Towards a Global Unified Physical Height System

The International Association of Geodesy (IAG), as the organisation responsible for advancing Geodesy, introduced in 2015 the International Height Reference System (IHRS) as the global conventional reference system for the determination of gravity field-related vertical coordinates. The definition of the IHRS is given in terms of potential parameters: the vertical coordinates are geopotential numbers (C_P = W₀ ‐ W_P) referring to an equipotential surface of the Earth's gravity field realised by the conventional value W₀ = 62 636 853.4 m²s^‐2. The spatial reference of the position P for the potential W_P = W(X) is given by coordinates X of the International Terrestrial Reference Frame (ITRF). At present, the main challenge is the realisation of the IHRS; i.e., the establishment of the International Height Reference Frame (IHRF): a global network with regional and national densifications, whose geopotential numbers referring to the global IHRS are known. According to the objectives of the IAG Global Geodetic Observing System (GGOS), the target accuracy of these global geopotential numbers is 3 x 10^-2 m²s^-2. In practice, the precise realisation of the IHRS is limited by different aspects; for instance, there are no unified standards for the determination of the potential values W_P; the gravity field modelling and the estimation of the position vectors X follow different conventions; the geodetic infrastructure is not homogeneously distributed globally, etc. This may restrict the expected accuracy of 3 x 10^-2 m²s^-2 to some orders lower (from 10 x 10^-2 m²s^-2 to 100 x 10^-2 m²s^-2). This contribution summarises advances and present challenges in the establishment of the IHRS/IHRF.