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.

The International Height Reference System (IHRS) was defined by the International Association of Geodesy (IAG) in 2015. The global International Height Reference Frame (IHRF) should provide access to the IHRS in a broad sense. To provide high accuracy local access, regional (or national) realisations will also be needed. This study aims at evaluating different approaches to compute a denser regional realisation of IHRS in case a high accuracy levelling network is available. Using Sweden as a case study region, a GNSS (Global Navigation Satellite System) and geoid based pointwise realisation is compared with three types of levelling assisted realisations. The latter are made by applying least squares adjustments of the precise levelling observations with fixed potential value(s) from either the global IHRF station in Sweden or the pointwise potentials of a larger number of stations. It is concluded that making a minimum constraint adjustment with one station fixed is not the best option. It is favourable to fix a reasonable number of pointwise stations at an internal distance over which the relative uncertainty of levelling is significantly lower than the relative uncertainty of the pointwise solution. The investigation is made using levelling data from the third precise levelling of Sweden, the NKG2015 quasigeoid model and the NKG2016LU postglacial land uplift model.

The International Association of Geodesy defined the International Height Reference System (IHRS) in 2015. IHRS will be realised through the International Reference Frame (IHRF) primarily by geopotential numbers (or physical heights). On the global scale, a sparse core reference network will be the basis for the realisation. To ensure local access to the frame and the best possible conditions for height datum unification, denser realisations (or densifications) will be needed. The adopted realisations can be either regional, national, or local. According to the published recommendations on regional IHRS realisation, GNSS ellipsoidal heights and a gravimetric (quasi-) geoid model form the basis to compute a pointwise IHRS realisation, but it is possible to supplement this by local levelling to gain local access to the frame and improve the relative uncertainty. The main purpose of this article is to investigate different ways to incorporate levelling observations in the IHRS realisation process and explore potential improvements. The investigation is a case study over Sweden that uses an initial pointwise IHRS realisation and precise levelling observations from the Baltic Levelling Ring (BLR) project. The levelling network is adjusted with respect to the pointwise IHRF geopotential numbers using three different approaches regarding the a priori variance-covariance matrix used for weighting of the observations. The approaches are constrained adjustment, weighted adjustment with realistic a priori uncertainties (variance covariance matrix) and weighted adjustment with Variance Component Estimation (VCE) to iteratively tune the a priori variance-covariance matrix. It is shown that the pointwise IHRS realisation can be improved significantly by the inclusion of levelling observations. Both the estimated standard uncertainty of the adjusted IHRF geopotential numbers as well as the relative standard uncertainty between nodal benchmarks are reduced by approximately 40 percent in the Swedish case. To fully exploit the potential of precise levelling observations in the IHRS realisation process, it is recommended to use some form of weighted adjustment, preferably using VCE to obtain a realistic balance between the initial pointwise and levelling observations.