In 2015, the International Association of Geodesy defined the International Height Reference System (IHRS) as the conventional gravity field-related global height system. The IHRS is a geopotential ...reference system co-rotating with the Earth. Coordinates of points or objects close to or on the Earth’s surface are given by geopotential numbers
C
(
P
) referring to an equipotential surface defined by the conventional value
W
0
= 62,636,853.4 m
2
s
−2
, and geocentric Cartesian coordinates
X
referring to the International Terrestrial Reference System (ITRS). Current efforts concentrate on an accurate, consistent, and well-defined realisation of the IHRS to provide an international standard for the precise determination of physical coordinates worldwide. Accordingly, this study focuses on the strategy for the realisation of the IHRS; i.e. the establishment of the International Height Reference Frame (IHRF). Four main aspects are considered: (1) methods for the determination of IHRF physical coordinates; (2) standards and conventions needed to ensure consistency between the definition and the realisation of the reference system; (3) criteria for the IHRF reference network design and station selection; and (4) operational infrastructure to guarantee a reliable and long-term sustainability of the IHRF. A highlight of this work is the evaluation of different approaches for the determination and accuracy assessment of IHRF coordinates based on the existing resources, namely (1) global gravity models of high resolution, (2) precise regional gravity field modelling, and (3) vertical datum unification of the local height systems into the IHRF. After a detailed discussion of the advantages, current limitations, and possibilities of improvement in the coordinate determination using these options, we define a strategy for the establishment of the IHRF including data requirements, a set of minimum standards/conventions for the determination of potential coordinates, a first IHRF reference network configuration, and a proposal to create a component of the International Gravity Field Service (IGFS) dedicated to the maintenance and servicing of the IHRS/IHRF.
The vertical height system in Kenya is anchored on a single levelling-based tidal gauge, which is referred to as mean sea level. The fusion of existing height systems into the world height system is ...one of the primary objectives of the International Height Reference System (IHRS) implementation. Computing the datum offset with regard to the global IHRS datum and the zero-height geopotential value can help achieve this goal in part. This paper studies the approach of using a Global Geopotential model (GGM) with the GNSS-levelling as a convenient method for vertical datum offsets’ computation that may connect two or more vertical datums. To reduce the geoid omission error of the GGMs, an optimized GGM is developed and utilized up to a maximum of 3600° and order. For the first time, the numerical analyses of this work reveal the zero-height geopotential and its associated standard error of the Kenyan vertical datum, from which the datum offsets with the IHRS were estimated. Values of 62636850.996±0.104m2s−2 and −24.5±1.04cm were obtained as the geopotential of the zero-height and vertical datum offset with respect to the global value, respectively.
•The unification of current height systems into the global height system is a key objective of the IHRS realization.•Vertical datum parameters computed using geopotential numbers and/or external geoid models.•A combined GGM is created by combining spherical harmonic coefficients of different GGMs.•A maximum degree and order of 3600 will keep the effect of the omission error below 1 cm.•The geopotential value of 62636850.996 and a datum offset value of 24.5cm were adopted as vertical datum parameters.
Height unification using GOCE Rummel, R.
Journal of Geodetic Science (Online),
12/2012, Volume:
2, Issue:
4
Journal Article
Peer reviewed
Open access
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 Vxx , Vyy, Vzzand Vxz. 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.
Highly accurate international height reference frames with long-term stability, global consistency, and homogeneity are crucial for monitoring sea level variations, understanding climate change, ...managing disasters, and supporting other applications that benefit scientific research and societal well-being. Currently, there are over 100 local height reference systems worldwide. Unifying these systems is a pivotal step toward constructing international height reference frames. The method introduced in this study—the gravity frequency shift via Satellite Frequency Signal Transfer (SFST)—represents a groundbreaking relativistic geodetic approach, demonstrating its potential to surpass the constraints of conventional techniques. The advent of high-precision optical atomic clocks (OAC) with an accuracy level of 1×10−18 has facilitated this method's implementation. The International Association of Geodesy (IAG) has established the International Height Reference System (IHRS) and its practical realization, the International Height Reference Frame (IHRF). Our study focuses on two neighbouring height systems: the China Height System (CHS) and the Nepal Height System (NHS), separated by the Himalayas and the Tibetan plateau. We aim to unify these two systems by determining the geopotential and orthometric height differences between their respective height datum stations: the Qingdao Height Datum Station (QHDS) and the Madar Height Datum Station (MHDS) using a simulation experiment with the method mentioned above. Using an OAC with an accuracy of 1×10−18, we identified a geopotential difference of −8.348±0.464m2s−2 and an orthometric height difference of 0.786±0.047 m between QHDS and MHDS. These results suggest that the introduced method could unify any two height systems with few-centimeter-level precision, emphasizing its significance in contributing to the construction of the IHRS/IHRF with today's required precision. In summary, the SFST technique is a novel geodetic method that offers an alternative for height system unification, delivering centimeter-level precision, surpassing traditional methods, and supporting the development of the IHRF.
