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# ESD Ideas: A 6-year oscillation in the whole Earth system?

Anny Cazenave¹,², Julia Pfeffer², Mioara Mandea³, and Veronique Dehant⁴

¹Laboratoire d'Etudes en Géophysique et Océanographie Spatiales, Toulouse, 31400 France

²Magellium, Ramonville St Agne, 31520 France

³Centre National d'Etudes Spatiales, Paris, 75039 Cedex 01 France

⁴Royal Observatory of Belgium, Brussels, B1180 Belgium

**Correspondence:** Anny Cazenave (anny.cazenave@gmail.com)

Received: 21 February 2023 – Discussion started: 8 March 2023

Revised: 4 July 2023 – Accepted: 5 July 2023 – Published: 4 August 2023

**Abstract.** An oscillation of about 6 years has been reported in Earth's fluid core motions, magnetic field, rotation, and crustal deformations. Recently, a 6-year cycle has also been detected in several climatic parameters (e.g., sea level, surface temperature, precipitation, land hydrology, land ice, and atmospheric angular momentum). Here, we suggest that the 6-year oscillations detected in the Earth's deep interior, rotation, and climate are linked together and that the core processes previously proposed as drivers of the 6-year cycle in the Earth's rotation additionally cause the atmosphere to oscillate together with the mantle, inducing fluctuations in the climate system with similar periodicities.

Numerous studies have reported a ~6-year cycle in the rotation of the Earth's mantle (or equivalently in the length of day – LOD) (e.g., Abarca de Rio et al., 2000, and many subsequent publications). While LOD oscillations related to seasonal changes and the El Niño–Southern Oscillation (ENSO) are well explained by the exchange of angular momentum from the atmosphere (and to a lesser degree, from the oceans and hydrosphere) to the mantle, the 6-year signal in LOD has been attributed to deep Earth processes, namely the exchange of angular momentum between the core and the mantle (see Rekier et al., 2022, and references therein) (Fig. 1). However, the exact nature of the torques at work is still debated. One mechanism invokes electromagnetic coupling. Relying on geomagnetic data (that display a clear 6-year cycle, in particular in the secular acceleration) and inferred core flow modeling, Gillet et al. (2010) showed that the 6-year signal in LOD can be predicted by the geostrophic wave-like pattern induced by torsional Alfven waves traveling from the inner core to the outer core, with a fundamental mode of 6 years. Another proposed mechanism is a gravitational coupling between the mantle and the inner core (e.g., Chao, 2017).

A recent study by Chen et al. (2019) also reported a strong 6-year signal in the motion of the Earth's axis of rotation. Mass redistributions in the surface fluid envelopes (atmosphere, oceans, and land hydrosphere) appear to be unable to explain this observation, suggesting instead deep Earth sources, as is the case for LOD. Using satellite laser ranging and GRACE (Gravity Recovery and Climate Experiment) space gravimetry data, Chao and Yu (2020) reported a 6-year variation in the degree-2, order-2 spherical harmonics of the gravity field (or equivalently in the ellipticity of the Earth's Equator). They attributed it to a gravitational coupling between the solid inner core and the Earth's mantle. Other studies (Watkins et al., 2018; Ding and Chao, 2018) based on GPS (Global Positioning System) data also reported a 6-year cycle in crustal deformations. According to these authors, loading from the surface fluid envelopes (atmosphere, oceans, and land hydrosphere) cannot explain this 6-year signal. They rather suggest core–mantle coupling as the source of the surface deformations.

More recently, a series of observations have incidentally reported a 6-year oscillation in the Earth's climate. Moreira et al. (2021) discovered that the rate of change of the global
<figure><img src="image_3.png" /><figcaption>**Figure 1.** Schematic representation of the different layers of the Earth system, from the solid inner core to the atmosphere, and of the coupling mechanisms at the outer core–mantle boundary. The thin black curves around the Earth represent the magnetic field lines.</figcaption></figure>

mean sea level displays a clear 6-year signal, also seen in
the main contributors to the global mean sea level variations,
in particular the mass balance of glaciers and the Greenland
and Antarctica ice sheets. A cycle of ~6–7 years has also
been reported in the European surface temperature (Meyer
and Kantz, 2019). Further analysis of combined land and sea
surface temperature indicates that this 6-year cycle is a global
phenomenon. Recently, Pfeffer et al. (2023) reported novel
observations of a 6-year cycle in land water storage based
on data analysis of the GRACE and GRACE-FO (follow-
on) missions. This 6-year cycle in GRACE-based land water
storage appears to be highly correlated with observed pre-
cipitation and hydrological model-based water storage. This
signal is clearly visible in specific river basins or above large
aquifers in all continental areas. It is particularly significant
over the Amazon and Orinoco river basins in South Amer-
ica, the Congo Basin and the Great Lakes region in Africa,
and the Mississippi Basin and Central Valley in North Amer-
ica, as well as over several areas of the Eurasian continent
(Pfeffer et al., 2023). Besides, several climate modes (re-
flecting the natural variability of the Earth climate) also dis-
play significant energy around 6 years (Moreira et al., 2021).
This is the case in the MEI (Multivariate ENSO Index),
PDO (Pacific Decadal Oscillation), and AMO (Atlantic Mul-
tidecadal Oscillation). As the definition of these climate in-
dices is based on the combination of a variety of atmospheric
and oceanic variables (e.g., atmospheric pressure, sea surface
temperature, and surface winds), this suggests that the 6-year
cycle affects the climate system as a whole.

