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We present an update of the geomagnetic data assimilation tool pygeodyn, use it to analyse ground and satellite-based geomagnetic data sets, and report new findings on the dynamics of the Earth's outer core on interannual to decadal timescales. Our results support the idea that quasi-geostrophic Magneto-Coriolis waves, recently discovered at a period of 7 yr, also operate on both shorter and longer timescales, specifically in period bands centred around 3.5 and 15 yr. We revisit the source of interannual variations in the length of day and argue that both geostrophic torsional Alfven waves and quasi-geostrophic Magneto-Coriolis waves can possibly contribute to spectral lines that have been isolated around 8.5 and 6 yr. A significant improvement to our ensemble Kalman filter algorithm comes from accounting for cross-correlations between variables of the state vector forecast, using the 'Graphical lasso' method to help stabilize the correlation matrices. This allows us to avoid spurious shrinkage of the model uncertainties while (i) conserving important information contained in off-diagonal elements of the forecast covariance matrix, and (ii) considering a limited number of realizations, thus reducing the computational cost. Our updated scheme also permits us to use observations either in the form of Gauss coefficient data or more directly as ground-based and satellite-based virtual observatory series. It is thanks to these advances that we are able to place global constraints on core dynamics even at short periods.

We present investigations of rapidly-rotating convection in a thick spherical shell geometry relevant to planetary cores, comparing results from Quasi-Geostrophic (QG), 3D and hybrid QG-3D models. The 170 reported calculations span Ekman numbers, Ek, between 10−4 and 10−10, Rayleigh numbers, Ra, between 2 and 150 times supercritical, and Prandtl numbers, Pr, between 10 and 10−2. The default boundary conditions are no-slip at both the ICB and the CMB for the velocity field, with fixed temperatures at the ICB and the CMB. Cases driven by both homogeneous and inhomogeneous CMB heat flux patterns are also explored, the latter including lateral variations, as measured by Q*, the peak-to-peak amplitude of the pattern divided by its mean, taking values up to 5. The Quasi-Geostrophic (QG) model is based on the open-source pizza code. We extend this in a hybrid approach to include the temperature field on a 3D grid. In general, we find convection is dominated by zonal jets at mid-depths in the shell, with thermal Rossby waves prominent close to the outer boundary when the driving is weaker. For the thick spherical shell geometry studied here the hybrid method is best suited for studying convection at modest forcing, Ra ≤ 10 Rac when Pr = 1, and departs from the 3D model results at higher Ra, displaying systematically lower heat transport characterized by lower Nusselt and Reynolds numbers. We find that the lack of equatorially anti-symmetric and z-correlations between temperature and velocity in the buoyancy force contributes to the weaker flows in the hybrid formulation. On the other hand, the QG models yield broadly similar results to the 3D models, for the specific aspect ratio and range of Rayleigh numbers explored here. We cannot point to major disagreements between these two datasets at Pr ≥ 0.1, although the QG model is effectively more

The 1969 geomagnetic impulse provided the first compelling evidence for rapid changes in Earth's core-generated magnetic field, taking place on timescales of a few years or less. We show here it originated at the core-mantle boundary (CMB) largely as a localized change in the field acceleration under north and central America. We find the impulse events in 1969 and 2017 involved similar amplitudes of field acceleration change with similar localized dipole structures. However in 1969 the acceleration change pattern was north-south rather than east-west oriented, and it propagated poleward rather than westward. Moreover, there was a distinctive local surge in the CMB secular variation leading up to the 1969 event. We propose the 1969 impulse resulted from hydromagnetic waves arriving at the CMB that were triggered by a convective burst near to the core surface; this event involved localized flux expulsion and inward propagating waves.

The solution to a probabilistic inverse problem is the posterior probability distribution for which a full analytic expression is rarely possible. Sampling methods are therefore often used to generate a sample from the posterior. Decision‐makers may be interested in the probability of features related to model parameters (e.g., existence of pollution or the cumulative clay thickness) rather than the individual realizations themselves. Such features and their associated uncertainty, are simple to compute once a sample from the posterior distribution has been generated. However, sampling methods are often associated with high computational costs, especially when the prior and posterior distribution is non‐trivial (non‐Gaussian), and when the inverse problem is non‐linear. Here we demonstrate how to use a neural network to directly estimate posterior statistics of continuous or discrete features of the posterior distribution. The method is illustrated on a probabilistic inversion of airborne EM data from Morrill Nebraska, where the forward problem is nonlinear and the prior information is non‐Gaussian. Once trained the application of the network is fast, with results similar to those obtained using much slower sampling methods.

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.

During the last decade, rapid or extreme geomagnetic field intensity variations associated with rates greater than the maximum currently observed have been inferred from archeomagnetic data in the Near-East and in Western Europe. The most extreme events, termed geomagnetic spikes, are defined as intensity peaks occurring over a short time (a few decades), and are characterized by high variation rates, up to several μT/yr. Magnetic flux expulsion from the Earth’s outer core has been suggested as one possible explanation for these peaks but has not yet been examined in detail. In this study, we develop a two-dimensional kinematic model for magnetic flux expulsion whose key control parameter is the magnetic Reynolds number Rm, the ratio of magnetic diffusion time to advection time. This model enables the tracking of magnetic field lines which are distorted and folded by a fixed flow pattern.