In this work, we analyzed the quality of height transformation between the old height system SVS2000 (vertical datum Trieste) and the new height system SVS2010 (vertical datum Koper). Based on the ...height differences of the benchmarks between the old and the new height systems stabilised in the area of eastern Slovenia, we determined the height transformation surface for two areas of different sizes. For both areas we analyzed the influence of different interpolation methods and the influence of using height differences of benchmarks of different orders of the levelling net. We found that the quality of height transformation is satisfactory for most surveying services. We have also analyzed the quality of the height transformation based on the average height difference of the benchmarks by using the SiVis software, which is intended for the transformation of ellipsoidal heights obtained by GNSS measurements, between the old and the new height systems.
Recently, a new national height reference system was implemented: the Slovenian Height System 2010 (SVS2010). This new system replaced the Slovenian Height System 2000 (SVS2000). It is a new ...realisation of a national height system, which is based on new levelling and gravity surveys and recent tide gauge data. Its implementation changes the height datum (from Trieste to Koper) as well as the type of heights (from normal-orthometric to normal). Consequently, differences between the old and new height reference systems from 1.4 cm to 30.8 cm were detected. Unfortunately, there is no simple transformation between the two height reference systems. The surveyor must choose an appropriate method of local transformation or recalculation based on the given data and the required accuracy. To provide all necessary information for the users, the Surveying and Mapping Authority of the Republic of Slovenia has, in cooperation with the Faculty of Civil and Geodetic Engineering at the University of Ljubljana, prepared a new Technical instruction for the use of the new national height system. Online software called SiVis is also available for converting GNSS-based heights into both height reference systems (SVS2000 and SVS2010). Due to some problems with the (old) AMG2000/Trst geoid model near the national boundary, this model was extrapolated to a buffer covering parts of neighbouring countries. EPSG codes for both national height reference systems of Slovenia were also created.
All realizations of the European Vertical Reference System (EVRS) computed so far are solely based on geopotential differences obtained by spirit leveling/gravimetry. As such, there are no direct ...connections between height benchmarks separated by large water bodies. In this study, such connections are added by means of model-based hydrodynamic leveling resulting in a new, yet unofficial realization of the EVRS. The model-derived mean water levels used in computing the hydrodynamic leveling connections were obtained from the Nemo-Nordic (Baltic Sea) and 3D DCSM-FM (northwest European continental shelf) hydrodynamic models. The impact of model-based hydrodynamic leveling on the European Vertical Reference Frame is significant, especially for France and Great Britain. Compared to a solution which only uses spirit leveling/gravimetry, the differences in these countries reach tens to hundreds of
kgal
mm
. We also observed an improved agreement with normal heights obtained by differencing GNSS and the European gravimetric quasi-geoid 2015 (EGG2015) heights. In Great Britain, the south-north slope of 48 mm
deg
-
1
present in the solution which uses only spirit leveling/gravimetry data reduced to 2.2 mm
deg
-
1
. In France, the improvement is confined to the southwest. The choice of the period over which water levels are averaged has an impact on the results as it determines, among others, the set of tide gauges available to establish the hydrodynamic leveling connections. When using an averaging period that can be considered as the least preferred choice based on three established criteria, the positive impact for France has gone. For Great Britain, the estimated south-north slope became 12.6 mm
deg
-
1
. This is larger than the slope obtained using the most preferred averaging period but still substantially lower compared to the slope associated with a solution that uses only spirit leveling/gravimetry.
