The investigation of geomagnetic variations has revealed the presence in Earth’s core of a planetary-scale, axially columnar and eccentric gyre flow. Together with the magnetic anomaly of low intensity presently seen beneath the South Atlantic, these structures show that longitudinal hemisphericity is a common feature of the geodynamo. Here, we propose that these hemispherical features result from the onset properties of spherical shell rotating convection in presence of an imposed axial magnetic field, with spatially homogeneous fixed-flux thermal boundary conditions. For an Earth-like range of background magnetic field amplitudes, we find hemispherical critical convection modes that are largely supported by a magneto-Archimedes-Coriolis (MAC) balance and where viscosity plays a secondary role. The morphology of the critical modes is in agreement with the general circulation of the gyre. Pursuing this analysis with self-sustained dynamo simulations, we find that hemispherical modes inherited from convection onset can be maintained if the MAC balance is not perturbed by inertia, the force coming at the next order in the force balance. The presence of the eccentric gyre is therefore conditional to the magnetic energy matching or exceeding the kinetic energy in the system, the so-called strong-field dynamo regime. The simulations also feature low magnetic intensity anomalies that rotate westward together with the gyre flow. We highlight a strong correlation between the gyre longitudinal position, the low intensity focus of magnetic intensity, and the eccentricity of the dynamo-generated dipole, showing that these hemispherical structures are indeed linked by the properties of magnetic induction.

We present a new web tool, Planetary Dynamo Simulation Explorer, to survey available published simulations of rapidly rotating spherical dynamos.With numerical codes and computers being increasingly efficient, recent years have seen a surge in the number of publications presenting such computations.Our tool comes as an interactive catalogue that allows exploring existing dynamos with respect to input and output dimensionless parameters, choosing from various dynamo setups (e.g. choice of boundary conditions, couplings at play, etc.), with the possibility to test scaling laws on a filtered set of simulations.It also links each dynamo to its associated publication and possibly to online datasets. Alongside the cataloguing work, and to enhance comparability across various setups, conversion rules are explicitly derived and aggregated from previous studies and applied on a broad scale for the first time.Thought of as a collaborative and scalable initiative, the web interface allows uploading new simulation metadata.The whole interface, displayed as a website, is designed for the community to have a better overview while driving transparency, open-source initiatives, and FAIR principles (Findable, Accessible, Interoperable, Reusable).We encourage the community to explore and contribute to it at https://geodyn.univ-grenoble-alpes.fr/explorer/

Understanding Earth's core dynamics over millennial timescales requires models that jointly describe the evolution of the geomagnetic field and core surface flow, while accommodating the sparse, irregular, and uncertain nature of archaeomagnetic and palaeomagnetic data. We present a new Bayesian core field and core flow modelling framework that utilises archaeo/palaeomagnetic data directly, combining a reduced stochastic representation of core surface dynamics derived from numerical geodynamo statistics with a probabilistic treatment of observational and chronological uncertainties. A key innovation is an efficient discrete marginalisation of age uncertainties, which avoids the convergence difficulties associated with co-estimating ages in high-dimensional Hamiltonian Monte Carlo inversions. The framework aims to reconstruct the coupled evolution of the geomagnetic field and core surface flow over the past 9000 years while preserving dynamical correlations implied by the prior geodynamo time series. Tests using synthetic data generated from an Earth-like geodynamo demonstrate that the method reliably recovers large-scale geomagnetic field variations and key aspects of core dynamics, including long-term westward drift and the evolution of planetary-scale eccentric gyres. These results show that, when combined with physically informed priors, archaeo/palaeomagnetic data can constrain millennial-scale core flow, paving the way for reconstructions based on real data.

