International Height Reference System Research Articles

Assessment of geoid models for geopotential values determination in Mexico'S continuous monitoring network

The requirements of the reference systems related to the vertical part are aimed at adopting a global height system that allows taking advantage of the development of satellite technology that provides terrestrial data with higher quality. Due to this need, the International Association of Geodesy (IAG) has proposed the realization and implementation of the International Height Reference System (IHRS), based on geopotential numbers obtained from the gravity potential difference at a point on the Earth's surface (W(P)) referred to the geoid (W0), whose value adopted by convention corresponds to 62636853.4 m2s-2. Nowadays, efforts are underway worldwide to materialize this system. Considering this, the present work entails the analysis of information gathered from SIRGAS continuous monitoring stations in Mexico: MTY2, IDGO, INEG, MERI, and ICAM, to estimate its gravity potential from sufficiently precise geocentric coordinates and absolute gravity values, which when combined with heights derived from geoid models, allows obtaining a modern height system such as the IHRS. The analysis aims to evaluate the feasibility of estimating the gravity potential at the stations, by using precise geocentric coordinates and absolute gravity values which when combined with high-resolution geoid models such as EGM2008, GGM10, EIGEN6C4, XGM2019e_2159, SGGUGM2, and the xGEOID20B, to implement a modern height reference system in Mexico; as well as to contribute to the International Height Reference Framework (IHRF), which in its latest version only includes the MERI station, located in Mérida, Yucatán. Therefore, we consider that for their characteristics the stations analyzed can be included to densify the frame in the implementation of the system. The results show the differences in gravity potential in the different regions of the country, reinforcing the need to consider more reference stations. Additionally, benchmark points close to the selected stations were analyzed to determine the reference potential value of the GGM10, with which it was also possible to analyze the behavior between the observed geoid and the different geoid models, toward the modernization of the official height system, which is based on orthometric heights called NAVD88, which shows us the differences between the geoid observed with the official height system and the analyzed models. Finally, the study examines the consistency of the calculated orthometric heights with geopotential numbers derived from the different geoid models.

Connecting the Brazilian Vertical System to the International Height Reference Frame by estimating the vertical datum parameters

One of the challenges in the unification of the global vertical datum is to determine the vertical offset between the local vertical datum and the global vertical datum. Since 2015, the scientific community has been working on the unification of the global vertical datum, following the publication of the resolution for the definition and realization of an International Height Reference System. This paper aims to estimate the vertical offset in Brazil (Imbituba and Santana Data) by combining a regional gravity field model, using the Geodetic Boundary Value Problem approach applying the Remove-Compute-Restore procedure, and GNSS/leveling data. In the Imbituba vertical datum 1271 stations were used and 66 stations were connected to the Santana tide gauge. The results showed that the geopotential value of Imbituba was 62,636,849.87 ± 0.224 m2s-2, and the vertical offset concerning the reference surface (W0) was 0.358 ± 0.023 m. In Santana, the geopotential value was 62,636,836.88 ± 4.108 m2s-2, and the vertical offset was 1.689 ± 0.420 m. The offset between Imbituba and Santana was computed once the physical connection between Brazil's two local vertical data is a challenge. The estimated value was 1.331 ± 0.421 m. This means the Santana vertical datum is 1.331 m higher than the Imbituba vertical datum.

Estimation of the zero-height geopotential value and datum offset for the Kenya vertical network using an optimized earth model

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.

Unifying the Nepal height system and China height system based on gravity frequency shift approach

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.

Global Geopotential Models assessment in Ecuador based on geoid heights and geopotential values

Abstract 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.