Conservation of angular momentum is a fundamental
property of rotating systems as long as they are not subject to
external torques. Angular momentum change in any part of

the system is compensated for by equal and opposite changes
in the rest of the system. This is exactly what happens in the
Earth system at the seasonal frequency, where changes in the
rotation of the solid Earth (i.e., the mantle) result from oppo-
site changes in the atmospheric angular momentum (AAM)
caused by seasonal changes of the tropospheric wind cir-
culation (Chen et al., 2019, and references herein). It has
been further established that the transfer of angular momen-
tum from the atmosphere (with a marginal contribution from
the ocean and land hydrosphere) to the solid Earth also oc-
curs at ENSO frequencies (around 2–3 years). For the sea-
sonal and ENSO frequencies, AAM and LOD variations are
in phase, indicating a transfer of angular momentum from
the surface fluid envelopes to the mantle (note that LOD and
mantle rotation variations are of opposite signs). For the 6-
year cycle, the situation is totally different. First, the AAM
also presents a clear 6-year oscillation, but most importantly,
LOD and AAM variations are almost perfectly in opposition
in terms of phase (Pfeffer et al., 2023). This was previously
noticed by Chen et al. (2019) and Rekier et al. (2022), who
found that correcting LOD for the angular momentum con-
tribution of the surface fluid envelopes (mostly atmosphere
because the ocean and hydrosphere contribute little) does not
cancel the LOD 6-year variations (unlike at the seasonal and
ENSO frequencies) but rather enhances them. Such an un-
expected observation has profound consequences for the dy-
namics of the Earth system. The phase opposition of LOD
and AAM means that, at the 6-year frequency, the Earth’s
mantle and the atmosphere oscillate in phase together as a
coupled system (Pfeffer et al., 2023). As LOD changes are
likely to be explained by deep Earth processes, core dynam-
ics may be the driver of the AAM 6-year oscillation and other
surface changes and hence of the reported 6-year cycle in the
Earth’s climate. Several other global observables oscillate al-
most synchronously with LOD and AAM at the 6-year fre-
quency, in particular the magnetic and gravity fields (Mandea
et al., 2012), as well as the mean Earth surface temperature
(Pfeffer et al., 2023). However, the exact nature of the cou-
pling mechanism between mantle and surface fluid envelopes
at the 6-year frequency remains to be elucidated.

A periodic oscillation in the Earth magnetic field dipole
of approximately ~60–65 years has been known for some
time (Roberts et al., 2007); this is also the case in the LOD,
mean Earth temperature, and global mean sea level (e.g.,
Zotov et al., 2016). Using seismic observations, Yang and
Song (2023a, b) have recently reported a ~65-year oscilla-
tion of the inner core, nearly in phase opposition with LOD,
and noted that climate, LOD, and magnetic field fluctuations
at 60–65 years are almost synchronous (as observed here for
the 6-year cycle). They conclude that the multidecadal cli-
mate variations are linked to core–mantle oscillations, sug-
gesting strong coupling interactions between the main layers
of the Earth system, from the deep interior to the surface fluid
envelopes. In our view, a similar scenario may apply to the
6-year cycle that affects the Earth system as a whole. How-
ever, in both cases, exact coupling mechanisms between the different layers of the planet that are able to reproduce the observations are still to be discovered.

**Code availability.** Data analyses were performed using public versions of the MATLAB and PYTHON softwares.

**Data availability.** All datasets used in this study are available on demand to the authors.

**Author contributions.** All the authors contributed to parts of the research and analysis. AC coordinated the study and wrote the paper. JP performed the analyses and contributed to the interpretation of the results. VD and MM also contributed to the interpretation.

**Competing interests.** The contact author has declared that none of the authors has any competing interests.

**Disclaimer.** Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Acknowledgements.** The work described in this paper is performed in the context of the GRACEFUL project of the European Research Council. The FRS-FNRS is thanked for its support through the Research Project PDR (project no. T.0066.20). We thank the reviewers, Jianli Chen and Richard Holme, for their useful comments on our paper, as well as the editor, James Dyke, for the editorial work. We also thank Hervé Schindler for drawing Fig. 1.

**Financial support.** This research has been supported by the European Research Council, H2020 European Research Council (grant no. 855677).

**Review statement.** This paper was edited by James Dyke and reviewed by Jianli Chen and Richard Holme.

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