A geodynamo simulation is presented where the Earth's core density, rotation rate, convective power and electrical conductivity are matched, while viscous losses are maintained minor in the force balance and power budget. Improving over earlier preliminary calculations, the simulation is integrated over near 1700 years in physical time, and realistically renders the time scale range between interannual hydromagnetic waves and secular convective motions. The solution has been obtained by gradually approaching these conditions along a path in model parameter space. A quasi-geostrophic, magneto-Archimedes-Coriolis (QG-MAC) force balance is confirmed, with the characteristic length scale of the system remaining near the planetary scale. Without the need for extrapolation, the morphology, variations and dynamics of the velocity, convective density anomaly and magnetic fields are in excellent quantitative agreement with geomagnetic and geodetic observations supplied over the past centuries by navigation, observatories and satellites. In particular, the simulation reveals the contribution of interdecadal magneto-Coriolis waves to geomagnetic variations in the vicinity of 60-yr periods. This direct validation of the convective geodynamo paradigm additionally offers a quantitative and first principle-based physical link between the observable signals and deep Earth geodynamic parameters. The model confirms that a convective power (or Ohmic dissipation) level near 3 TW is needed to account for the observed geomagnetic variations, and that the top of the core should be convectively neutral or unstable. Explaining the core-originated interannual to decadal variations of the length of day through electromagnetic core-mantle coupling requires a lower mantle conductance on the order of 10^9 S. It may also become possible to constrain the outer core electrical conductivity from the observed patterns of interannual magneto-Coriolis waves. Finally, the simulation can be considered a reliable source of prior information for solving geomagnetic inverse and prediction problems.

The geomagnetic field has undergone hundreds of polarity reversals over Earth's history, at a variable pace. In numerical models of Earth's core dynamics, reversals occur with increasing frequency when the convective forcing is increased past a critical level. This transition has previously been related to the influence of inertia in the force balance. Because this force is subdominant in Earth's core, concerns have been raised regarding the geophysical applicability of this paradigm. Reproducing the reversal rate of the past million years also requires forcing conditions that do not guarantee that the rest of the geomagnetic variation spectrum is reproduced. These issues motivate the search for alternative reversal mechanisms. Using a suite of numerical models where buoyancy is provided at the bottom of the core by inner-core freezing, we show that the magnetic dipole amplitude is controlled by the relative strength of subsurface upwellings and horizontal circulation at the core surface. A relative weakening of upwellings brings the system from a stable to a reversing dipole state. This mechanism is purely kinematic because it operates irrespectively of the interior force balance. It is therefore expected to apply at the physical conditions of Earth's core. Subsurface upwellings may be impeded by stable stratification in the outermost core. We show that with weak stratification levels corresponding to a nearly adiabatic core surface heat flow, a single model reproduces the observed geomagnetic variations ranging from decades to millions of years. In contrast with the existing paradigm, reversals caused by this stable top core mechanism become more frequent when the level of stratification increases i.e. when the core heat flow decreases. This suggests that the link between mantle dynamics and magnetic reversal frequency needs to be reexamined.

High quality continuous satellite magnetic data gives unprecedented insights into core surface motions but the inversion process remains under-determined, thus requiring additional information. We make use of the pygeodyn inversion tool, in which the core surface dynamics is forecasted with stochastic equations anchored to prior information from a geodynamo free run. There is no clear overview of the relative importance of the different ‘ingredients’ entering in the core flow inversion process, or of the robustness of the inferred flow features. We document the impact of three factors (or ‘ingredients’): (1) choice of geodynamo prior, (2) choice of geomagnetic field model, and (3) choice of maximum spherical harmonic degree for secular variation. We compare three field models (CHAOS-7, COV-OBS.x2 and Kalmag) and three truncation degree for secular variation. The six dynamo priors allow us to analyse the influence of changing the input parameters towards Earth-like values, changing the dynamo set-up (isotropic boundary conditions or not, stratified or not), and the torques at play.We quantitatively show that changing the prior has a greater impact on the core surface flow than the choice of magnetic field model used as observations. This difference becomes less pronounced in the past due to the data quality decreasing and the field models showing more divergence. Furthermore, we find that the slowly evolving ‘background’ component of flow is more variable among models than the transient component. Transient flow motions appear very coherent for all considered dynamo priors and field models. The recovery from satellite measurements of subdecadal wave dynamics and of a growing eastward motion under the Pacific are robust and appear data driven. Finally, we quantify the efficiency of core flows for generating magnetic variations as a function of frequency. Normalized to their magnitude, rapid changes generate relatively more magnetic signal than slow variations. This is interpreted as the signature of a slow core dynamics approaching a state where induction is mitigated because of dynamical adjustment. As a consequence, a larger part of core surface motions enters the null-space of the kinematic core flow inverse problem towards long time-scales.

