The permanent tide and the International Height Reference Frame IHRF

TL;DR

This paper analyzes the tidal aspects of the International Height Reference Frame (IHRF), proposing simplified models and correction formulas to improve consistency and clarity in handling permanent tides and geopotential references.

Contribution

It introduces a simplified definition of IHRF geopotential numbers and recommends modeling primarily in the zero-tide system for consistency.

Findings

Empirical W0 estimate is inconsistent across tidal systems.

Proposed correction formulas facilitate transformation to zero-tide and mean-tide models.

Advocates for modeling in the zero-tide system with mean-tide potential as an add-on.

Abstract

The International Height Reference System (IHRS) adopted by the IAG in 2015 contains two novelties. First, the mean-tide system is adopted for handling the permanent tide. Second, the reference level of height system is defined by the equipotential surface where the geopotential has a conventional value W0=62636853.4 m2s-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. The W0 is by definition independent of the tidal system adopted for the equipotential surface, but for different tidal systems, different functions are involved in the W of the equation W=W0. I find that the empirical determination of the adopted estimate W0 is inconsistent from the viewpoint of tidal systems. However, the adopted estimate and the consistent estimate from the same data round off to the same value. I propose a simplified definition of IHRF geopotential numbers that would make it possible to transform between IHRF and zero-tide geopotential numbers using a simple datum-difference surface. IHRF should adopt a conventional (best) estimate of the permanent tidal potential such as is contained in the IERS Conventions and use it as a basis for other conventional formulas. The tide-free coordinates of the ITRF, 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, in the middle, or after the processing, and finally to the mean-tide IHRF. To reduce the confusion around the multitude of tidal systems I propose that modelling should primarily done in the zero-tide system, with the mean-tide potential as an add-on.