Strategy for the Realization of the International Height Reference System (IHRS)

1 Deutsches Geodätisches Forschungsinstitut, Technische Universität München 2 Helmholtz-Zentrum Potsdam, Deutsches GeoForschungsZentrum 3 Astronomical and Physical Geodesy, Technische Universität München 4 Politecnico di Milano 5 Federal Office of Topography, swisstopo 6 Lantmäteriet, Swedish mapping, cadastral and land registration authority 7 University of Calgary 8 Research Institute of Geodesy, Topography and Cartography

2) Everyone using GNSS positioning and requiring physical heights demands with consistency at the cm-level and worldwide.
H = h -N in theory, but in practice, e.g.
 Physical heights H usually refer to different local vertical reference levels (more than 100 worldwide).
 Different ellipsoid parameters (a, GM) are used in geometry and gravity.
 H and h are given in different reference epochs (usually dH/dt is unknown).
 Different solid Earth tide systems for H, h and N are used.
 Different reductions are applied to H, h and N (ocean and atmospheric tides, ocean, atmospheric and hydrologic loading, post-glacial rebound, etc.).

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A global unified height system is needed to ensure consistency between h, H, N, worldwide and at the cm-level Vertical coordinates in terms of potential

International Height Reference System (IHRS) IAG Resolution No. 1, Prague, July 2015
1) Vertical coordinates are potential differences with respect to a conventional W 0 value: 2) The position P is given by the coordinate vector X P (X P , Y P , Z P ) in the ITRF, i.e.W(P) = W(X P ) 3) The determination of X(P), W(P) (or C(P)) includes their variation with time, i.e., Ẋ(P), Ẇ(P) (or Ċ(P)).
The realization of the IHRS is understood to be a component of the Global Geodetic Reference Frame (UN GGRF resolution 2015).

Realization of the IHRS
A reference frame realizes a reference system in two ways:  physically, by a solid materialization of points (or observing instruments),  mathematically, by the determination of coordinates referring to that reference system.
 The coordinates of the points are computed from the measurements, but following the definition of the reference system.
Immediate objectives regarding the IHRS:  Establishment of an International Height Reference Frame (IHRF) with high-precise primary coordinates X P , Ẋ P , W P , Ẇ P .
 Identification and compilation/outlining of the required standards, conventions and procedures to ensure consistency between the definition (IHRS) and the realization (IHRF); i.e., an equivalent documentation to the IERS conventions is needed for the IHRS/IHRF.
Possibilities for the determination of W P Possibilities for the determination of W P 1) Levelling + Gravimetry: 2) Combined (high-resolution) gravity field models: 3) High-resolution gravity field modelling:

1) W P from Levelling + Gravimetry
 This strategy is needed to integrate the existing height systems into the IHRS, but its accuracy is not enough for establishing the core network of the IHRS realisation. This method is not (yet) suitable. Main drawback: incomplete gravity signal due to lack of data and restricted accessibility to terrestrial gravity data.

Selection of possible IHRF reference stations
1) Geodetic observatories (GGOS core stations) 2) Existing VLBI stations collocated with GPS 3) Existing SLR stations collocated with GPS 4) Existing DORIS stations collocated with GPS Selection of possible IHRF reference stations 1) Geodetic observatories (GGOS core stations).
3) Existing SLR stations collocated with GPS. 4) Existing DORIS stations collocated with GPS.
In progress (expected to be ready by the end of the year): 1) Tide gauges connected to the vertical networks (in coordination with TIGA).
2) Reference stations of the new Global Absolute Gravity Reference System (in coordination with H. Wziontek).3) Densification with continuously operating GNSS stations in cooperation with the regional IAG sub-commissions (e.g.SIRGAS and the Sub-commission for the geoid in South America).
Still open: 1) Collocation with time laboratories (to provide high-precise potential values for reference clocks).
Once the reference stations are selected, next steps are: 1) To contact local experts to collect the gravity data.
2) To compute a preliminary IHRF solution (first results expected to be presented during IAG2017).