A first step towards a national realisation of the international height reference system in Sweden with a comparison to RH 2000

Abstract The International Height Reference System (IHRS) was defined by the International Association of Geodesy in 2015. Since then, the international geodetic community has been working on the specification and establishment of its realisation, the International Height Reference Frame (IHRF). This frame will primarily be realised by geopotential numbers (or physical heights) in a sparse global reference network. In Sweden, only one such global station is planned. Regional and national realisations (or densifications) computed in accordance with the IHRS definition are needed to enable the best possible unification of height datums. The main purpose of this article is to make a case study for Sweden regarding the national realisation of IHRS and to investigate in what way preliminary IHRF differs from the current Swedish levelling-based realisation of the European Vertical Reference System, RH 2000. The two different quasigeoid models that we consider best over Sweden at the present time are used to compute the preliminary IHRS realisations in the study. The realisations are compared to each other and to RH 2000. It is shown that a very significant part of the difference to RH 2000 is due to the different postglacial land uplift epochs, permanent tide concepts, and zero levels. The standard deviation for the difference between one of the preliminary national IHRS realisations and RH 2000 is reduced from 75.5 to 19.2 mm after correction of the postglacial land uplift and permanent tide effects. The corresponding mean differences are –208.5 and –454.7 mm, respectively. The magnitude of the mean difference thus increases when the corrections in question are applied.

Unification of a Global Height System at the Centimeter-Level Using Precise Clock Frequency Signal Links

The International Association of Geodesy (IAG) aims to establish the International Height Reference System (IHRS) as one of its primary scientific objectives. Central to the realization of the IHRS is global vertical datum unification, which requires the connection of existing local vertical height reference systems (VHS) robustly and consistently. However, conventional methods are not suitable for estimating the offsets between two distant local height systems. In this paper, we propose a framework for connecting two local VHSs using ultraprecise clock frequency signal links between satellites and ground stations, referred to as the satellite frequency signal transmission (SFST) approach. The SFST approach allows for the direct determination of the geopotential and height differences between two ground datum stations without any location restrictions between the two VHSs. The simulation results show that the VHSs of China and the US can be unified with an accuracy of several centimeters, provided that the stability of atomic clocks used on-board the satellite and at on-ground datum locations reaches 4.8×10−17τ−1/2 for an averaging time τ (in seconds). We conclude that the SFST approach shows promise for achieving centimeter-level accuracy in unifying the global vertical height datum and represents a new paradigm for the realization of the IHRS.

On the connection of the Ecuadorian Vertical Datum to the IHRS

Abstract In this work, the determination of the discrepancy between the Ecuadorian Vertical Datum (EVD) and the International Height Reference System (IHRS) is presented. The vertical offset was estimated at the EVD based on the fixed geodetic boundary value problem approach. The focus of the experiment was the determination of the anomalous potential in the EVD, which in turn enable determination of the respective geopotential value. Taking a geopotential space-based approach, two estimates of the EVD offset with respect to the IHRS were obtained that amount to −1.51 and −1.61 m2/s2.

Determining the new height of Mount Qomolangma based on the International Height Reference System

ABSTRACT To achieve the goal that China and Nepal jointly announce the new height of Mount Qomolangma (MQ), the campaign of Qomolangma Height Survey (QHS) was carried out from 2019 to 2020. A high precision geoid model realizing the common height datum for both sides is necessary for determining the unique height of MQ. However, high altitude and rugged topography make it extremely difficult to conduct terrestrial gravity measurements in this region, the accuracy of geoid model is restricted by terrestrial gravity data gaps. In the campaign of 2020 QHS, the airborne gravity survey was carried out over MQ and its surrounding areas, the airborne gravity data covering an area of 12,700 km2 were successfully collected. For the first time, the high precision observations of terrestrial gravity and BeiDou Navigation Satellite System (BDS) at the peak of MQ were collected. These datasets pave the way for the precise determination of the orthometric height of MQ. According to the definition of the International Height Reference System (IHRS), we developed the IHRS-based gravimetric quasigeoid model by combining the airborne and terrestrial gravity data. Validations against highly accurate GNSS leveling data at 61 benchmarks demonstrate that the accuracy of the quasigeoid model is 3.8 cm, and the addition of airborne gravity data improves the accuracy by 51.3%. Based on the IHRS, the final orthometric height of the snow surface of the peak of MQ is determined to be 8848.86 m.

