Impact of Length-of-Day inclusion on geomagnetic secular variationforecast by a recurrent neural network

The primary challenge in forecasting the Earth's magnetic field lies in capturing rapid, non-linear events like geomagnetic jerks. Conventional models relying solely on geomagnetic data often struggle to replicate the variation of those abrupt changes, such as the 2014–2015 geomagnetic jerk.

This study introduces a multiple data approach that simultaneously co-estimates geomagnetic snapshots and Length-of-Day (LOD) variations using a machine learning method. Specifically, we use an Extended Kalman Filter-trained Recurrent Neural Network (EKF-RNN; Sato et al., in press) to model the complex, non-linear dynamics of the Earth's core, including the geomagnetic jerks.

The training and validation datasets for our neural network were derived from the MCM geomagnetic field model (Ropp & Lesur, 2023), which is based on vector geomagnetic data from global magnetic observatories as well as the CHAMP and Swarm-A satellites (Ropp et al., 2020). To constrain the internal dynamics of the Earth’s core, we incorporated LOD data from the Earth Orientation Parameters series C04, provided by the International Earth Rotation and Reference Systems Service. The LOD dataset combines historical observations with modern space geodetic techniques including Very Long Baseline Interferometry, Satellite Laser Ranging, Global Navigation Satellite Systems and Lunar Laser Ranging, offering a continuous record from 1962 to present (Bizouard & Gambis, 2011).

After removing predictable tidal and atmospheric signals, LOD variations reflect exchanges of angular momentum between the Earth's core and mantle. Since electromagnetic waves such as torsional Alfvén waves generated in the Earth's core are linked to rapid geomagnetic accelerations, inclusion of LOD data may make a key constraint on the geomagnetic forecast. Our results show that a model trained only by geomagnetic secular acceleration (SA) failed to capture the 2014–2015 geomagnetic jerk, whereas adding LOD data showed an improved accuracy during the same event. Specifically, the SA misfit decreased from 4.98 to 2.43 nT/yr². The improvement was most significant when training with the second-order derivatives (i.e., SA snapshots themselves), indicating that the EKF-RNN successfully uncovered the underlying physical connection between geomagnetic acceleration and the Earth’s rotation. This study confirms that a multiple data approach, combining independent yet physically linked observation data, is essential for the next generation of geomagnetic forecast models.