1) Establishment of IHRS stations in the SIRGAS region
 To select some (1 to 5) continuously operating SIRGAS reference stations in each country (well distributed and materialized by a monument on the ground; stations on the top of buildings are not welcome). To survey gravity data around the selected SIRGAS reference stations (about 150 gravity points well distributed around each station up to a distance of about 200 km). Coordinates of gravity points determined with GNSS positioning (2 cm). It is desirable that the gravity surveys refer to absolute gravity stations.
2) Integration of the existing Latin American height systems into the IHRS/IHRF  First order levelling (with gravity data) of SIRGAS reference stations (optimal if IHRF stations are levelled). Reference tide gauges connected to SIRGAS. Combination of ellipsoidal heights, levelling-based physical heights, tide gauge registrations, satellite altimetry observations and height-resolution gravity field modelling.

SIRGAS and the IHRS/IHRF
3) SIRGAS member countries should take advantage of the SIRGAS-WG3 activities:  Capacity building and software for the processing of gravity data  Capacity building and software for the adjustment of levelling networks and computation of geopotential numbers  Until now: Rio (2012), La Paz (2014), Curitiba (2015), Quito (2016), San José (2017)  Once the levelling networks are properly adjusted, a workshop about the integration of the existing height systems into the IHRS/IHRF can be planned.

On-going activities
1) Selection of core stations for the IHRF  in agreement with the GGOS Bureau for Networks and Observations, main requirement are gravity data around (~200 km) core stations for high-resolution gravity field modelling.

3) Estimation of potential values
 Evaluation of different methodologies and compilation of guidelines for high-resolution gravity field modelling.
2) Identification of required standards and conventions

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only gravity field modelling: Satellite orbits and gradiometry analysis Satellite tracking from ground stations (SLR) Satellite-to-satellite tracking (CHAMP, GRACE) Satellite gravity gradiometry (GOCE) Satellite altimetry (oceans only) High-resolution gravity field modelling: Stokes or Molodensky approach Satellite altimetry (oceans only) Gravimetry, astro-geodetic methods, levelling, etc. Refer to local vertical datums with unknown potential value W 0,local = ? To determine W P , it is necessary to estimate the level difference between the global W 0 and the local W 0,local  W = W 0 -W 0i  Expected accuracy of W: cm in well-surveyed regions, dm in sparsely surveyed regions, extreme cases up to 1 m.P from Levelling + Gravimetry Example: W (in cm) for the South American height systems w.r.t.the IHRS W 0 value.

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Example:  Global network with known X coordinates  Differences between the W P values derived from EGM2008 (Pavlis et al. 2008) and EIGEN6C4 (Förste et al. 2014), both at n=2190  Differences larger than ±200 x 10 -2 m 2 s -2 (up to ±20 m 2 s -2 )  Desired accuracy for W P : ±3 x 10 -2 m 2 s -2 2) W P from combined (high-resolution) GGMs 3) W P from high-resolution gravity field modelling At present, the only possibility to get closer to the accuracy required for the realisation of the IHRS gravity field modelling: Satellite orbits and gradiometry analysis Satellite tracking from ground stations (SLR) Satellite-to-satellite tracking (CHAMP, GRACE) Satellite gravity gradiometry (GOCE) Satellite altimetry (oceans only) High-resolution gravity field modelling: Stokes or Molodensky approach Satellite altimetry (oceans only) Gravimetry, astro-geodetic methods, levelling,etc.Homogeneously distributed gravity points around the IHRF reference stations up to 210 km (~ 2°).The gravity data may exist or have to be observed. Minimum accuracy of the gravity values: ±20 μGal. Gravity point positions with GPS. In mountain areas ~50% more gravity points. Uncertainties of GGM and DTM must be added.A global network  worldwide distribution, including  A core network  to ensure perdurability and long term stability  Regional and national densifications  local accessibility 2) Collocated with:  fundamental geodetic observatories  connection between X, W, g and time  to support the GGRF;  continuously operating reference stations  to detect deformations of the reference frame;  reference tide gauges and national vertical networks  vertical datum unification;  reference stations of the new Global Absolute Gravity Reference System (see IAG Resolution 2, Prague 2015).

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in agreement with the GGOS Bureau for Products and Standards, main requirement is the harmonization with the IERS conventions.4)Vertical datum unification Roadmap for the integration of the existing local height systems into the IHRF.Coordinated work between: GGOS Focus Area Unified Height System  International Gravity Field Service (IGFS)  IAG Commission 2 (Gravity field)  IAG Commission 1 (Reference Frames)  IAG Inter-commission Committee on Theory (ICCT)  Regional/national vertical reference systems Working Group on the Strategy for the Realization of the International Height Reference System (IHRS), more information at http://ihrs.dgfi.tum.de