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 x 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' x 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 (Sanchez 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' x 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 similar to 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.

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.

One of the key activities in Geodesy 2010, the Swedish strategic plan for geodetic activities during the period 2011–2020, is the restoration of the gravity network and data in order to improve the accuracy of the national quasigeoid model. One weak point has been that very few gravity observations have been available over Lake Vänern, Sweden’s largest lake. During the extremely cold winters 2010 and 2011, the ice became sufficiently thick to make ice observation of gravity. The main purpose of this paper is to present the 2011 ice gravity campaign, summarise the experiences made and investigate how much the new ice observations improve the computed quasigeoid model in the area. This is investigated under the assumption that a modern Earth Gravitational Model based on GRACE and GOCE is used. It is found that new ice measurements improve the quasigeoid with a RMS of about 2–3 cm in and around the lake with a maximum improvement of 7 cm.

When GNSS height determination improves in the future, users will ask for increasingly better geoid models. It is not unlikely that a standard error of 5 mm will more or less be required in a couple of years. The main purpose of this paper is to investigate the gravity data requirements to compute a Swedish gravimetric quasigeoid model to that order. The propagation of errors in the terrestrial gravity observations and the Earth Gravitational Model (EGM) are studied using both variance-covariance analysis in the spectral domain and least squares collocation. These errors are also checked by computing a new gravimetric quasigeoid model and comparing it with GNSS/levelling height anomalies. It is concluded that it will be possible to compute a 5 mm model over Sweden in the case that the gravity data set is updated to fulfil the following requirements: the resolution should be at least 5 km and there should be no data gaps nearby. Finally, the standard errors of the uncorrelated and correlated gravity anomaly noises should be below 0.5 and 0.1 mGal, respectively.