Explore the vast range of titles available.

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 primary objective of the 1-cm geoid experiment in Colorado (USA) is to compare the numerous geoid computation methods used by different groups around the world. This is intended to lay the foundations for tuning computation methods to achieve the sought after 1-cm accuracy, and also evaluate how this accuracy may be robustly assessed. In this experiment, (quasi)geoid models were computed using the same input data provided by the US National Geodetic Survey (NGS), but using different methodologies. The rugged mountainous study area (730 km × 560 km) in Colorado was chosen so as to accentuate any differences between the methodologies, and to take advantage of newly collected GPS/leveling data of the Geoid Slope Validation Survey 2017 (GSVS17) which are now available to be used as an accurate and independent test dataset. Fourteen groups from fourteen countries submitted a gravimetric geoid and a quasigeoid model in a 1′ × 1′ grid for the study area, as well as geoid heights, height anomalies, and geopotential values at the 223 GSVS17 marks. This paper concentrates on the quasigeoid model comparison and evaluation, while the geopotential value investigations are presented as a separate paper (Sánchez et al. in J Geodesy 95(3):1. https://doi.org/10.1007/s00190-021-01481-0 , 2021). Three comparisons are performed: the area comparison to show the model precision, the comparison with the GSVS17 data to estimate the relative accuracy of the models, and the differential quasigeoid (slope) comparison with GSVS17 to assess the relative accuracy of the height anomalies at different baseline lengths. The results show that the precision of the 1′ × 1′ models over the complete area is about 2 cm, while the accuracy estimates along the GSVS17 profile range from 1.2 cm to 3.4 cm. Considering that the GSVS17 does not pass the roughest terrain, we estimate that the quasigeoid can be computed with an accuracy of ~ 2 cm in Colorado. The slope comparisons show that RMS values of the differences vary from 2 to 8 cm in all baseline lengths. Although the 2-cm precision and 2-cm relative accuracy have been estimated in such a rugged region, the experiment has not reached the 1-cm accuracy goal. At this point, the different accuracy estimates are not a proof of the superiority of one methodology over another because the model precision and accuracy of the GSVS17-derived height anomalies are at a similar level. It appears that the differences are not primarily caused by differences in theory, but that they originate mostly from numerical computations and/or data processing techniques. Consequently, recommendations to improve the model precision toward the 1-cm accuracy are also given in this paper.

The increasing importance of terrestrial gravimetry in monitoring global change processes, in providing a reference for satellite measurements and in applications in metrology necessitates a stable reference system reflecting the measurement accuracy achievable by modern gravimeters. Therefore, over the last decade, the International Association of Geodesy (IAG) has developed a system to achieve accurate, homogeneous, long-term global recording of Earth’s gravity, while taking advantage of the potential of today’s absolute gravity measurements. The current status of the International Gravity Reference System and Frame is presented as worked out by the IAG Joint Working Group 2.1.1 “Establishment of a global absolute gravity reference system” during the period 2015–2019. Here, the system is defined by the instantaneous acceleration of free-fall, expressed in the International System of Units (SI) and a set of conventional corrections for the time-independent components of gravity effects. The frame as the systems realization includes a set of conventional temporal gravity corrections which represent a uniform set of minimum requirements. Measurements with absolute gravimeters, the traceability of which is ensured by comparisons and monitoring at reference stations, provide the basis of the frame. A global set of such stations providing absolute gravity values at the microgal level is the backbone of the frame. Core stations with at least one available space geodetic technique will provide a link to the terrestrial reference frame. Expanded facilities enabling instrumental verification as well as repeated regional and additional comparisons will complement key comparisons at the level of the International Committee for Weights and Measures (CIPM) and ensure a common reference and the traceability to the SI. To make the gravity reference system accessible to any user and to replace the previous IGSN71 network, an infrastructure based on absolute gravity observations needs to be built up. This requires the support of national agencies, which are encouraged to establish compatible first order gravity networks and to provide information about existing absolute gravity observations.

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.

This paper studies the contribution of airborne gravity data to improvement of gravimetric geoid modelling across the mountainous area in Colorado, USA. First, airborne gravity data was processed, filtered, and downward-continued. Then, three gravity anomaly grids were prepared; the first grid only from the terrestrial gravity data, the second grid only from the downward-continued airborne gravity data, and the third grid from combined downward-continued airborne and terrestrial gravity data. Gravimetric geoid models with the three gravity anomaly grids were determined using the least-squares modification of Stokes’ formula with additive corrections (LSMSA) method. The absolute and relative accuracy of the computed gravimetric geoid models was estimated on GNSS/levelling points. Results exhibit the accuracy improved by 1.1 cm or 20% in terms of standard deviation when airborne and terrestrial gravity data was used for geoid computation, compared to the geoid model computed only from terrestrial gravity data. Finally, the spectral analysis of surface gravity anomaly grids and geoid models was performed, which provided insights into specific wavelength bands in which airborne gravity data contributed and improved the power spectrum.