One of the most prominent changes in Earth’s magnetic field over the past two centuries is the growth of the South Atlantic Anomaly (SAA)—a region of significantly weakened field intensity. Recent studies have suggested that weak field anomalies such as the SAA are recurrent features of the geomagnetic field, preferentially occurring around certain longitudes and generally drifting westward. These observations have sparked hypotheses linking the weak field anomalies to heat-flux heterogeneities at the core-mantle boundary and/or an eccentric planetary-scale gyre as observed in modern core surface flow reconstructions. To further investigate the underlying mechanisms, we generate core surface flow models that are compatible with the observed geomagnetic field changes. Several recent studies have made use statistics derived from geodynamo simulations to provide physically motivated priors on the core surface flow. Here, we adapt these methods to infer possible core flow solutions spanning the past 9000 years, constrained by archaeomagnetic and sedimentary palaeomagnetic data. Synthetic data are used to explore the extent to which archaeo-/palaeomagnetic observations can recover large-scale core flow variations. The integrated core-field and core-flow modelling approach is then applied to real-world data and the results are discussed within the context of recurrent weak field anomalies.

Probing the possible presence and physical properties of a stably stratified layer atop Earth's core is crucial to better determine the past history and heat budget of the planet. This has previously been done by ascribing a variety of interannual to decadal geomagnetic variations to hydromagnetic waves internal to the layer. This study presents the first self-consistent simulation of the stratified layer dynamics in interplay with the underlying core convection, in physical conditions matching those of Earth's core. Magneto-Archimedes-Coriolis waves of decadal periods appear in stratified layers deeper than a few tens of kilometers and with Brunt-Vaisala frequency matching the rotation rate of the planet. However, the level at which core convection excites these waves is generally insufficient to account for observed geomagnetic variations in this period range. Strong stratification is furthermore deleterious to a number of observed features that unstratified models are successful at reproducing. Fluid flow at the core surface decouples from the interior and becomes strongly dissimilar to geomagnetic inferences. Magnetic jerks and their corresponding near-equatorial, rapidly alternating magnetic acceleration patterns also disappear, because the supporting interannual magneto-Coriolis waves are impeded by the stratified layer. This negative impact on the reproduction of the observed rapid geomagnetic variations limits the possible extent of a stable top layer to the first few tens of kilometers beneath Earth's core surface.

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 approximate 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.

Abstract Understanding the composition of lavas erupted at the surface of the Earth is key to reconstruct the long‐term history of our planet. Recent geochemical analyses of ocean island basalt samples indicate the preservation of ancient mantle heterogeneities dating from the earliest stages of Earth's evolution (Péron & Moreira, 2018, https://doi.org/10.7185/geochemlet.1833), when a global magma ocean was present. Such observations contrast with fluid dynamics studies which demonstrated that in a magma ocean the convective motions, primarily driven by buoyancy, are extremely vigorous (Gastine et al., 2016, https://doi.org/10.1017/jfm.2016.659) and are therefore expected to mix heterogeneities within just a few minutes (Thomas et al., 2023, https://doi.org/10.1093/gji/ggad452). To elucidate this paradox we explored the effects of the Earth's rapid rotation on the stirring efficiency of a magma ocean, by performing state‐of‐the‐art fluid dynamics simulations of low‐viscosity, turbulent convective dynamics in a spherical shell. We found that rotational effects drastically affect the convective structure and the associated stirring efficiency. Rotation leads to the emergence of three domains with limited mass exchanges, and distinct stirring and cooling efficiencies. Still, efficient convective stirring within each region likely results in homogenization within each domain on timescales that are short compared with the solidification timescales of a magma ocean. However, the lack of mass exchange between these regions could lead to three or four large‐scale domains with internally homogeneous, but distinct compositions. The existence of these separate regions in a terrestrial magma ocean suggests a new mechanism to preserve distinct geochemical signatures dating from the earliest stages of Earth's evolution.