Analysis of high-resolution global gravity field models for the estimation of International Height Reference System (IHRS) coordinates in Argentina

Abstract Following the definition and realization of the International Height Reference System (IHRS), the vertical coordinate of a given point at the Earth’s surface can be obtained from the computation of the geopotential value from a harmonic expansion of a Global Gravity Model of High-Resolution (GGM-HR) or based on the computation of a local or regional pure gravimetric geoid or quasigeoid. Therefore, an evaluation of the accuracy of GGMs-HR and the geoid model available is needed in order to assess its capability to infer IHRS coordinates. In this study, different GGMs-HR are evaluated against 2287 benchmarks in Argentina. Moreover, the most recent geoid model of Argentina is also evaluated. Geoid undulations at these benchmarks are obtained based on ellipsoidal and orthometric heights in the local vertical datum. Results suggest that among the evaluated GGMs-HR, XGM2019e provides the best agreement with the observed geoid heights, but none of them is accurate enough in order to infer vertical coordinates in the IHRS. Similar conclusions are obtained for the local geoid model for Argentina demonstrating the necessity for a more precise geoid model, following the standards and recommendations given for the IHRS.

A contribution for the study of RTM effect in height anomalies at two future IHRS stations in Brazil using different approaches, harmonic correction, and global density model

AbstractThe high-frequency effects of the gravity field can be obtained from residual terrain modeling (RTM) technique. However, for the International height reference system (IHRS), this is an open problem. Over the last decades, various approaches have been proposed for the practical solution of Newton’s Integral, such as point-mass, tesseroid, prism, and polyhedron. Harmonic correction (HC) and the use of more realistic mass density values have also been studied. In this work, in order to calculate RTM height anomalies at BRAZ and PPTE IHRS future stations in Brazil, such approaches and issues have been evaluated. Density values have been obtained from CRUST 1.0 global model. For the HC, the traditional mass condensation technique and Poisson’s equation have been used. The resulting values proposed by different approaches are very close to each other, with differences at the submillimeter-level. The RTM height anomaly values reached 1.5 and 1.4 mm at the BRAZ and PPTE stations, respectively. HC at BRAZ station can be disregarded without prejudice since its order of magnitude was 10−5 m. The use of CRUST 1.0 density values has proposed slight improvements of 0.8 and 0. 4 mm at BRAZ and PPTE station, respectively, in relation to the use of Harkness constant density value.

Computation and Analysis of Geopotential Number in São Paulo, Brazil

In recent decades, important steps have been taken to implement the physical concepts of Geodesy in practice, con- cerning height systems. Despite the difficulties involving gravity field modeling, with the establishment of conventions, standards, and computation strategies, the realization of the International Height Reference System (IHRS) is well underway. For a global system, there are constraints for some countries, especially for those with sparse gravity data, mountain regions, and vast areas. In terms of methodology, the computation can be performed directly using the Global Geopotential Models (GGM), recovering existing geoid models, or determining pointwise the gravity potential using integral formulas. In general, the regional gravity modeling is given by numerical integration or least-squares collocation and more recently adopting the spherical radial basis functions. The first approach allows determining the earth’s gravity component at a specific point and adjusting the integral formula according to the gravity coverage. Since so far there is no common sense about the best methodology, computation strategies are been analyzed. In this con- text, the paper aims to contribute to IHRF, computing the geopotential number in the scope of IHRF, using numerical integration to solve the Geodetic Boundary Value Problem and an existing recent quasi-geoid model in four stations in São Paulo state, Brazil. The first approach was performed considering two cases: a radius of 210 km and 110 km of gravimetric data coverage and the Global Geopotential Model GOCO05S truncated at 100 and 200, respectively. The results between solutions have shown a maximum difference of 94 cm, and a minimum difference of 10 cm.

Use of GNSS and a refined GGM (XGM2019e) for determining normal heights in the Imbituba Brazilian Vertical Datum and in the International Height Reference System

This paper aimed to evaluate the use of Global Navigation Satellite System (GNSS) ellipsoidal heights in conjunction with height anomalies provided by Global Geopotential Model (GGM) XGM2019e, refined by Residual Terrain Modelling (RTM) technique, to obtain normal heights in Brazil, referred to the Imbituba Brazilian Vertical Datum (IBVD) and the International Height Reference System (IHRS). For this purpose, a local modelling approach has been analyzed in contrast to the national modeling one on the reference geopotential value. For this, a methodology based on geopotential space was adapted. In the local modeling, two study subregions were defined using the spatial clustering analysis of IBVD and GGM/RTM height anomalies differences outliers. The parameters have been estimated using three different configurations. In the parameters validation step, Root Mean Square Errors (RMSE) of the discrepancies between transformed and Brazilian official normal heights were calculated. In both subregions more accurate results have been obtained with the local modeling. In the SP1 subregion the accuracy increased tenfold (0.97m to 0.10m) and SP2 improved from 0.39m to 0.17m. For the linkage to the future realization of IHRS, the accuracy analysis was not possible. However, discrepancies between calculated normal heights and Brazilian official normal heights have been analyzed.

