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1. Introduction

The objective of this paper is to gain knowledge on the rotational response to the periodic components of the

zonal tide between 7days and 1 year. This is an upgrade of past studies by considering all the perturbations

brought by hydro-atmospheric transports according to up-to-date global circulation models.

Recall the underlying physics to underline the interest of such a study. By raising an axisymmetric mass redis-

tribution within the Earth, the lunisolar zonal tides modify its axial moment of inertia; by virtue of the angular

momentum balance, the rotation speed ω, equivalently the length-of-day (LOD), changes accordingly. At the

zonal tide frequency σ, the relative fluctuation of the angular velocity

3()

can be related to the corresponding

component of the tidal generating potential through an admittance coefficient κ(σ; Agnew & Farrell,1978), of

which the definition is recalled in Section3. As those admittance coefficients depend on the rheology of the solid

Earth, on the ocean behavior, on the coupling between the fluid core and the mantle (Wahr etal.,1981), their

empirical estimates are of primary importance for understanding the Earth rheology.

Abstract This study is devoted to the determination of the admittance parameters describing the Earth

rotational response to the components of the zonal tide potential. First, in order to better grasp the physical

content of those admittance coefficients, we revisit the theoretical description of the length of day (LOD)

changes at sub-decadal time scale, where forcing is dominated by zonal tides and hydro-atmospheric mass

transports. This theoretical reminder specifies the rheological coefficients permitting to apply the hydro-

atmospheric corrections to isolate the tidal part of the LOD. Then, the admittances are determined from the

LOD series corrected from hydro-atmospheric contributions at the frequencies of the dominant zonal tidal

terms between 7 and 365days. In contrast of the former kindred studies, we both address the discrepancy of the

results brought by various EOP series and the hydro-atmospheric corrections on the LOD. Our study forwards

the complementary corrections brought by the ocean, the land water and sea level changes. Below 32days,

removing the atmospheric-oceanic excitation from LOD allows to much better constraint the admittance

complex coefficients κ than applying the atmospheric correction only: the discrepancy with respect to modeled

values is reduced up to 70%, and the frequency dependence of the imaginary part brought by the ocean

dynamical response is confirmed. A systematic effect with respect to the values modeled by Ray and Erofeeva

(2014), https://doi.org/10.1002/2013jb010830 has been detected and hints a defect of this model. Moreover, the

role of land water and associated sea level variation is notable at the semi-annual period.

Plain Language Summary This study is devoted to the determination of the admittance

coefficients describing the Earth rotational response to zonal tide components. In contrast of the former

kindred studies, it both addresses the discrepancy of the results brought by various EOP series and the hydro-

atmospheric corrections to be applied on length of day (LOD). It forwards the complementary corrections

brought by the ocean, the land water and sea level changes. Removing the atmospheric-oceanic excitation from

LOD allows to much better constraint the admittance complex coefficients κ than applying the atmospheric

correction only. The role of land water and associated sea level variation is notable at the semi-annual period.

This study also aims at synthesizing scattered theoretical results pertaining to the modeling of the length of

variation caused by zonal tides and concurrent effect of the mass transports taking place in the surface fluid

layer. Finally, a systematic effect with respect to the values modeled by Ray and Erofeeva (2014), https://doi.

org/10.1002/2013jb010830 has been detected and hints a defect of this model.

BIZOUARD ET AL.

© 2022. American Geophysical Union.

All Rights Reserved.

Admittance of the Earth Rotational Response to Zonal Tide

Potential

C. Bizouard1 , L. I. Fernández2,3, and L. Zotov4,5

1Observatoire de Paris, PSL, Paris, France, 2MAGGIA Lab. Fac. de Cs. Astronómicas y Geofísicas, University Nac. de La

Plata, La Plata, Argentina, 3CONICET, Buenos Aires, Argentina, 4Lomonosov Moscow State University, Moscow, Russia,

5National Research University Higher School of Economics, Moscow, Russia

Key Points:

• Admittance coefficients defining the

Earth's rotational response to zonal

tidal components are determined from

the length of day changes

• This study applies the full hydro-

atmospheric corrections to be

removed from the length of day before

estimating the admittances

• The dispersion between the estimated

admittances and their frequency

dependent model between 7 and

35days is reduced substantially

Correspondence to:

C. Bizouard,

christian.bizouard@obspm.fr

Citation:

Bizouard, C., Fernández, L. I., & Zotov,

L. (2022). Admittance of the Earth

rotational response to zonal tide potential.

Journal of Geophysical Research: Solid

Earth, 127, e2021JB022962. https://doi.

org/10.1029/2021JB022962

Received 11 AUG 2021

Accepted 28 JAN 2022

Author Contributions:

Conceptualization: C. Bizouard, L. I.

Fernández

Formal analysis: C. Bizouard, L. I.

Fernández

Investigation: C. Bizouard, L. I.

Fernández, L. Zotov

Methodology: C. Bizouard, L. I.

Fernández, L. Zotov

Software: C. Bizouard

Supervision: C. Bizouard

Validation: C. Bizouard, L. I. Fernández

Writing – original draft: C. Bizouard, L.

I. Fernández

Writing – review & editing: C.

Bizouard, L. I. Fernández, L. Zotov

10.1029/2021JB022962

RESEARCH ARTICLE

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