Erroneous statistical estimate of diffusion

We jointly invert for magnetic and velocity fields at the core surface over the period 1997–2017, directly using ground-based observatory time-series and measurements from the CHAMP and Swarm satellites. Satellite data are reduced to the form of virtual observatory time-series distributed on a regular grid in space. Such a sequential storage helps incorporate voluminous modern magnetic data into a stochastic Kalman filter, whereby spatial constraints are incorporated based on a norm derived from statistics of a numerical geodynamo model. Our algorithm produces consistent solutions both in terms of the misfit to the data and the estimated posterior model uncertainties. We retrieve core flow features previously documented from the analysis of spherical harmonic field models, such as the eccentric anticyclonic gyre. We find enhanced diffusion patterns under both Indonesia and Africa. In contrast to a steady flow that is strong under the Atlantic hemisphere but very weak below the Pacific, interannual motions appear evenly distributed over the two hemispheres. Recovered interannual to decadal flow changes are predominantly symmetrical with respect to the equator outside the tangent cylinder. In contrast, under the Northern Pacific we find an intensification of a high latitude jet, but see no evidence for a corresponding feature in the Southern hemisphere. The largest flow accelerations that we isolate over the studied era are associated with meanders, attached to the equatorward meridional branch of the planetary gyre in the Eastern hemisphere, that are linked to the appearance of an eastward equatorial jet below the Western Pacific.

Statistical analyses have shown that the sunward component of the interplanetary magnetic field, Bx (GSM), moderately but significantly affects the auroral intensity. These observations have been interpreted as signatures of a similar IMF Bx control on Birkeland currents, yet to be observed directly. Such a control, attributed to differences in magnetic tension on newly opened magnetic field lines, would lead to stronger region 1 (R1) Birkeland currents for Bx negative (positive) conditions in the northern (southern) hemisphere than when Bx is positive (negative). In this paper we perform a detailed investigation of three different sets of magnetic field measurements, from the CHAMP and Swarm low‐Earth‐Orbit satellites, from the AMPERE products derived from the Iridium satellite constellation, and from the SuperMAG ground magnetometer network, each analyzed using different techniques, to test these predictions. The results show that a change in sign of Bx changes the Birkeland currents by no more than ≈10%. The current patterns show little support for an inter‐hemispheric asymmetry of the kind proposed to explain auroral observations. Instead we propose an alternative interpretation, which is consistent with most of the auroral observations and with the current observations in the present paper, except for those based on AMPERE: The solar wind‐magnetosphere coupling is more efficient when the dipole tilt angle and Bx have the same sign than when they are different. We suggest the higher coupling is because the dayside reconnection region is closer to the subsolar point when the dipole tilt angle and Bx have the same sign.

We present a new climatological model of the ionospheric current system, determined from magnetic measurements taken by the CHAMP and Swarm satellites. The model describes the horizontal currents in the ionosphere, below the satellites, and the field‐aligned (Birkeland) currents that connect the ionosphere with the magnetosphere. The model provides ionospheric current values at any location as continuous functions of solar wind speed, interplanetary magnetic field (IMF), dipole tilt angle, and the F10.7 index of solar flux. Geometric distortions due to variations in the Earth's main magnetic field are taken into account, thus allowing for precise comparisons between the two hemispheres. The model is the first of its kind to describe the full 3D electric currents, and not only the field‐aligned or the equivalent horizontal current. We use this capability to demonstrate a key difference between seasons: During winter, the total horizontal current is almost entirely confined to the auroral oval, for all IMF orientations, where it connects upward and downward Birkeland currents. During more sunlit conditions, the horizontal current extends beyond the auroral oval, and is a sum of currents connecting Birkeland currents and currents that circulate in the ionosphere. The westward electrojet is the only large‐scale current structure that is persistent across seasons. Comparison with average convection maps suggests that it is comprised largely of Hall currents, which connect to Birkeland currents in the winter but not in summer.

The eleventh generation of the International Geomagnetic Reference Field (IGRF) was adopted in December 2009 by the International Association of Geomagnetism and Aeronomy Working Group V-MOD. It updates the previous IGRF generation with a definitive main field model for epoch 2005.0, a main field model for epoch 2010.0, and a linear predictive secular variation model for 2010.0-2015.0. In this note the equations defining the IGRF model are provided along with the spherical harmonic coefficients for the eleventh generation. Maps of the magnetic declination, inclination and total intensity for epoch 2010.0 and their predicted rates of change for 2010.0-2015.0 are presented. The recent evolution of the South Atlantic Anomaly and magnetic pole positions are also examined

This special issue of Earth, Planets and Space, synthesizes the efforts made during the construction of the twelfth generation of the International Geomagnetic Reference Field (IGRF-12) that was released online in December 2014 (http://www.ngdc.noaa.gov/IAGA/vmod/ igrf.html). The IGRF-12 is a series of standard mathematical models describing the large scale internal part of the Earth’s magnetic field between epochs 1900.0 and 2015.0 with a forecast to epoch 2020.0. This activity has been maintained since 1968 by a working group of volunteer scientists from several international institutions but grew out from discussions started in the early 1960s (Barton, 1997). The IGRF task force operates under the auspices of the International Association of Geomagnetism and Aeronomy/Association Internationale de Géomagnétisme et d’Aéronomie (IAGA/AIGA), which is one of the International Union of Geodesy and Geophysics/Union Internationale de Géodésie et Géophysique (IUGG/UIGG), an “international organization dedicated to advancing, promoting, and communicating knowledge of the Earth system, its space environment, and the dynamical processes causing change” (http://www.iugg.org/).