2004 Unified Global Height Reference System

8/6/2019 2004 Unified Global Height Reference System

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Journal of Geodynamics 40 (2005) 400413

A unified global height reference system as a basis for IGGOS

Johannes Ihde a,, Laura Sanchez b

a Bundesamt fur Kartographie und Geodasie, Richard-Strauss-Allee 11, D-60598 Frankfurt am Main, Germanyb Instituto Geografico Agustn Codazzi, Carrera 30 No. 48-51, Bogota, Colombia

Received 1 July 2003; received in revised form 1 July 2004; accepted 21 June 2005

Abstract

The definitionof a global height reference system is based on a mean sea surface, gravity field parameters, anda three-dimensional

terrestrial reference frame (TRF). Tide gauge records, satellite altimetry, gravity measurements on Earth and from space, TRF

coordinates, and spirit levelling have to be combined for the realization of the vertical reference frame. Observations and parameters

have to be consistent with respect to the used standards, conventions and models. They have to provide globally unified reference

surfaces (geoid or quasigeoid, respectively, and mean sea surface). The continental reference systems of Europe (EUREF, ECGN)

and South America (SIRGAS) are considering these requirements in their strategies. They are presented here, and slightly different

definitions and realizations for a globally unified height reference system are discussed.

2005 Elsevier Ltd. All rights reserved.

Keywords: Global height system; Mean sea surface; Tide gauges; Satellite altimetry; Earth gravity field; Geodetic space techniques; Terrestrial

reference frame

1. Introductionthe height problem

The International Terrestrial Reference Frame (ITRF) of the International Earth Rotation and Reference Systems

Service (IERS) is defined as a three-dimensional, geocentric reference system. It is realized by the combination of

different space techniques resulting in an accuracy in the order of 109 for the three position components of stations

forming the reference frame. In order to ensure the long-time stability with the same accuracy, time variations of

coordinates are included in terms of station velocities. Geodetic heights, i.e., the vertical component of positions, may

be derived as geometrical heights referring to a reference ellipsoid. They are independent of the Earth gravity field and

the datum is related to the fundamental geodetic parameters and standards (e.g., GRS80). The ITRF Product Centre of

the IERS is actualising this terrestrial reference frame in intervals of several years.For many applications in science and practice, physical heights based on differences of the potential of the Earths

gravity field (geopotential) are required, in particular for geodynamics, engineering, precise navigation, flooding

protection, coastal research, etc. There are about a hundred different physical height systems worldwide, related to

different tide gauges, realized by spirit levelling as static systems, and reduced for the gravity effect by different

models. The tide gauges are related to a mean sea level (MSL) at an arbitrarily selected epoch which differs from a

Corresponding author.

E-mail address: [email protected] (J. Ihde).

0264-3707/$ see front matter 2005 Elsevier Ltd. All rights reserved.

doi:10.1016/j.jog.2005.06.015


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J. Ihde, L. Sanchez / Journal of Geodynamics 40 (2005) 400413 401

Fig. 1. Transformation parameters of national height reference systems to the United European Levelling Network (UELN) (in cm).

mean global equipotential surface (the geoid) up to the order of a meter. The accuracy of the heights in these systemsis limited regionally by the error propagation of spirit levelling and globally by the datum realization with different

tide gauges and different epochs by 106 to 107. The repetition rate of physical height determination is in general

only 1050 years. As an example, the differences of the datums of the national height systems in Europe with respect

to the Normaal Amsterdams Peil (NAP) are given in Fig. 1 (Sacher et al., 1999a).

We see that the accuracy of present realizations of physical height reference systems in a global scale is about two

orders of magnitude less than that of the ITRF. The repetition time rate differs by one order of magnitude. In the frame

of global geodesy at centimetre-level, physical heights appear as inconsistent elements.

The use of the terrestrial reference frame, e.g., the ITRF, for physical height determination requires the transfor-

mation of the geometric heights, related to the ellipsoid, to physical heights referring to its reference surface (geoid

or quasigeoid, respectively). To keep the ITRF position accuracy, one has to know the height reference surface with

the same accuracy, which is not feasible at present. The comparison of geometrical heights with physical heights of

the European Vertical Reference Network (EUVN, Ihde et al., 2000) may demonstrate the problem. Fig. 2 showsthe differences between GPS heights (ITRF96, epoch 1997.4) on the one hand and heights of the United European

Levelling Network (UELN) referring to the Normaal Amsterdams Peil (NAP) plus height anomalies of the European

geoid EGG97 on the other hand. The long wavelength variations of some decimetres over Europe characterise the

errors of the physical heights. They include systematic errors of spirit levelling, different methods of data reduction,

differences of the epoch definition of the national levelling networks, and influences of the height datum differences

to the EGG97 (Ihde and Sacher, 2002).

