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Eleven-year solar cycles over the last millennium revealed by radiocarbon in tree rings


The Sun provides the principal energy input into the Earth system and solar variability represents a significant external climate forcing. Although observations of solar activity (sunspots) cover only the last about 400 years, radionuclides produced by cosmic rays and stored in tree rings or ice cores serve as proxies for solar activity extending back thousands of years. However, the presence of weather-induced noise or low temporal resolution of long, precisely dated records hampers cosmogenic nuclide-based studies of short-term solar variability such as the 11-yr Schwabe cycle. Here we present a continuous, annually resolved atmospheric 14C concentration (fractionation-corrected ratio of 14CO2 to CO2) record reconstructed from absolutely dated tree rings covering nearly all of the last millennium (ad 969–1933). The high-resolution and precision 14C record reveals the presence of the Schwabe cycle over the entire time range. The record confirms the ad 993 solar energetic particle event and reveals two new candidates (ad 1052 and ad 1279), indicating that strong solar events that might be harmful to modern electronic systems probably occur more frequently than previously thought. In addition to showing decadal-scale solar variability over the last millennium, the high-temporal-resolution record of atmospheric radiocarbon also provides a useful benchmark for making radiocarbon dating more accurate over this interval.

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Fig. 1: From annual Δ14C records to solar modulation.
Fig. 2: Two new event candidates detected in the 1,000-yr record.
Fig. 3: Frequency analysis of band-pass filtered Δ14C records.
Fig. 4: Amplitude and period distributions.

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The excel data that support the findings of this study are available in PANGEA at data are provided with this paper.


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We thank A. Arnold and R. Howard of the Nottingham Tree Ring Dating Laboratory for their careful dissection of the samples of English oak, and S. Arnold for her careful sample preparations. S. St George and the University of Minnesota are acknowledged for carefully reviewing the manuscript and for their positive and constructive comments, which considerably improved this study. The Laboratory of Ion Beam Physics is partially funded by its consortium partners PSI, EAWAG and EMPA. N.B. is funded by the Swiss National Science Foundation (SNSF grant number SNF 197137). I.U. acknowledges support from the Academy of Finland (project number 321882 ESPERA).

Author information

Authors and Affiliations



L.W., M.C. and N. Brehm designed the study with input from H.-A.S., A.B., C.T. and N. Bleicher. A.B., C.T. and N. Bleicher supplied the annually resolved tree ring samples and are responsible for the documentation of the dendrochronology. Radiocarbon measurements and analyses were performed by S.B., N. Brehm and L.W. The modelling and interpretation of the 14C data to extract the solar modulation was done by N. Brehm, M.C. and L.W. with input from F.A., J.B., B.K., R.M., S.K.S., I.U. and H.-A.S. N. Brehm, M.C. and L.W. wrote the manuscript with input from all co-authors.

Corresponding authors

Correspondence to Nicolas Brehm, Marcus Christl or Lukas Wacker.

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Extended data

Extended Data Fig 1 Comparison of IntCal13 raw data with ETH data.

Annually resolved radiocarbon measurements as Δ14C (red, left axis) compared with the raw data of IntCal13 (blue) at the top. The 14C age offsets in years (QL minus ETH, right axis) of the two datasets (green dots) with a moving average (green line, Savitzky-Golay filter) over time are shown on the bottom (8 years correspond to an offset of 1‰ in Δ14C). The error bars indicate two sigma errors.

Extended Data Fig 2 Comparison of Mediterranean Jordanian Juniper data with ETH data.

The published radiocarbon measurements on Jordanian juniper (JJ) performed in Oxford (OxA)53 and Arizona (AA)53 are compared with the raw values of IntCal13 (blue curve) and the new annual ETH measurements on British and Swiss oak samples (green) for selected time intervals (between dotted blue lines). The radiocarbon offsets of JJ from IntCal (as already observed by Manning et al.53) are substantially larger in some intervals and less consistant than the offsets of JJ to the ETH data. The error bars indicate two sigma errors.

Extended Data Fig. 3 Depiction of our in-house multi carbon box model.

The fluxes are given in Gt/yr and the 12C box contents are given in Gt of carbon.

Extended Data Fig. 4 Simulation of the Suess effect.

Simulated decrease of ∆14C of the northern (green) and southern (red) hemisphere compared with measured ETH 14C data (blue) and southern hemisphere Intcal13 data42(orange) using a constant 14C production rate of 6.6 kg/yr and using the global emission data of Boden et al.58 (black). The error bars indicate two sigma errors.

Extended Data Fig. 5 Direct comparison of reconstructed solar modulation parameter with sunspots.

Sunspots32 (black) with the solar modulation parameter calculated from ETH (blue) and QL (orange) data. The blue band indicates the estimated 2 sigma errors of the reconstructed solar modulation parameter of the ETH data by using 1000 Monte Carlo simulations.

Extended Data Fig. 6 Reconstruction of additionally produced 14C during SEP events.

(a) Different Monte Carlo simulations with the distribution in simulated ∆14C increases (b) and additional production (c) of the different datasets.

Extended Data Fig. 7 Direct peak to peak comparison with Sunspots.

Comparison of 6–18 yr band passed peak to peak distances of ETH (a/b blue) and QL (c/d orange) with band passed peak to peak distances of sunspots (black). In a/c the histogram of all distances is shown and in b/d only peak distances with a mean amplitude of more than 1.2 ‰ are shown.

Extended Data Fig. 8 Random data generation with increasing sinusoidal amplitude.

The blue histograms show amplitude, period, and point to point distance distributions (∆∆14C) after 6–18 yr bandpass filtering of random data containing an artificial periodic 10.4 yr signal with different amplitudes. From top to bottom the amplitude of the periodic signal is increased from 0‰ up to 3‰. The artificial data errors were adjusted such that the width of the ∆∆14C distribution is the same as the ∆∆14C distribution of our measured samples with a width of 2.03‰.

Supplementary information

Supplementary Information

Supplementary Discussion, Figs. 1–3 and Tables 1–17.

Source data

Source Data Fig. 1

Numerical data for Fig. 1.

Source Data Fig. 2

Numerical data for Fig. 2.

Source Data Extended Data Fig. 1

Numerical data for Extended Data Fig. 1.

Source Data Extended Data Fig. 2

Numerical data for Extended Data Fig. 2.

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Brehm, N., Bayliss, A., Christl, M. et al. Eleven-year solar cycles over the last millennium revealed by radiocarbon in tree rings. Nat. Geosci. 14, 10–15 (2021).

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