SUMMARY The Earth’s magnetic field at the core–mantle boundary is the gradient of a harmonic potential function if the mantle is electrically insulating, and the horizontal components of the field can be derived from its radial component in the mantle. Therefore, these components give no further observational information on the core dynamics. However, it can still be envisioned that the horizontal components of the induction equation at Earth’s core surface yield further knowledge on the fluid motions at the top of the core independently of the observations. Here, we show that they provide a linear relationship between the surface velocity and the surface shear (strain shear) that depends on the mantle electrical conductivity. This offers a protocol to calculate the surface shear that we validate with synthetics obtained from dynamo simulations in the limit of a weak mantle conductance. First, using numerical simulations with stress-free boundary condition at the core surface, we retrieve the expected relationship between the horizontal flow uΣ and the shear, ${\bf u}_\Sigma =r\partial _r {\bf u}_{\Sigma }$. Next, we investigate simulations with no-slip boundary condition and insulating mantle, and we obtain the same relationship, even though the shear is not imposed as a boundary condition. Finally, we calculate the flow shear at the top of the core from a magnetic field model based on satellite measurements. The application to geophysical data indicates larger values of the surface flow shear than in the synthetic case, suggesting a possible role of the mantle electrical conductivity. The surface flow shear, in the simulations, much differs from the radial shear in the flow, deeper in the core, which is influenced by the mostly quasi-geostrophic geometry. This implies that we cannot rely on the relationship between the flow and the radial shear for quasi-geostrophic motions to exploit the horizontal components of the induction equation and gain further information on the flow at the Earth’s core surface.

SUMMARY During the accretion stage, large impacts provided sufficient energy to melt the entire mantle into a terrestrial magma ocean. Processes occurring in the magma ocean may have led to the formation of heterogeneities still found in modern ocean island basalts. So far, no definitive mechanism exists to explain the survival of early heterogeneities for approximately 4.5 Ga. Addressing this question requires understanding the efficiency of convective mixing during both the early molten and the solid-state stages experienced by the Earth’s mantle. While mixing in the solid mantle and in an essentially crystallized magma ocean has been relatively well documented, the efficiency of convective mixing in a liquid magma ocean has received less attention. In this paper we characterized the mixing efficiency of a convecting fluid in a rotating spherical shell, accounting for inertial effects, by computing finite-time Lyapunov exponents (i.e. the Lagrangian strain rate). We conducted a series of numerical experiments for a regime where the influence of the buoyancy force dominates that of rotation and we derived scaling laws to predict the mixing efficiency. We found that for a terrestrial magma ocean, in its fully liquid state, mixing time is of the order of a few minutes or less, even for initially large (∼1000 km) heterogeneities. Therefore, passive early mantle heterogeneities cannot survive a fully molten magma ocean stage. This suggests that short-lived heterogeneities (e.g. 182Hf−182W) were either created at the end of the accretional stage, or were stored in deeper regions of the Earth.

SUMMARY Our understanding of the geodynamo has recently progressed thanks to geomagnetic data of improved quality, and analyses resting on numerical simulations of increasing realism. Here, these two advances are combined in order to diagnose the state and present dynamics of Earth’s core in physically realistic conditions. A sequential, ensemble-based framework assimilates the output of geomagnetic field models covering the past 180 yr into a numerical geodynamo simulation, the physical realism of which is also advanced as data is assimilated. The internal dynamical structure estimated for the geodynamo at present reproduces previously widely documented features such as a planetary-scale, eccentric westwards gyre and localization of buoyancy release beneath the Eastern (0°E−180°E) hemisphere. Relating the typical magnetic variation timescale of the assimilated states to the power at which they operate, the present convective power of the geodynamo is estimated at 2.95 ± 0.2 TW, corresponding to an adiabatic heat flow out of the core of 14.8 ± 1 TW if the top of the core is convectively neutrally stratified at present. For the first time, morphologically and dynamically relevant trajectories are obtained by integrating the estimated states forward for a few decades of physical time using a model reaching the physical conditions of Earth’s core. Such simulations accurately account for the spatio-temporal content of high-resolution satellite geomagnetic field models and confirm earlier interpretations in terms of rapid core dynamics. The enforcement of a realistic force balance approaching a Taylor state allows for propagation of weak (velocity perturbation of about 0.6 $\mathrm{km\,yr^{-1}}$) axisymmetric torsional waves with period about 5 yr, supported by a magnetic field of root-mean-squared amplitude of 5.6 mT inside the core. Quasi-geostrophic magneto-Coriolis waves of interannual periods and significantly stronger velocity perturbation (about $7 \mathrm{km\,yr^{-1}}$) are also reproduced, with properties that converge towards those recently retrieved from the analysis of geomagnetic variations before fully achieving Earth’s core conditions. The power spectral density of magnetic variations falls off rapidly at frequencies exceeding the inverse Alfvén time (about $0.6\mathrm{yr^{-1}}$), which indicates that the excitation of hydromagnetic waves occurs preferentially at large spatial scales. The possibility to account for geomagnetic variations from years to centuries in physically realistic models opens the perspective of better constraining properties of the deep Earth through geomagnetic data assimilation.