The permanent tide and the International Height Reference Frame IHRF

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 W0 = 62,636,853.4 m2 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 W0. By definition, W0 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 = W0. I find that, in the empirical determination of the adopted estimate W0, 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.

Determination of the height of Mount Everest using the shallow layer method

Shallow layer method (SLM) based on the definition of the geoid can determine the gravity field inside the shallow layer. In this study, the orthometric height of Mount Everest (HME) is calculated based on SLM, in which the key is to construct the shallow layer model. The top and bottom boundaries of the shallow layer model are the natural surface of the Earth and the surface at a certain depth below the reference geoid, respectively. The model-combined strategies to determine the geoid undulation (N) based on SLM are applied to calculate the HME by two approaches: (1) direct calculation by combining N and geodetic height (h); (2) calculation by the segment summation approach (SSA) using the gravity field inside the shallow layer. On December 8, 2020, the Chinese and Nepalese governments announced an authoritative value of 8848.86 m, which is referred to a geoid determined by the International Height Reference System (IHRS) (i.e., the geopotential is 62636853.4 m2s-2). Here, our results (combined strategies (1) EGM2008 and CRUST1.0, (2) EGM2008 and CRUST2.0, (3) EIGEN-6C4 and CRUST1.0, and (4) EIGEN-6C4 and CRUST2.0) are referred to the geoid defined by WGS84 (i.e., the geopotential is 62636851.7 m2s-2). The differences between our results and the authoritative value (8848.86 m) are 0.448 m, −0.009 m, −0.295 m, and −0.741 m by the first approach, and 0.539 m, 0.083 m, −0.214 m, and −0.647 m by the second approach. When the reference surface WGS84 geoid is converted to the IHRS geoid, the differences are 0.620 m, 0.163 m, −0.123 m, and −0.569 m by the first approach, and 0.711 m, 0.225 m, −0.042 m, and −0.475 m by the second approach.

Determination of the geopotential value on the permanent GNSS stations in Vietnam based on the Geodetic Boundary Value Problem approach

SUMMARY In the realisation of the International Height Reference System, the determination of the geopotential value and its variations in time plays an important role. In this study, the geodetic boundary value problem approach is applied for direct determination of the gravity potential value using a GOCE global gravity field model enhanced with terrestrial gravity data. This determination is carried out on the Global Navigation Satellite System-Continuously Operating Reference Stations (GNSS-CORS) stations towards the realisation of the International Height Reference System in Vietnam. First, the effects of the GOCE global gravity field model omission error, the indirect bias term on the disturbing potential and the systematic cumulative errors in levelling data are estimated. These errors affect the estimated geopotential value. The results calculated on the GNSS/levelling points show that the effect of the GOCE DIR-R5 (up to degree/order 260) omission error on the offset potential value is quite significant. This effect was eliminated using high-resolution terrestrial gravity data using the remove-compute-restore technique. The indirect bias term on the disturbing potential can be safely neglected by using a GOCE global gravity field model for degrees higher than 60 for this study region. The systematic cumulative errors in levelling data can be modelled and removed using a third-order polynomial model. Then, the mean zero-height gravity potential of the Vietnam local vertical datum is estimated equal to ${\rm{W}}_0^{{\rm{LVD}}}$ = 62 636 846.69 m2 s–2 with standard deviation of 0.70 m2 s–2 based on the proposed approach. Finally, the geodetic boundary value problem approach was used to determine the geopotential on the surface of three GNSS-CORS stations in Vietnam. Based on time-series of the vertical component derived from the GNSS observations as well as InSAR data, temporal variations in geopotential are also estimated on these permanent GNSS stations. The purpose is to monitor deformation of the vertical datum. The results indicate that the geopotential value needs to be monitored and determined with the time-dependent component on the three Vietnamese permanent GNSS stations for a vertical datum. These stations may contribute to increase the density of reference points in the International Terrestrial Reference Frame, which is being researched and implemented by the International Association of Geodesy.