Denker (2001) investigated the effects of height datum inconsistencies on gravity field modelling. The effect on

gravity anomalies is in the order of 0.2 mgal and affects the geoid modelling by global gravity models (GGM) or by

Stokes integration using terrestrial gravity data in the order of 0.1 m (Fig. 3).

The realization of a global reference surface for physical height systems, the relation of individual tide gauge records

with respect to the reference surface, the separation of sea level changes and vertical crustal movements at tide gauges,


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402 J. Ihde, L. Sanchez / Journal of Geodynamics 40 (2005) 400413

Fig. 2. EUREFs EUVN Project (2001) with 200 GPS/levelling points. Differences between gravimetric height components and GPS heights

(EGG97 +HEUVN) hITRF.

and the connection with the terrestrial reference system are actually unsolved problems. To proceed towards a unified

physical height system we need at the centimetre accuracy level:

- a unique global height datum;

- consistent parameters, models and processing procedures of TRF and gravity field;- a closed theory for the combination of parameters (space techniques, gravity);

- consideration of time depended influences;

- concepts for the realization.

2. Fundamentals of height systems

Satellite geodesy has rigorously revolutionized geodesy. Technologies of positioning and gravity field determination

have basically changed. While classical three-dimensional positioning required the combination of geometric and

gravity field parameters (anomalies or geoid), it may now be done by pure geometry, i.e., satellite geodesy provides the

geometrical shape of the Earth. The long wavelengths of the gravity field are determined globally by dynamic satellite

orbit determination or by the new satellite gravity field missions. Satellite altimetry allows the geoid determination


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Fig. 3. Effect of height differences between national height reference systems in Europe on the gravimetric geoid (in m) (Denker, 2001).

over the oceans with high resolution and provides in combination with the geometric or dynamic sea surface the

sea surface topography as physical heights. However, to derive physical heights over the continents we have to know

the gravity field there with high resolution as well.

The determination of the potential of the gravity field WP at a point P of the Earth surface is in general possible in

two ways: by solving the boundary value problem (BVP), i.e., by deriving the disturbing potential TP at the knownthree-dimensional position and adding it to the normal potential UP: WP = UP + TP, or by using the spirit levelling:

WP = W0 + cP, where the geopotential number cP is the resultof the spirit levellingcP = W0 WP =P

0 g dh and W0 is

the potentialof the heightreference surface. Molodenskys solution of the BVPgives the disturbing potential at the Earth

surface TP =R

4

(g+G1 . . .)S() dand the height anomaly = TP/Q = (WPUP)/Q. In combination with

the geometric heights h from three-dimensional positioning we get then the physical heights in terms of Molodenskys

normal heights HNP = hP+ P. From spirit levelling we get the normal heights by HNP = cP/, where is the mean

normal gravity.

3. The height reference systems in South America and Europe: present status

The realization of a unified global height reference system is one of the objectives of IAG Commission 1 ReferenceFrames in cooperation with Commission 2 Gravity Field and the IAG Services. The scientific investigations on the

concept and the requirements for the practical realization of unified height systems are carried out within the IAG Inter-

Commission Project 1.2 Vertical Reference Frames and in the Subcommission 1.3 Regional Reference Frames,

in particular SC1.3a EUREF for Europe and SC1.3b SIRGAS for South America. At present, the physical height

systems are defined and realized as static systems. They use one (Europe) or several (South America) tide gauges as

the reference datum.

3.1. South America

The present three-dimensional reference system in South America is defined and realized by the SIRGAS Project

(Sistema de Referencia Geocentrico para las Americas, Geocentric Reference System for the Americas). It corresponds


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to the IERS Terrestrial Reference System (ITRS), and is a continental densification of the IERS Terrestrial Reference

Frame (ITRF). The SIRGAS Project was established in 1993 during the International Conference on the Definition

of a South American Geocentric Datum in Asuncion, Paraguay. The sponsoring institutions were the International

Association of Geodesy (IAG), the Pan-American Institute of Geography and History (PAIGH) and the US National

Imagery and Mapping Agency (NIMA). Its principal objectives were to define and to realize a geocentric reference

system for South America (Working Group I) and to establish a geocentric datum for each country (Working Group

II). The first result was a reference frame of 58 fundamental GPS stations with coordinates referred to ITRF94,epoch 1995.4 (SIRGAS, 1997). The establishment of the geocentric datum for the individual countries has been

carried out by connecting the national geodetic networks with the SIRGAS reference frame. In 2001, the Seventh

United Nations Regional Cartographic Conference for the Americas (UNRCC-A) recommended that all the American

countries integrate their national reference systems into SIRGAS.

