Forecasting yearly geomagnetic variation through sequential estimation of core low and magnetic diffusion

Earth’s internal magnetic field is generated through motion of the electrically conductive iron-alloy fluid comprising its outer core. Temporal variability of this magnetic field, termed secular variation (SV), results from two processes: one is the interaction between core fluid motion and the magnetic field, the other is magnetic diffusion. As diffusion is widely thought to take place over relatively long, millennial time scales, it is common to disregard it when considering yearly to decadal field changes; in this frozen-flux approximation, core fluid motion may be inferred on the core–mantle boundary (CMB) using observations of SV at Earth’s surface. Such flow models have been used to forecast variation in the magnetic field. However, recent work suggests that diffusion may also contribute significantly to SV on short time scales provided that the radial length scale of the magnetic field structure within the core is sufficiently short. In this work, we introduce a hybrid method to forecast field evolution that considers a model based on both a steady flow and diffusion, in which we adopt a two-step process: first fitting the SV to a steady flow, and then fitting the residual by magnetic diffusion. We assess this approach by hindcasting the evolution for 2010–2015, based on fitting the models to CHAOS-6 using time windows prior to 2010. We find that including diffusion yields a reduction of up to 25% in the global hindcast error at Earth’s surface; at the CMB this error reduction can be in excess of 77%. We show that fitting the model over the shortest window that we consider, 2009–2010, yields the lowest hindcast error. Based on our hindcast tests, we present a candidate model for the SV over 2020–2025 for IGRF-13, fit over the time window 2018.3–2019.3. Our forecasts indicate that over the next decade the axial dipole will continue to decay, reversed-flux patches will increase in both area and intensity, and the north magnetic (dip) pole will continue to migrate towards Siberia

Predictions of the geomagnetic secular variation based on the ensemble sequential assimilation of geomagnetic field models by dynamo simulations

The IGRF offers an important incentive for testing algorithms predicting the Earth’s magnetic field changes, known as secular variation (SV), in a 5-year range. Here, we present a SV candidate model for the 13th IGRF that stems from a sequential ensemble data assimilation approach (EnKF). The ensemble consists of a number of parallel-running 3D-dynamo simulations. The assimilated data are geomagnetic field snapshots covering the years 1840 to 2000 from the COV-OBS.x1 model and for 2001 to 2020 from the Kalmag model. A spectral covariance localization method, considering the couplings between spherical harmonics of the same equatorial symmetry and same azimuthal wave number, allows decreasing the ensemble size to about a 100 while maintaining the stability of the assimilation. The quality of 5-year predictions is tested for the past two decades. These tests show that the assimilation scheme is able to reconstruct the overall SV evolution. They also suggest that a better 5-year forecast is obtained keeping the SV constant compared to the dynamically evolving SV. However, the quality of the dynamical forecast steadily improves over the full assimilation window (180 years). We therefore propose the instantaneous SV estimate for 2020 from our assimilation as a candidate model for the IGRF-13. The ensemble approach provides uncertainty estimates, which closely match the residual differences with respect to the IGRF-13. Longer term predictions for the evolution of the main magnetic field features over a 50-year range are also presented. We observe the further decrease of the axial dipole at a mean rate of 8 nT/year as well as a deepening and broadening of the South Atlantic Anomaly. The magnetic dip poles are seen to approach an eccentric dipole configuration

Sequential assimilation of geomagnetic observations: perspectives for the reconstruction and prediction of core dynamics

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 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

Modeling and Predicting the Short‐Term Evolution of the Geomagnetic Field

We propose a reduced dynamical system describing the coupled evolution of fluid flow and magnetic field at the top of the Earth's core between the years 1900 and 2014. The flow evolution is modeled with a first‐order autoregressive process, while the magnetic field obeys the classical frozen flux equation. An ensemble Kalman filter algorithm serves to constrain the dynamics with the geomagnetic field and its secular variation given by the COV‐OBS.x1 model. Using a large ensemble with 40,000 members provides meaningful statistics including reliable error estimates. The model highlights two distinct flow scales. Slowly varying large‐scale elements include the already documented eccentric gyre. Localized short‐lived structures include distinctly ageostophic features like the high‐latitude polar jet on the Northern Hemisphere. Comparisons with independent observations of the length‐of‐day variations not only validate the flow estimates but also suggest an acceleration of the geostrophic flows over the last century. Hindcasting tests show that our model outperforms simpler predictions bases (linear extrapolation and stationary flow). The predictability limit, of about 2,000 years for the magnetic dipole component, is mostly determined by the random fast varying dynamics of the flow and much less by the geomagnetic data quality or lack of small‐scale information