Coastal sea level is observed at tide gauge stations, which usually also serve as height reference stations for national networks. One of the main issues with using tide gauge data for sea level ...research is that only a few stations are connected to permanent GNSS stations needed to correct for vertical land motion. As a new observation technique, absolute positioning by SAR using off the shelf active radar transponders can be installed instead. SAR data for the year 2020 are collected at 12 stations in the Baltic Sea area, which are co-located to tide gauges or permanent GNSS stations. From the SAR data, 3D coordinates are estimated and jointly analyzed with GNSS data, tide gauge records and regional geoid height estimates. The obtained results are promising but also exhibit some problems related to the electronic transponders and their performance. At co-located GNSS stations, the estimated ellipsoidal heights agree in a range between about 2 and 50 cm for both observation systems. From the results, it can be identified that, most likely, variable systematic electronic instrument delays are the main reason, and that each transponder instrument needs to be calibrated individually. Nevertheless, the project provides a valuable data set, which offers the possibility of enhancing methods and procedures in order to develop a geodetic SAR positioning technique towards operability.
The International Height Reference System (IHRS), adopted by International Association of Geodesy (IAG) in its Resolution No. 1 at the XXVI General Assembly of the International Union of Geodesy and ...Geophysics (IUGG) in Prague in 2015, contains two novelties. Firstly, the mean-tide concept is adopted for handling the permanent tide. While many national height systems continue to apply the mean-tide concept, this was the first time that the IAG officially introduced it for a potential field quantity. Secondly, the reference level of the height system is defined by the equipotential surface where the geopotential has a conventional value
W
0
= 62,636,853.4 m
2
s
–2
. This value was first determined empirically to provide a good approximation to the global mean sea level and then adopted as a reference value by convention. I analyse the tidal aspects of the reference level based on
W
0
. By definition,
W
0
is independent of the tidal concept that was adopted for the equipotential surface, but for different concepts, different functions are involved in the
W
of the equation
W
=
W
0
. I find that, in the empirical determination of the adopted estimate
W
0
, the permanent tide is treated inconsistently. However, the consistent estimate from the same data rounds off to the same value. I discuss the tidal conventions and formulas for the International Height Reference Frame (IHRF) and the realisation of the IHRS. I propose a simplified definition of IHRF geopotential numbers that would make it possible to transform between the IHRF and zero-tide geopotential numbers using a simple datum-difference surface. Such a transformation would not be adequate if rigorous mean-tide formulas were imposed. The IHRF should adopt a conventional (best) estimate of the permanent tide-generating potential, such as that which is contained in the International Earth Rotation and Reference Systems Service Conventions, and use it as a basis for other conventional formulas. The tide-free coordinates of the International Terrestrial Reference Frame and tide-free Global Geopotential Models are central in the modelling of geopotential for the purposes of the IHRF. I present a set of correction formulas that can be used to move to the zero-tide model before, during, or after the processing, and finally to the mean-tide IHRF. To reduce the confusion around the multitude of tidal concepts, I propose that modelling should primarily be done using the zero-tide concept, with the mean-tide potential as an add-on. The widespread use of the expression “systems of permanent tide” may also have contributed to the confusion, as such “systems” do not have the properties that are generally associated with other “systems” in geodesy. Hence, this paper mostly uses “concept” instead of “system” when referring to the permanent tide.
Since the 1960s, the analysis of disturbed satellite orbits to infer Earth’s gravity field functionals has been an important element in determining the Earth’s gravitational field. The long ...wavelengths of the gravitational field are recovered through the analysis of non-Keplerian variations in the orbital path of artificial satellites, from their tracking from ground stations (Satellite Laser Ranging, Doppler Orbitography and Radiopositioning Integrated by Satellite, and Precise Range And Range-Rate Equipment), from satellite-to-satellite tracking, or by microwave interferometry. In addition, differences in gravitational acceleration in three mutually orthogonal dimensions can be determined by employing a differential accelerometer carried on artificial satellites (satellite gravity gradiometry, SGG). Satellite gravimetry provides global information (long wavelengths) of the Earth’s gravitational field, which is the fundamental basis for the implementation of Global Geopotential Models (GGMs). The GGMs are one of the key tools for the representation of the Earth’s gravity field and, therefore, for the establishment of a Global Height System (i.e., International Height Reference System), whose fundamental reference surface is defined in terms of a geopotential value. In this study, the validation of high-resolution GGMs (coefficients up to degree 2190) was performed based on their performance in Ecuador by comparing geoid heights estimated by the GGMs with the corresponding values derived from Global Navigation Satellite System/leveling records. Furthermore, geopotential values from the GGMs are compared with the corresponding value obtained for the Ecuadorian Vertical Datum by solving the fixed geodetic boundary value problem. The obtained results indicated that the precision of the high-resolution GGMs does not reach the established requirements for the geopotential computation in the International Height Reference Frame fundamental stations.
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