conventional approach for comparing vertical reference frames

Abstract

Towards a vertical datum standardisation under the umbrella of Global Geodetic Observing System

Abstract

Unification of European height system realizations

Abstract

Height unification using GOCE

Abstract

Referencing regional geoid-based vertical datums to national tide gauge networks

Abstract

Regional geoid-model-based vertical datums – some Australian perspectives

Abstract

Evaluation of W₀ in Canada using tide gauges and GOCE gravity field models