High-resolution geoid modeling using least squares modification of Stokes and Hotine formulas in Colorado

The Colorado geoid experiment was initiated and organized as a joint study by the Joint Working Group (JWG) 2.2.2 (1-cm geoid experiment) of the International Association of Geodesy (IAG) in 2017, and different institutions and research groups contributed to this study. The aim of this experiment was to clarify the repeatability of gravity potential values as International Height Reference System (IHRS) coordinates from different geoid determination approaches carried out with the same input dataset. The dataset included the terrestrial and airborne gravity observations, a digital terrain model, the XGM2016 global geopotential model and GPS/leveling data for model validations belonging to a mountainous area of approximately 550 km × 730 km in Colorado, US. The dataset was provided by National Geodetic Survey (NGS) department. In this frame, this article aims providing a discussion on Colorado geoid modeling through individual experimental results obtained by Istanbul Technical University-Gravity Research Group (ITU-GRG). This contribution mainly focused on modeling the Colorado geoid using the least squares modifications of Stokes and Hotine integral formulas with additive corrections. The computations using each formula were carried out using ITU-GRG software, including the solution variants based on terrestrial-only, airborne-only and combined gravity datasets. Then, the calculated experimental geoid models were validated using historical and recently measured profile-based GPS/leveling datasets, and they were also compared with the official solutions submitted by different institutions for the “1-cm geoid experiment” of IAG JWG 2.2.2. For all validation results, the Hotine and Stokes integral formulas yielded similar performances in terms of geoid accuracy; however, the models computed using the combined data had better accuracy than those using the terrestrial-only and airborne-only solutions. The geoid model solutions using the combined data had an accuracy of 2.69 cm for the Hotine method and 2.87 cm for the Stokes method in the test results using GPS/leveling data of the GSVS17 (Geoid Slope Validation Survey 2017) profile. Airborne data from the Gravity for the Redefinition of the American Vertical Datum (GRAV-D) project contributed significantly towards improving the geoid model, especially in the mountainous parts of the area.

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

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 W0 = 62,636,853.4 m2 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.

Estimation of vertical datum offset for the South African vertical datum, in relation to the international height reference system

The vertical offset and the geopotential value over South Africa is estimated on the four fundamental benchmarks in relation to the international height reference system (IHRS). It is estimated to obtain discrepancies between the South African local vertical datum (W_P) and the global vertical datum (W_0). A single-point-based geodetic boundary value problem (GBVP) approach was used following Molodensky theory for estimating the height anomalies from the disturbing potential (T_P) using Bruns’s formula. The gravity potential at each tide gauge benchmark (TGBM) in South Africa deviates from the potential of the global reference surface by 0.589,-1.993,-2.593 and 2.154 m2s-2 for Cape Town, Port Elizabeth, East London and Durban, respectively. The corresponding vertical datum offsets between the international height reference system and the four fundamental benchmarks over South Africa are 6.013, -20.347, -26.478, and 21.996 cm for Cape Town, Port Elizabeth, East London and Durban, respectively. These offsets can be used for the unification of the South African vertical datum at the four tide gauge benchmarks in a manner that is consistent to the international height reference system.

Measurement of Height of Mt. Sagarmatha

The height measurement of the highest peak of the world “Sagarmatha” was conducted by Nepal for the first time. The methodology for the measurement was finalized from the workshop held in Kathmandu with the constructive comments from national and international experts. Trignometrical levelling, precise levelling, GNSS survey and gravity survey was conducted. Previous air borne gravity data and present surface gravity data was used to determine the precise regional geoid for this program. Thus orthometric height was determined as 8848.86 m from the ellipsoid height observed at the top of Sagarmatha and precise geoid determined. The height was determined on the base of International Height Reference System (IHRS) and final height was announced jointly from Nepal and China on 8th of December 2020 from Kathmandu and Beijing through virtual media.