Report of the IAU/IAG Joint Working Group on Theory of Earth Rotation and Validation

2020

A&A

In this research, we computed the nutation of the figure axis for a non-rigid Earth model due to the mass redistribution resulting from the lunisolar attraction on the deformable Earth, thus extending our previous work on the precessional motion. The basic Earth model is a two-layer structure composed of a fluid core and an anelastic mantle. We used the Hamiltonian approach, leading to closed-form analytical formulae that describe the nutations in longitude and obliquity of the figure axis as a sum of Poisson and Oppolzer terms. Those formulae were evaluated assuming different Earth rheologies by means of the Love number formalism. In particular, we first computed the effect using the standard model of the International Earth Rotation and Reference Systems Service Conventions (2010) solid tides, and then the Love numbers computed by Williams and Boggs, accounting for the complete oceanic tide contribution, which should provide more consistent and updated values for the nutations. The main amplitudes correspond to the 18.6 yr nutation component and reach 201 μas and −96 μas in the in-phase components in longitude and obliquity, respectively. The obtained values differ greatly from those considered in the current nutation model, IAU2000, of the International Astronomical Union (IAU) – and later similar studies – which includes this effect under the denomination of non-linear terms and derives its numerical contribution on the basis of the Sasao, Okubo, and Saito framework. The differences are significant and reach more than 30 μas for some nutation amplitudes. They can be likely attributed to several factors: an incomplete modelling of the redistribution potential; a different treatment of the permanent tide; and the use of different oceanic tide models.

Section: Discussionsupporting

confidence: 59%

Section: Introductionmentioning

confidence: 99%

Nutation of the non-rigid Earth: Effect of the mass redistribution

Baenas

2020

A&A

“…The magnitudes are below the present uncertainty of the determinations of individual amplitudes that is 2-3 µas (Belda et al [2017], Gattano et al [2017]), but even though our results are relevant according to recent recommendations of the International Astronomical Union (IAU) and the International Association of Geodesy (IAG) made through its Joint Working Group on Theory of Earth rotation (Ferrándiz and Gross [2016], Ferrándiz et al [2020]). They prompt the estimation of the impact on accuracy of the many approximations made in theories, besides urging an improvement of their consistency (see, e.g., Escapa et al [2017]).…”

Section: Numerical Results and Discussionmentioning

confidence: 53%

“…After many years with no relevant improvement of the unexplained variance, the International Astronomical Union (IAU) and the International Association of Geodesy (IAG) established two successive Joint Working Groups (JWG) to get more insight into the problem, focusing on the potential deficiencies and inaccuracies of theories and the consistency issues that may cause systematic errors. The final report of the IAU/IAG JWG on Theory of Earth rotation and validation (Drewes & Kuglitsch [2019]) led to the approval of Resolution 5 of the 2019 IAG General Assembly, which encouraged a prompt improvement of the Earth rotation theory regarding its accuracy, consistency, and ability to model and predict the essential Earth orientation parameters EOP (Ferrándiz et al [2020]).…”

Section: Introductionmentioning

confidence: 99%

Forced nutations of a two-layer Earth in canonical formulation with dissipative Hori-like kernel

Baenas

Advances in Space Research

2020

Self Cite

In this research, a modification of the Lie-Hori perturbation method developed by the authors in a recent investigation is used to compute the forced nutations of a non-rigid Earth model, including dissipative processes at the core-mantle boundary. The study is tackled within the Hamiltonian formalism of a two-layer Earth, where the viscous and electromagnetic couplings between mantle and core are introduced via generalized forces. The modified Lie-Hori method is introduced within the framework of the generalized Hamiltonian formalism. It, therefore, allows for calculating first-order perturbations in both conservative and non-conservative systems, while the classical Lie-Hori procedure is not designed to include generalized forces in the kernel to account for dissipative processes. Unlike other methods, ours presents the advantage of keeping the same dimensionality of the original problem, avoiding the doubling of the dimension of the phase space. With this mathematical refinement, differences in the derived nutation amplitudes at the microarcsecond level have been found when compared with the former, first approximation for dissipative systems based on damped oscillators -the only existing previous solution. Those figures are of relevance according to recent recommendations of the International Astronomical Union (IAU) and the International Association of Geodesy (IAG) based on the final report of the Joint Working Group on Theory of Earth rotation and validation.

“…It entails that the models of the rotation of the Earth must incorporate theories of precession and nutation at the second order. As a matter of fact, the need for a prompt improvement in Earth rotation theory was recently reported by the International Astronomical Union (IAU)/International Association of Geodesy (IAG) Joint Working Group (JWG) on Theory of Earth Rotation and Validation (Ferrándiz et al 2020).…”

Section: Introductionmentioning

confidence: 99%

The Rotation of the Nonrigid Earth at the Second Order. II. The Poincaré Model: Nonsingular Complex Canonical Variables and Poisson Terms

Getino

et al. 2021

Self Cite

We develop a Hamiltonian analytical theory for the rotation of a Poincaré Earth model (rigid mantle and liquid core) at the second order with respect to the lunisolar potential and moving ecliptic term. Since the Andoyer variables considered in the first-order solution present virtual singularities, i.e., vanishing divisors, we introduce a set of nonsingular complex canonical variables. This choice allows for applying the Hori canonical perturbation method in a standard way. We derive analytical expressions for the first- and second-order solutions of the precession and nutation of the angular momentum axis (Poisson terms). Contrary to first-order theories, there is a part of the Poisson terms that does depend on the Earth’s structure. The resulting numerical amplitudes, not incorporated in the International Astronomical Union nutation standard, are not negligible considering current accuracies. They are at the microarcsecond level for a few terms, with a very significant contribution in obliquity of about 40 μas for the nutation argument with period −6798.38 days. The structure-dependent amplitudes present a large amplification with respect to the rigid model due to the fluid core resonance. The features of such resonance, however, are different from those found in first-order solutions. The most prominent is that it does not depend directly on the second-order nutation argument but rather on the combination of first-order arguments generating it. It entails that some first-order approaches, like those based on the transfer function, cannot be applied to obtain the second-order contributions.