Author Correction: Multi-centennial fluctuations of radionuclide production rates are modulated by the Earth's magnetic field.

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New perspectives in the study of the Earth's magnetic field and climate connection: The use of transfer entropy.

The debated question on the possible relation between the Earth's magnetic field and climate has been usually focused on direct correlations between different time series representing both systems. However, the physical mechanism able to potentially explain this connection is still an open issue. Finding hints about how this connection could work would suppose an important advance in the search of an adequate physical mechanism. Here, we propose an innovative information-theoretic tool, i.e. the transfer entropy, as a good candidate for this scope because is able to determine, not simply the possible existence of a connection, but even the direction in which the link is produced. We have applied this new methodology to two real time series, the South Atlantic Anomaly (SAA) area extent at the Earth's surface (representing the geomagnetic field system) and the Global Sea Level (GSL) rise (for the climate system) for the last 300 years, to measure the possible information flow and sense between them. This connection was previously suggested considering only the long-term trend while now we study this possibility also in shorter scales. The new results seem to support this hypothesis, with more information transferred from the SAA to the GSL time series, with about 90% of confidence level. This result provides new clues on the existence of a link between the geomagnetic field and the Earth's climate in the past and on the physical mechanism involved because, thanks to the application of the transfer entropy, we have determined that the sense of the connection seems to go from the system that produces geomagnetic field to the climate system. Of course, the connection does not mean that the geomagnetic field is fully responsible for the climate changes, rather that it is an important driving component to the variations of the climate.

Multi-centennial fluctuations of radionuclide production rates are modulated by the Earth's magnetic field.

The production of cosmogenic isotopes offers a unique way to reconstruct solar activity during the Holocene. It is influenced by both the solar and Earth magnetic fields and thus their combined effect needs to be disentangled to infer past solar irradiance. Nowadays, it is assumed that the long-term variations of cosmogenic production are modulated by the geomagnetic field and that the solar field dominates over shorter wavelengths. In this process, the effects of the non-dipolar terms of the geomagnetic field are considered negligible. Here we analyse these assumptions and demonstrate that, for a constant solar modulation potential, the geomagnetic field exerts a strong modulation of multi-centennial to millennial wavelengths (periods of 800 and 2200 yr). Moreover, we demonstrate that the non-dipole terms derived from the harmonic degree 3 and above produce maximum differences of 7% in the global average radiocarbon production rate. The results are supported by the identification, for the first time, of a robust coherence between the production rates independently estimated from geomagnetic reconstructions and that inferred from natural archives. This implies the need to review past solar forcing reconstructions, with important implications both for the assessment of solar-climate relationships as well as for the present and future generation of paleoclimate models.