S. Sanchez, J. Wicht, Julien Baerenzung, Matthias Holschneider

• High-precision observations of the present-day geomagnetic field by ground-based observatories and satellites provide unprecedented conditions for unveiling the dynamics of the Earth’s core. Combining geomagnetic observations with dynamo simulations in a data assimilation (DA) framework allows the reconstruction of past and present states of the internal core dynamics. The essential information that couples the internal state to the observations is provided by the statistical correlations from a numerical dynamo model in the form of a model covariance matrix. Here we test a sequential DA framework, working through a succession of forecast and analysis steps, that extracts the correlations from an ensemble of dynamo models. The primary correlations couple variables of the same azimuthal wave number, reflecting the predominant axial symmetry of the magnetic field. Synthetic tests show that the scheme becomes unstable when confronted with high-precision geomagnetic observations. Our study has identified spurious secondary correlations asHigh-precision observations of the present-day geomagnetic field by ground-based observatories and satellites provide unprecedented conditions for unveiling the dynamics of the Earth’s core. Combining geomagnetic observations with dynamo simulations in a data assimilation (DA) framework allows the reconstruction of past and present states of the internal core dynamics. The essential information that couples the internal state to the observations is provided by the statistical correlations from a numerical dynamo model in the form of a model covariance matrix. Here we test a sequential DA framework, working through a succession of forecast and analysis steps, that extracts the correlations from an ensemble of dynamo models. The primary correlations couple variables of the same azimuthal wave number, reflecting the predominant axial symmetry of the magnetic field. Synthetic tests show that the scheme becomes unstable when confronted with high-precision geomagnetic observations. Our study has identified spurious secondary correlations as the origin of the problem. Keeping only the primary correlations by localizing the covariance matrix with respect to the azimuthal wave number suffices to stabilize the assimilation. While the first analysis step is fundamental in constraining the large-scale interior state, further assimilation steps refine the smaller and more dynamical scales. This refinement turns out to be critical for long-term geomagnetic predictions. Increasing the assimilation steps from one to 18 roughly doubles the prediction horizon for the dipole from about  tree to six centuries, and from 30 to about  60 yr for smaller observable scales. This improvement is also reflected on the predictability of surface intensity features such as the South Atlantic Anomaly. Intensity prediction errors are decreased roughly by a half when assimilating long observation sequences.…