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.

中文翻译：

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基于发电机模拟地磁场模型集合序列同化的地磁长期变化预测

IGRF 为测试预测地球磁场变化（称为 5 年范围内的长期变化 (SV)）的算法提供了重要的激励。在这里，我们提出了第 13 次 IGRF 的 SV 候选模型，该模型源于顺序集成数据同化方法（EnKF）。该集成由许多并行运行的 3D 发电机模拟组成。同化数据是涵盖 1840 年至 2000 年 COV-OBS.x1 模型和 2001 年至 2020 年 Kalmag 模型的地磁场快照。考虑到相同赤道对称性和相同方位波数的球谐函数之间的耦合，谱协方差定位方法允许将集合大小减小到大约 100，同时保持同化的稳定性。过去 20 年对 5 年预测的质量进行了测试。这些测试表明同化方案能够重建整体 SV 演化。他们还表明，与动态演化的 SV 相比，保持 SV 不变可以获得更好的 5 年预测。然而，动态预测的质量在整个同化窗口（180 年）内稳步提高。因此，我们根据我们的同化建议对 2020 年的瞬时 SV 估计值作为 IGRF-13 的候选模型。集合方法提供了不确定性估计，它与 IGRF-13 的残余差异非常匹配。还提供了对 50 年范围内主要磁场特征演变的长期预测。我们观察到轴向偶极子以平均 8 nT/年的速度进一步减少，以及南大西洋异常的加深和扩大。