Nevertheless, in the vertical component of the positions, many practical and scientific applications are still based on

the classical height systems, which refer to local reference levels without a known relationship to the SIRGAS frame.

These classical height systems were established using the mean sea level (MSL) at selected tide gauges as a reference

level (Fig. 4). Their realization was done by sea level observations at the individual tide gauges and averaging over

different periods (1020 years). The vertical control was extended over each country using mainly spirit levelling, but

in general the levelled heights have not been corrected for the gravity effects. Therefore, the existing South American

height systems present large discrepancies between neighbouring countries (e.g., Hernandez et al., 2002; Sanchez andMartnez, 2002; Subiza et al., 2002; Laura et al., 2002). They do not permit the data exchange, neither in a continental

nor in a global scale, and they are not capable of supporting the practical height determination with GPS techniques

(Fig. 5).

The only alternative to this unsatisfactory status is the definition of a new vertical reference system that solves the

mentioned problems, allows its continuous improvement and serves as a complement to the three-dimensional system

SIRGAS. During the IAG Scientific Assembly held in Rio de Janeiro in 1997, the Working Group III Vertical Datum

of the SIRGAS Project was created for this purpose.

The main objective of SIRGAS WG III is to define a modern unified vertical reference system for the Americas

within a global concept and to establish the corresponding reference frame. According to its recommendations, the

new vertical system is composed by (Drewes et al., 2002):

- two types of heights: ellipsoidal heights as a geometrical component and normal heights as a physical component;

- the corresponding reference surface, i.e., the quasigeoid;

- a reference frame, i.e., a set of fundamental stations to realize it;

- its maintenance through time in order to control its possible deformations.

The realization of this new vertical datum started in May 2000 by a GPS campaign including 184 stations over

the whole continent (Luz et al., 2002). This campaign included the stations of the SIRGAS 1995 reference frame, the

principal tide gauges of each country, including those serving as a reference for the classical height systems, some

stations at the borders to connect the first-order levelling networks between neighbouring countries, and additional

primary vertical control points, which were selected by each country. The stations refer to SIRGAS, shall be connected

by spirit levelling, and their geopotential numbers and normal gravity corrections shall be known.

The final solution of the geocentric coordinates of the vertical reference frame (SIRGAS, Campaign 2000) wasdiscussed and adopted during the meeting of the SIRGAS Committee during the IAG Symposium on Recent Crustal

Deformations in South America and Surrounding Areas in Santiago de Chile, October 2002 ( SIRGAS, 2002). The

new coordinates refer to ITRF2000, epoch 2000.4. This set of coordinates in combination with the older ones (SIRGAS

1995) and the different GPS geodynamical projects developed in the continent (such as CASA, CAP, SAGA, SNAPP,

etc.) allow to model station displacements and recent crustal deformations (Drewes and Heidbach, in press).

By means of this reference frame, the geometrical component of the new vertical system is realized. The devel-

opment of the physical component; however, requires the determination of normal heights and the quasigeoid as

the corresponding reference surface. Regarding the first task, the South American countries have been requested to

control their first-order levelling networks, to check the existing gravity data, and to calculate geopotential numbers

as input data for the normal height determination. The second task, the quasigeoid computation, must be performed

in a common way by all countries. Another important aspect being discussed is the level of the quasigeoid that


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Fig. 4. Reference tide gauges of national height systems in South America.

means the reference potential W0 at sea level and its realization. It was decided to adopt a globally defined reference

surface.

The present situation in South America may be summarized as follows:

- national height networks referred to about 15 different tide gauges are in use;

- the levelling lines cover a length of about 400,000 km realized at different epochs and mostly without gravity

reductions;

- some spirit levellings connecting neighbouring countries give first indications of differences between the levels of

the national networks.


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Fig. 5. Differences between national height reference systems in South America.

