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# Synchronization of the climate system to eccentricity forcing and the 100,000-year problem

## Abstract

Over the past million years, glacial–interglacial cycles have had a period of about 100,000 years, similar to the 100,000-year period of change in the eccentricity of the Earth’s orbit. However, the change in incoming solar radiation—insolation—at this timescale is small, and therefore difficult to reconcile with the amplitude of the glacial cycles1,2,3,4,5. This issue, known as the 100-kyr problem, is compounded by a lack of explanation for the transition of the length of the cycles from 41,000 to 100,000 years at the mid-Pleistocene transition 1.2 million years ago6. Individual discrepancies have been explained, for example, through interactions between other orbital frequencies such as obliquity and the 413,000-year period of eccentricity3,4,5,6,7,8,9,10,11,12,13, but a unified explanation is lacking. Here we show that climate oscillations over the past four million years can be explained by a single mechanism: the synchronization of nonlinear internal climate oscillations and the 413,000-year eccentricity cycle. Using spectral analyses aided by a numerical model, we find that the climate system first synchronized to the 413,000-year eccentricity cycle about 1.2 million years ago and has remained synchronized ever since. This synchronization results in a nonlinear transfer of power and frequency modulation that increases the amplitude of the 100,000-year cycle. We conclude that the forced synchronization can explain the strong 100,000-year glacial cycles through the alignment of insolation changes and internal climate oscillations.

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## Acknowledgements

This research is supported by grants from the J. S. McDonnell Foundation (21st Century Science Initiative on Complex systems) and the National Science Foundation (Paleoclimate and P2C2 programmes). We are grateful to J. Nie who alerted us to the evidence for natural frequencies of oscillation in the 100- and 500-kyr bands and offered thoughtful comments. L. Lisiecki generously provided the LR04 untuned record and provided important comments that improved the original manuscript.

## Affiliations

1. ### Wave Propagation Laboratory, Department of Geological Sciences, University of North Carolina, Chapel Hill, 104 South Road, Mitchell Hall, CB#3315, North Carolina 27599-3315, USA

• José A. Rial
• , Jeseung Oh
•  & Elizabeth Reischmann

## Authors

### Contributions

J.A.R. developed the concept and wrote the original manuscript. J.O. tested results and calculated the statistics, E.R. wrote needed computer codes and revised the original manuscript.

### Competing interests

The authors declare no competing financial interests.

## Corresponding author

Correspondence to José A. Rial.

## PDF files

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### Supplementary Information

Supplementary Information

### DOI

https://doi.org/10.1038/ngeo1756

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