Articles | Volume 14, issue 4
Special issue:
ESD Ideas
04 Aug 2023
ESD Ideas |  | 04 Aug 2023

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

Anny Cazenave, Julia Pfeffer, Mioara Mandea, and Veronique Dehant

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.

Figure 1Schematic 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.

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 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 precipitation 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 America, the Congo Basin and the Great Lakes region in Africa, and the Mississippi Basin and Central Valley in North America, as well as over several areas of the Eurasian continent (Pfeffer et al., 2023). Besides, several climate modes (reflecting the natural variability of the Earth climate) also display 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 Multidecadal Oscillation). As the definition of these climate indices 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 opposite changes in the atmospheric angular momentum (AAM) caused by seasonal changes of the tropospheric wind circulation (Chen et al., 2019, and references herein). It has been further established that the transfer of angular momentum from the atmosphere (with a marginal contribution from the ocean and land hydrosphere) to the solid Earth also occurs at ENSO frequencies (around 2–3 years). For the seasonal 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 contribution 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 unexpected observation has profound consequences for the dynamics 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 dynamics 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 almost synchronously with LOD and AAM at the 6-year frequency, 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 coupling 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 oscillation 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 climate variations are linked to core–mantle oscillations, suggesting 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. However, 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 preformed 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.


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


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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Short summary
While a 6-year oscillation has been reported for some time in the motions of the fluid outer core of the Earth, in the magnetic field and in the Earth rotation, novel results indicate that the climate system also oscillates at this 6-year frequency. This strongly suggests the existence of coupling mechanisms affecting the Earth system as a whole, from the deep Earth interior to the surface fluid envelopes.
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