3.2. Europe

In Europe, about 20 national height reference systems are in use. The reference tide gauges of these height systems

(Fig.6) arelocated at various seas: Baltic Sea, North Sea, Mediterranean Sea, Black Sea, Atlantic Ocean.The differences

between the mean sea levels of the reference tide gauges amount to several decimetres (Fig. 1). They are caused by the

different oceanographic and meteorological influences and may be expressed by the difference between the mean sea

level and the geoid, i.e., the mean sea surface topography (MSST) at the corresponding tide gauges.

The used height datums go often back to historical definitions, and not all of them refer to mean sea level. There are

also zero levels referring to low tide (e.g., Ostend) or to high tide. For example, the Amsterdam zero point is defined

by mean high water in 1684.Three different types of heights are being used in Europe: normal heights, orthometric heights and normal-

orthometric heights. Normal heights are used in most countries of Central and Eastern Europe. Examples for the

use of orthometric heights are Belgium, Denmark, Finland, Italy and Switzerland.

After a break of 10 years, the work on the United European Levelling Network (UELN) was reactivated in 1994.

The objectives of the UELN-95 Project were to establish a unified height system for Europe at the 1 dm level with

simultaneous extension of UELN to Central and Eastern European countries (Augath, 1994, 1996). Starting point for

the UELN-95 Project was the repetition of the UELN-73/86 adjustment. The adjustment was performed by geopotential

numbers as a nodal point adjustment with variance component estimation for the individual countries and as a free

adjustment linked to the reference point of UELN-73 (Amsterdam). In 1998, more than 3000 nodal points were adjusted

and linked to the Normaal Amsterdams Peil. The normal heights in the system UELN-95/98 are available for more

than 20 participating countries (Sacher et al., 1999b).


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Fig. 6. Reference tide gauges of national height systems in Europe.

A combination of GPS, levelling and tide gauge observations was performed in the European Vertical Reference

NetworkEUVN (Ihde and Sacher, 2002). The initial objective of the EUVN Project was to unify different national

height datums in Europe within a few centimetres also in those countries, which were not covered by the UELN (Ihde et

al., 1999). In addition, this project was thought as the preparation of a geokinematic height reference system for Europe

and a start to connect levelled heights with GPS heights for the European geoid determination. At all EUVN points,

three-dimensional coordinatesXP in ITRS and in the European Terrestrial Reference System 1989 (ETRS89) as well as

geopotential numbers cP = W0 WP were derived. At the end, the EUVN is representing a geometric-physical referenceframe. In addition to the geopotential numbers the corresponding normal heights are given. The tide gauge stations

are connected to the sea level. EUVN consists of a total of 196 sites: 66 EUREF and 13 national permanent sites, 54

UELN and United Precise Levelling Network of Central and Eastern Europe (UPLN) stations, and 63 tide gauges. The

final GPS solution was constrained to ITRF96 coordinates (epoch 1997.4) by 37 stations. For many practical purposes,

it is useful to have also the ETRS89 coordinates available. To get conformity with other projects, the general relations

between ITRS and ETRS were used. The connecting levellings and computations of normal heights in UELN-95/98

were finished in 2000.

The Spatial Reference Workshop in Marne-la-Vallee recommended in November 1999 to the European Commission

the use of common European reference systems for geo-data referencing. With respect to the height component, the

workshop recommended that the European Commission:

- adopts the results of the EUVN/UELN initiatives, when available, as the definitions of the vertical datum and

gravity-related heights;

- includes the EUVN reference system so defined for the specifications of the products to be delivered to the EC,

within projects, contracts, etc;

- future promotes the wider use of the European vertical reference system within all member states, by appropriate

means.

The Technical Working Group of the IAG Subcommission for Europe (EUREF) is in charge of the definition of a

European Vertical Reference System (EVRS, Ihde and Augath, 2002; Ihde et al., 2002). The principles of its realization

were adopted at the EUREF Symposium 2000 in Troms by the Resolution No. 5:

The IAG Subcommission for Europe (EUREF)


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- decides to define a European Vertical Reference System (EVRS) characterized by:

the datum of Normaal Amsterdams Peil (NAP);

gravity potential differences with respect to NAP or equivalent normal heights;- endorses UELN-95/98 and EUVN as realizations of EVRS using the name EVRF2000,

- asks the EUREF Technical Working Group to finalize the definition and initial realization of the EVRS and to make

available a document describing the system.