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.

In the frame of the International Association of Geodesy Joint Working Group 2.2.2 “The 1 cm geoid experiment”, terrestrial and airborne gravity datasets along with GPS/leveling data were made available for the comparison of different geoid modeling methods and techniques in the wider area of Colorado, USA. We discuss the methods and procedures we followed for computing gravimetric quasi-geoid and geoid models and geopotential values from the available datasets. The procedures followed were based on the remove-compute-restore approach using XGM2016 as a reference geopotential model. The higher frequencies of the gravity field were computed via the residual terrain correction, using (a) the CGIAR-CSI SRTM digital elevation model with the classical technique and (b) a spectral one. Least-Squares Collocation was used for the downward continuation of the airborne data and for gridding. Finally, the geoid models were obtained by applying Least-Squares Collocation and spherical FFT-based methods, while the influence of the orthometric height correction on geoid heights was taken into account by employing simple and complete Bouguer reductions. All results were evaluated with available GPS/leveling benchmarks. Moreover, potential values were determined in support of the International Height Reference System/Frame. From the results acquired, a final accuracy of 5–7 cm for the determined geoid models was achieved depending on the adopted method and data combination, without considering the accuracy of the GPS/leveling data used for their evaluation. The contribution of the airborne gravity data was deemed as limited in combination solutions although the airborne only solution provided equal level of accuracy to the terrestrial and the combined ones. Better consistency was obtained on the points of the GSVS17 line, when compared to the GPS/leveling data, where an accuracy of 2.4 cm and 2.8 cm was reached for the FFT and LSC based methods, respectively.

In the summer of 2017, the National Geodetic Survey (NGS) conducted its third and final Geoid Slope Validation Survey in the rugged terrain of southern Colorado, USA. As in previous surveys, the intent is to acquire the most accurate and precise field observations to determine geoid slopes. In turn, these data can be used to quantify the accuracy of various geoid models as NGS looks ahead to creating a highly accurate gravimetric geoid model for use as a national vertical datum. Long period GPS sessions, spirit leveling, absolute gravity, and deflection of the vertical (DoV) observations were acquired along a 360 km line, ranging from 1900 to 3300 m in elevation, with a station spacing of approximately 1.6 km. Our absolute gravity and DoV datasets are unique in that they were collected at 222 field stations in highly mountainous terrain at an unprecedented observational accuracy of 10 µGal and 0.04″, respectively. Further, by employing tailored refraction corrections to the spirit leveling data, we improved the agreement between heights derived from the DoV and spirit leveling from ± 1.9 to ± 1.3 cm RMS, or by more than 30%, across the line. At all length scales, from 1.6 to 360 km, the agreement is better than 2 cm. Finally, as a description of the validation process, we compare the observations with recent NGS experimental geoid models. We find that typical agreement is at about 3–5 cm, with no single model being best at all length scales. The data from this project are freely available to the community and should serve as test beds for not only geoid modeling comparisons, but also the refinement of numerous field techniques.

Due to the lack of a natural reference for the absolute acceleration of free fall and gravity, absolute gravimeters are compared at international comparisons, where the gravity reference is realized based on a set of precise absolute measurements and the functional model for their processing. The main estimates of comparisons, specifically, the reference values, deviations of gravimeters (biases) and associated uncertainty estimates, are obtained by the method of constrained least squares. In this paper, based on data from six comparisons, we demonstrate and discuss the importance of several aspects that significantly influence the estimated parameters, such as the type of the constraint, the weighting schemes, the correlations between measurements or outlier detection. Following the state-of-the-art key comparisons in metrology, we are applying correlations between measurements of a particular gravimeter for the first time, showing the ability to obtain appropriate uncertainty estimates, strictly applying the law of error propagation. The processing of comparisons by the method of least squares is described step by step to provide a background for analyses of absolute gravimeter comparisons in the future, reflecting all specifics of these comparisons. Estimated parameters from uniformly elaborated comparisons represent an interesting statistical data set that has been used to analyse the significance of differences between FG5, FG5X and other types of gravimeters. We believe that the described method of processing, as well as the published results, will be especially useful in the realization of the International Gravity Reference System.