Turbulent motions of liquid metal in Earth’s outer core generate the geomagnetic field. Magnetic field observations from low-Earth-orbit satellites, together with advanced numerical simulations, indicate that present-day core motions are dominated by a planetary-scale gyre, a jet in the northern polar region and waves involving the magnetic field. In this Review, we explore the dynamics of core gyres, jets and waves and discuss their impact on the magnetism and rotation of the Earth. The planetary gyre is anticyclonic, offset from the rotation axis towards low latitudes under the Atlantic hemisphere and involves flow speeds of 15–50 km yr−1 that are fastest in a focused westward jet under the Bering Strait. A quasi-geostrophic, Magnetic–Archimedes–Coriolis force balance is thought to control the dynamics of the planetary gyre and high latitude jet. Waves in the core flow with periods ~7 years have been detected at low latitudes, that are consistent with an interplay among magnetic, Coriolis and inertial effects. The arrival of wave energy at the core surface accounts for many of the characteristics of interannual geomagnetic field variations. Fluctuations in outer core flow patterns, including the planetary gyre, account for decadal changes in Earth’s length of day, while interannual changes are well explained by wave processes. Systematic investigations of core–mantle coupling mechanisms in models that include wave dynamics promise new insights on poorly constrained physical properties, including deep mantle conductivity. Long-term satellite monitoring of changes in the Earth’s magnetic field is essential if further progress is to be made in understanding core dynamics, as the high-resolution magnetic record remains short compared with the timescales of waves and convection in the core. Gyres, jets and waves are thought to have an important role in Earth’s core dynamics. This Review explores these core processes, based on satellite observations and numerical simulations, and discusses the implications for deep-Earth coupling and forecasting geomagnetic field changes.

SUMMARY Elucidating the processes in the liquid core that have produced observed palaeointensity changes over the last 3.5 Gyr is crucial for understanding the dynamics and long-term evolution of Earth’s deep interior. We combine numerical geodynamo simulations with theoretical scaling laws to investigate the variation of Earth’s magnetic field strength over geological time. Our approach follows the study of Aubert et al., adapted to include recent advances in numerical simulations, mineral physics and palaeomagnetism. We first compare the field strength within the dynamo region and on the core–mantle boundary (CMB) between a suite of 314 dynamo simulations and two power-based theoretical scaling laws. The scaling laws are both based on a Quasi-Geostropic (QG) force balance at leading order and a Magnetic, Archimedian, and Coriolis (MAC) balance at first order and differ in treating the characteristic length scale of the convection as fixed (QG-MAC-fixed) or determined as part of the solution (QG-MAC-free). When the data set is filtered to retain only simulations with magnetic to kinetic energy ratios greater than at least two we find that the internal field together with the root-mean-square and dipole CMB fields exhibit power-law behaviour that is compatible with both scalings within uncertainties arising from different heating modes and boundary conditions. However, while the extrapolated intensity based on the QG-MAC-free scaling matches Earth’s modern CMB field, the QG-MAC-fixed prediction shoots too high and also significantly overestimates palaeointensities over the last 3.5 Gyr. We combine the QG-MAC-free scaling with outputs from 275 realizations of core–mantle thermal evolution to construct synthetic true dipole moment (TDM) curves spanning the last 3.5 Gyr. Best-fitting TDMs reproduce binned PINT data during the Bruhnes and before inner core nucleation (ICN) within observational uncertainties, but PINT does not contain the predicted strong increase and subsequent high TDMs during the early stages of inner core growth. The best-fitting models are obtained for a present-day CMB heat flow of 11–16 TW, increasing to 17–22 TW at 4 Ga, and predict a minimum TDM at ICN.