In the EVRS conventions (2000), the system description is given in two parts (Ihde and Augath, 2001). The definition

part includes conventions for the datum, the vertical component, and the tidal system for a unique global vertical

system:

The vertical datum is the zero level for which the Earth gravity field potential W0 is equal to the normal

potential of the mean Earth ellipsoid U0: U0 = W0. The height components are the differences WP between

the potential WP of the Earth gravity field through the considered point P and the potential of the EVRS zero

level W0. The potential difference WP is also designated as geopotential number cP =WP WP = cP. Normal

heights are equivalent to the geopotential numbers. The EVRS is a zero tide system in agreement with the IAG

Resolutions.

For the realization, the available results of the continental EUVN and UELN Projects in connection with the GRS80

parameters were adopted (EVRF2000). This implies an inconsistency of the system, because the realization is differentto the definition, but it is a good approximation of a unique global vertical reference frame. Transformation parameters

between the national height systems and the EVRF are available for geo-information referencing in a unique system

(Sacher et al., 1999a).

The present situation in Europe may be summarized as follows:

- National height networks referred to about 20 different tide gauges are in use.

- The United European Levelling Network (UELN) is a common adjustment of geopotential numbers of the national

first-order height networks at different epochs with a line length of about 170,000 km.

- EVRS conventions are in preparation for geo-spatial data referencing of the European Commission (Ihde and Augath,

2001).

Recently, it was proposed to establish a kinematic European Combined Geodetic Network (ECGN) to com-

bine the geometric and height reference systems with Earth gravity field parameter estimation ( Ihde et al., 2004).

It is in agreement with the planned IAG Project of an Integrated Global Geodetic Observation System (IGGOS,

Rummel et al., 2002). ECGN is a network for the combination of time series of spatial geometric observations

(GNSS: GPS/GLONASS and in the future GALILEO), gravity field related observations and parameters (grav-

ity, Earth and ocean tides), and supplementary information (meteorological parameters, surrounding information

of the stations, e.g., eccentricities and ground water level). The project is a common action of the Commis-

sion 1, Sub-Commission EUREF, and the Commission 2, Sub-Project European Gravity, of the IAG in its new

structure.

The call for participation is structured into two stages. The first call is directed to the implementation of the ECGN

stations following the concept of the project. The ECGN stations have the standard observation techniques GNSS

(GPS/GLONASS, GALILEO), gravity (super conducting gravimeter and/or absolute gravimeter),levelling connectionsto nodal points of UELN/EVRS, meteorological parameters and other supplemented measurements. Standard for the

ECGN stations is a local network for the derivation of eccentricities in a 1 mm accuracy level in all three spatial

components. All ECGN stations are permanent GPS stations. Guidelines for the observations have to be followed. At

present, 18 European countries proposed 65 stations for this project.

In parallel to the first call, the ECGN Working Group has to prepare the second step, i.e., the call for analysis

and investigations. The main action of the ECGN Working Group in the first step is a pilot study of combination of

different observations with available stations to get experiences in combination of spatial information with gravity field

related data. For data collection of super conducting gravimeter data, the data centre of the Global Geodynamic Project

(GGP) could be used. Levelling data of ECGN will be collected at the UELN/EVRS data centre. Local data centres for

absolute gravity data and super conducting gravimeter data should be installed in the first stage by the ECGN Working

Group.


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Table 1

Comparison of EUREF and SIRGAS concepts

EUREF SIRGAS

EVRS conventions (2000) WG III Vertical Datum (2001)

Physical heightGeopotential differences WP = W0 WP = cP Geopotential numbers cPNormal heights Hn are equivalent Normal heights Hn are equivalent

Geometrical height

{EUVN/ETRS89} Ellipsoidal heights h in SIRGAS (=ITRF)

Zero level

W0 = U0 (mean Earth ellipsoid) W0 from a global gravity model (GGM)

BVP

TP = UP + TP, TP from a European geoid TP from a GGM (quasigeoid)

Reductions

Zero tide system Time dependency (velocities)

Specification of realizationRealization at present by UELN (levelling network, NAP), in

future the use of ECGN stations is planned

Realization by a set of fundamental stations (SIRGAS,

tide gauges, stations at borders between countries)

3.3. Comparison of EUREF and SIRGAS concepts

The comparison of the concepts of EUREF and SIRGAS for the development of the height systems shows

an agreement in the main components which may serve as a contribution to a unified World Height System

(Table 1).

