Waves in Earth's core and geomagnetic field forecast

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We use advanced numerical geodynamo series to derive a reduced stochastic model of the dynamics at the surface of Earth's core. Considering order 3 autoregressive (AR-3) processes allows to replicate the simulated spatiotemporal spectrum over a broad range of time-scales, spanning millennia to a fraction of year, including the cut-off found for periods shorter than approximately 2 years and associated with magnetic dissipation. We show how to derive such a forward model from a variety of input simulation series, and present its implementation into the pygeodyn data assimilation algorithm, based on a sequential ensemble method. The updated scheme is applied to perform magnetic field hindcasts and core flow reanalyses. For all observable length-scales, the rate of change of the observed magnetic field is most of the time accounted for within the spread of the forward model trajectories. AR-3 predictions on average supersede by about 35 % linear extrapolations on short (2 yr) time-scales, reducing high-frequency spurious variations in reanalysed flow motions. This improvement is reduced to ≈10% for 5 yr increments, with a large variability from one epoch to the other depending on the overall curvature of the magnetic field evolution. We perform a reanalysis over the period 1880–2023 covered by observatory and satellite records. We find enhanced kinetic energy in three period ranges around 12.5, 6.5 and 3.5 years. At all three periods, fluid motions share geometrical properties compatible with quasi-geostrophic magneto-Coriolis waves: equatorial symmetry, larger amplitude near the equator, flow dominated by low azimuthal wave number and modulated in longitude, phase speed much faster than the fluid velocity and decreasing with the period. At 6.5 yr period we trace back to the mid-1990's the patterns previously detected from satellite data. We also find in the 1960–70's a similar wave-train, possibly in link with the 1969 geomagnetic jerk. The AR-3 model, in conjunction with early satellite records, likely helps isolate such coherent features on interannual time-scales. Similar wave-like motions also show up at 3.5 yr period around 1970 and during the past decades. At periods around 12.5 yr we detect recurrent patterns starting as far back as 1920, and modulated over decadal time-scales. Our results show growing evidence for core dynamics governed by the presence of hydro-magnetic waves over a wide range of periods. This may allow deterministic and/or empirical descriptions of the signal that may help sound deep Earth's properties, and improve predictions of the magnetic field evolution.