The permanent tide and the International Height Reference Frame IHRF

Abstract

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\u2009=\u200962,636,853.4 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\u2009=\u2009W0. 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.