4. Concept of the realization of a World Height System (WHS)

Concepts for the realization of a World Height System (WHS), i.e., the unification of height systems, and the

connected role of fundamental parameters were discussed during the last twenty yeas in IAG Sections, Com-

missions and Special Study Groups, and in several publications. Concerning the strategies for the unification

of existing height networks, a general agreement between most of the authors can be assumed (e.g., Rummel

and Teunissen, 1988; Rapp and Balasubramania, 1992; Balasubramania, 1994; Rapp, 1994; Rapp et al., 1994;

Kearsley, 1998; Bursa et al., 2002a). More controversial was the discussion about the zero level of a WHS

(e.g., Bursa et al., 1998a,b, 2002b; Yurkina, 1996; Ihde and Augath, 2001; Hipkin, 2002; Rummel and Heck,

2001).

Let us start with the general concept mentioned above: the Earth surface (solid and fluid) is determined by the

time dependent geometry XP and the potential of the Earth gravity field WP in superficial points P. From this point

of view, the height determination is a part of the determination of the external Earth gravity field. It has to be con-

sidered, that the mean sea surface (MSS) as the mean geometrical fluid surface of the Earth does not coincide with

the surface described by the solution of the BVP. The difference is the sea surface topography, the non equipo-

tential part of the MSS. The mean sea level (MSL) has to be distinguished between discrete MSL, e.g., at a tide

gauge, and a mean value over an area or over the globe. The discrete MSL is the MSS as the average over a cer-

tain time period and over a limited area. Global MSL means the average over a certain time period and over the

globe.

4.1. Elements of a physical height system

A height system can be described by three elements: the reference surface, the height datum and the type of height

coordinates. The elements have to be established by conventions regarding the definition and the realization including

the time variations.


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4.1.1. Reference surface

The reference surface for physical heights is a defined surface of the Earth gravity field, e.g., coinciding at sea level

with the equipotential surface W0. It has to be mentioned that in sea level the geoid is identical with the quasigeoid. For

geometrical heights the reference surface is given by a mathematical function, e.g., an ellipsoid. The level ellipsoid is

an equipotential surface of the normal Earth gravity field U0. For the combination of physical and geometrical heights,

the relation between the reference surfaces has to be defined and to be determined.

4.1.2. Height datum

The definition of the height datum relates the heights at the Earth surface to the heightreference surface. As discussed

above, the level of the reference surface of a World Height System (WHS) shall be the mean sea surface (MSS) or

mean sea level (MSL). For the combination of physical heights with geometrical heights the reference ellipsoid shall

have the same dimension as the MSL and shall be located geocentrically. In this case, the reference ellipsoid is the

mean Earth ellipsoid (ME) with U0ME = W0MSL.

Several authors propose to use U0 (or W0) as the primary parameter of the level ellipsoid instead of the semi-major

axis a. Bursa mentions as a principal advantage that W0 is independent from the tidal system. Yurkina (1996) states:

Since the potential W0 enters directly into the fundamental equations of the theory of the Earths figure it is natural to

adopt GM, J2, and W0 as the primary geodetic parameters. The semi-major axis of the reference ellipsoid has also a

physical meaning, however, this is secondary. It has to be considered, that in case of using the geometrical referencesurface a decision on the tidal system has to be done.

The mean Earth ellipsoid is the best fitting ellipsoid to the geoid. Defining the level of the geoid by the MSL,

the realization of the height datum needs further specifications for the determination of the MSL. The International

Hydrographic Organization (IHO) defines the MSL as the average height of the sea surface at a tide station for all

stages of the tides over a 19-year period usually determined from hourly height readings measured with respect to

a fixed pre-determined reference level (Chart Datum). For the global MSL it has to be defined, over which area the

individual MSLs shall be averaged. A natural limit are the ice-free zones of the oceans. Because of the changes of

MSL with time an epoch for the average level has also to be defined.

As a consequence, the following conventions for the global MSL are proposed here:

- the MSL is the average of the heights of the free oceans;- it is averaged in an area from 60 to +60 latitude;

- it has to be calculated over a minimum time period of 18.6 years;

- it shall be referred to the epoch 2000.0;

- it shall be reduced to the level of the zero tide system.

4.1.3. Type of height coordinates

The basis of any physical height coordinates is the geopotential at the Earth surface WP relative to the reference

surface W0, i.e., the geopotential number cP = W0 WP. Normal heights hN= cP/ are seen as the most natural ones.