SUMMARYGeomagnetic jerks—abrupt changes in the acceleration of Earth’s magnetic field that punctuate geomagnetic records— have been richly documented over the past decades by taking advantage of the complementary strengths of ground observatory and satellite measurements. It has recently been proposed that these events originate from the interplay and timescale separation between slow convection and rapid hydromagnetic wave propagation in Earth’s outer core, with these latter waves playing a key role in the generation of jerk signals. To assess the generality of this explanation, here we analyse a catalogue of 14 events obtained during a 14 000-yr-long temporal sequence from a numerical geodynamo simulation that is the closest to date to Earth’s core conditions regarding timescale separation. Events are classified according to their dynamic origin and the depth at which they are triggered in the outer core. The majority of jerk events are found to arise from intermittent local disruptions of the leading-order force balance between the pressure, Coriolis, buoyancy and Lorentz forces (the QG-MAC balance), that leads to an inertial compensation through the emission of rapid, non-axisymmetric, quasi-geostrophic Alfvén waves from the region where this force balance is disrupted. Jerk events of moderate strength arise from the arrival at low latitudes at the core surface of hydromagnetic wave packets emitted from convective plumes rooted at the inner core boundary. As in an earlier simulation, these account well for jerk features that have recently been documented by satellite and ground observations. The more realistic timescales in the simulation reported here allow further details to be distinguished, such as multiple temporal alternations of geomagnetic acceleration pulses at low latitudes, long-range synchronization of pulse foci in space and rapid longitudinal drift of these foci at the core surface. The strongest events in the catalogue arise from disruption of the leading-order force balance near or at the core surface, from the combined influence of the arrival of buoyancy plumes and magnetic field rearrangement. The hydromagnetic waves that are sent laterally and downwards generate signals that clearly illustrate the presence of nearly synchronous ‘V-shaped’ magnetic variation patterns over a wide portion of Earth’s surface and also at mid to high latitudes, despite the source being confined to low latitudes at the core surface. Other well-known characteristics of strong geomagnetic jerks such as surges in the intensity of the secular variation and inflexions in the length-of-day variations are also reproduced in these events. Irrespectively of the event strength, our results support the hypothesis of a single physical root cause—the emission of magneto-inertial waves following a disruption of the QG-MAC balance—for jerks observed throughout the geomagnetic record.

Significance The physics responsible for most of the interannual geomagnetic field changes, continually recorded by satellites for 20 years, is a long-standing open issue. By analyzing magnetic data, we detect Magneto–Coriolis waves in the Earth’s outer core that account for a significant part of this signal. We further propose theoretical advances in the physical characterization of these waves, enabling a deeper understanding of the dynamics behind the geomagnetic signal. It should allow one to better sketch the heterogeneous magnetic field deep within the core, shedding further light on the mechanisms that sustain the geodynamo. Our interpretation does not require the presence of a stratified layer at the top of the core, with potent consequences regarding the Earth’s thermal history.

In December 2019, the International Association of Geomagnetism and Aeronomy (IAGA) Division V Working Group (V-MOD) adopted the thirteenth generation of the International Geomagnetic Reference Field (IGRF). This IGRF updates the previous generation with a definitive main field model for epoch 2015.0, a main field model for epoch 2020.0, and a predictive linear secular variation for 2020.0 to 2025.0. This letter provides the equations defining the IGRF, the spherical harmonic coefficients for this thirteenth generation model, maps of magnetic declination, inclination and total field intensity for the epoch 2020.0, and maps of their predicted rate of change for the 2020.0 to 2025.0 time period.

