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# Admittance of the Earth Rotational Response to Zonal Tide Potential

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## Abstract and Figures

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 365 days. 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 32 days, 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.
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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 7days 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 Section3. 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 etal.,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 365days. 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 32days,
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.
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:
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
The dispersion between the estimated
dependent model between 7 and
35days 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
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
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