All information used for its determination is given by observations and unique mathematical functions at the Earths

surface: the geopotential number cP and the mean normal gravity . The orthometric heights h0 = cP/g combine

observed data (cP) with a physical model, the mean gravity g, inside the body of the Earth. The equivalent disturbing

geopotential TP as a solution of the classical BVP is given at the geoid P, inside the Earth. Depending on the gravitymodels used for the reduction from P to P several co-geoids are derived.

Another problem is the tidal system. The IAG Resolution No. 16 adopted at the IUGG General Assembly in Hamburg

1983 recommends theuse of thezero tide systemfor geodetic reductions, i.e., the permanent tidal effect of sun, moon and

the planets shall not be reduced. The gravity community is following this recommendation, in geometric reductions it is

not adopted (Makinen, 2001). ITRF solutionsare reduced to a tide-free system. The main problem of the tide free system

is that the value for the Love number kof the permanent tide is not known with sufficient accuracy. The parameters are

not observable. As a matter of fact, there is no reason to use the tide free system. The observed MSL as the average of sea

surface heights over a period of 18.6 years corresponds to a mean crust. From the theoretical point of view, the zero tide

systemhas to be preferred. However, it will be not easy to change thesituation, because theparameters of theITRF and all

the densification networks would have to be changed. The IAG will have to decide either to realize the 1983 Resolution

No. 16 or to recommend another procedure. This is necessary for combination processes of gravity and geometric


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data (Ihde and Augath, 2001). In any case, validated Earth and ocean tide models have to be used (Baker and Bos,

2003).

4.2. Observations

The realization of MSL is done by satellite altimetry combined with tide gauge observations, GPS observations attide gauges, and a global gravity model (GGM), e.g., from the actual satellite gravity missions CHAMP, GRACE and

GOCE. The permanent monitoring of MSL is an important task, e.g., of a future altimetry service. Long-term time

dependent variations have to be considered for parameters describing the WHS, the MSL and its influence to W0, the

geopotential numbers at the Earth surface cP, and the geometry of the Earth surface XP (Baker, 1993; Nerem et al.,

1994)

The vertical gradient of the geopotential, the gravity gP =WP/h, gives more sensitive information about vertical

deformations. Therefore, a WHS with a consistent long-time accuracy of 109 or better with respect to the geometrical

terrestrial reference system has to be based on a network of fundamental stations which combines space and gravity

techniques. Investigations of observations in such stations demonstrate the possibility of complement and mutual

control of independent geometrical and physical techniques.

5. Discussion and conclusions

The determination and monitoring of the solid and fluid surface of the Earth by combining geometric and gravity

techniques is a main task of geodesy. It includes the monitoring of the sea surface as a key item in global change

research. The Earth surface is completely determined if its geometry and gravity potential is known. In this under-

standing the height determination is a special case of the determination of the external Earth gravity field. Space

techniques allow a positioning accuracy of 109 in global and continental scale. Gravity field parameters including

the physical height component are at present 23 orders of magnitude less accurate determinable than the geometrical

parameters. The main reason is that for the vertical component no global height reference system exists which is com-

parably defined and realized as the terrestrial reference system. Maintenance of the long-time stability of the terrestrial

reference system with an accuracy of 109 in the global scale needs a combination with gravity field parameters.

This supports the establishment of a WHS with consistent conventions and parameters to geometrical and gravity

systems.

Therealizationof a unifiedglobal height referencesystem, here calledWorldHeight System (WHS)needsdefinitions

and conventions comparable with conventions of the International Earth Rotation Service (IERS). A World Height

System (WHS) and a World Height Frame (WHF) as conventional vertical reference systems could be the counterparts

to the International Terrestrial Reference System (ITRS) and the International Terrestrial Reference Frame (ITRF) as

the conventional terrestrial reference system in accordance with the IERS conventions. Another possibility would be

to integrate the WHS into these conventions. Part of the objectives for the introduction of a WHS is the definition of

a set of consistent reference system parameters. The mean Earth ellipsoid plays a central role. The reference potential

W0 is suitable for the realization of a WHS.

For the realization of a WHF and its combination with the ITRF a set of fundamental stations is necessary for

modelling time dependent phenomena of the solid Earth, the Earth gravity field, the oceans, the atmosphere andthe hydrosphere for different applications in positioning. The fundamental stations have to integrate two groups of

observations: the geometric and the gravity techniques.

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