In December 2019, the 13th revision of the International Geomagnetic Reference Field (IGRF) was released by the International Association of Geomagnetism and Aeronomy (IAGA) Division V Working Group V-MOD. This revision comprises two new spherical harmonic main field models for epochs 2015.0 (DGRF-2015) and 2020.0 (IGRF-2020) and a model of the predicted secular variation for the interval 2020.0 to 2025.0 (SV-2020-2025). The models were produced from candidates submitted by fifteen international teams. These teams were led by the British Geological Survey (UK), China Earthquake Administration (China), Universidad Complutense de Madrid (Spain), University of Colorado Boulder (USA), Technical University of Denmark (Denmark), GFZ German Research Centre for Geosciences (Germany), Institut de physique du globe de Paris (France), Institut des Sciences de la Terre (France), Pushkov Institute of Terrestrial Magnetism, Ionosphere and Radio Wave Propagation (Russia), Kyoto University (Japan), University of Leeds (UK), Max Planck Institute for Solar System Research (Germany), NASA Goddard Space Flight Center (USA), University of Potsdam (Germany), and Université de Strasbourg (France). The candidate models were evaluated individually and compared to all other candidates as well to the mean, median and a robust Huber-weighted model of all candidates. These analyses were used to identify, for example, the variation between the Gauss coefficients or the geographical regions where the candidate models strongly differed. The majority of candidates were sufficiently close that the differences can be explained primarily by individual modeling methodologies and data selection strategies. None of the candidates were so different as to warrant their exclusion from the final IGRF-13. The IAGA V-MOD task force thus voted for two approaches: the median of the Gauss coefficients of the candidates for the DGRF-2015 and IGRF-2020 models and the robust Huber-weighted model for the predictive SV-2020-2025. In this paper, we document the evaluation of the candidate models and provide details of the approach used to derive the final IGRF-13 products. We also perform a retrospective analysis of the IGRF-12 SV candidates over their performance period (2015–2020). Our findings suggest that forecasting secular variation can benefit from combining physics-based core modeling with satellite observations.

SUMMARY Ground observatory and satellite-based determinations of temporal variations in the geomagnetic field probe a decadal to annual timescale range where Earth’s core slow, inertialess convective motions and rapidly propagating, inertia-bearing hydromagnetic waves are in interplay. Here we numerically model and jointly investigate these two important features with the help of a geodynamo simulation that (to date) is the closest to the dynamical regime of Earth’s core. This model also considerably enlarges the scope of a previous asymptotic scaling analysis, which in turn strengthens the relevance of the approach to describe Earth’s core dynamics. Three classes of hydrodynamic and hydromagnetic waves are identified in the model output, all with propagation velocity largely exceeding that of convective advection: axisymmetric, geostrophic Alfvén torsional waves, and non-axisymmetric, quasi-geostrophic Alfvén and Rossby waves. The contribution of these waves to the geomagnetic acceleration amounts to an enrichment and flattening of its energy density spectral profile at decadal timescales, thereby providing a constraint on the extent of the $f^{-4}$ range observed in the geomagnetic frequency power spectrum. As the model approaches Earth’s core conditions, this spectral broadening arises because the decreasing inertia allows for waves at increasing frequencies. Through non-linear energy transfers with convection underlain by Lorentz stresses, these waves also extract an increasing amount of energy from the underlying convection as their key timescale decreases towards a realistic value. The flow and magnetic acceleration energies carried by waves both linearly increase with the ratio of the magnetic diffusion timescale to the Alfvén timescale, highlighting the dominance of Alfvén waves in the signal and the stabilizing control of magnetic dissipation at non-axisymmetric scales. Extrapolation of the results to Earth’s core conditions supports the detectability of Alfvén waves in geomagnetic observations, either as axisymmetric torsional oscillations or through the geomagnetic jerks caused by non-axisymmetric waves. In contrast, Rossby waves appear to be too fast and carry too little magnetic energy to be detectable in geomagnetic acceleration signals of limited spatio-temporal resolution.