With more than five years of magnetic data from the Swarm satellite constellation we now have a new and more detailed picture of the time-varying magnetic field generated in Earth's liquid metal outer core. We present a summary of this picture based on a geomagnetic field model (the latest update in the CHAOS model series) derived using the latest Swarm data as well as early missions and ground magnetic observatories. We are able to determine the time derivative of the field, known as the secular variation, at the core-mantle boundary out to at least spherical harmonic degree 18 while the rapidly changing core field secular acceleration is now known to degree 10. We present comparisons with alternative analysis techniques and possible explanations for recently observed field accelerations in terms of core dynamics.

We present a new model of time-dependent flow at low latitudes in the Earth's core between 2000 and 2017, derived from magnetic field measurements made onboard the Swarm and CHAMP satellites and at ground magnetic observatories. The model, called CoreFlo-LL.1, consists of a steady background flow without imposed symmetry plus a time-dependent flow that is separated into geostrophic and quasi-geostrophic components. Core flow mode amplitudes are determined at four month intervals by a robust least squares fit to ground and satellite secular variation data. The l_1 norm of the square root of the mode enstrophies, and the l_2 norm of the flow acceleration, are minimised during the inversion procedure. We find that the equatorial region beneath the core-mantle boundary is a place of vigorous, localized, fluid motions; time-dependent flow focused at low latitudes close to the core surface is able to reproduce rapid field variations observed at non-polar latitudes at and above Earth's surface. Magnetic field acceleration pulses are produced by alternating bursts of non-zonal azimuthal flow acceleration in this region. Such bursts are prominent in the longitudinal sectors from 80-130E and 60-100W throughout the period studied, but are also evident under the equatorial Pacific from 130E to 150W after 2012. We find a distinctive interannual alternation in the sign of the non-zonal azimuthal flow acceleration at some locations, involving a rapid cross-over between flow acceleration convergence and divergence. Such acceleration sign changes can occur within a year or less, and when the structures involved are of large spatial scale they can give rise to geomagnetic jerks at the Earth's surface. For example, in 2014, we find a change in the sign of the non-zonal azimuthal flow acceleration under the equatorial Pacific, as a region of flow acceleration divergence near 130E changes to a region of flow acceleration convergence. This occurs at a maximum in the amplitude of the time-varying azimuthal flow under the equatorial Pacific and corresponds to a geomagnetic jerk at the Earth's surface.

Data from the Swarm mission have helped identify two important features in the time varying magnetic field (its secular variation) at high latitude. First is a band of magnetic field structures, arranged in a circular configuration around the north geographic pole, that is undergoing very rapid temporal change. The location of this rapid secular variation is localised to the tangent cylinder, the cylinder of fluid within the liquid core that is aligned with the rotation axis and tangent to the solid inner core. Based on local models of the dynamics in this region, the secular variation has been recently attributed to a westwards accelerating jet within Earth's liquid core that has strengthened significantly in the last two decades to current speeds of around 50km/yr. These local modelling results are corroborated by global models of core-fluid flow, inferred from the global structure of magnetic change.
The second feature is a remarkable and recent change in the location of the north magnetic pole (the location on Earth's surface where the magnetic field is locally vertical). Over the last few hundred years, the magnetic pole has shown some time variability but has been located in Canada. However, beginning in the mid 1990's it began to move northwards and is currently at its closest likely proximity to the north geographic pole. The current trajectory of the north magnetic pole will take it towards Russia in the coming decades. By contrast, in the south, there is little evidence of either strong secular variation near the southern tangent cylinder or of any recent deviation of the south magnetic pole from its historical position.
The dynamics occurring at and around the south pole therefore shows a striking difference compared with those of the north.

I shall review the latest observational evidence for both features using data from Swarm and other sources, and discuss their dynamical origin.

Arose over the past decade a new generation of geodynamo simulations. These start to show not only static but also dynamical Earth-like features. They however struggle to target interannual geomagnetic changes, such as those witnessed by recent satellite missions. Here we fit multi-dimensional stochastic processes of the core surface dynamics to cutting-edge geodynamo simulation series. The obtained reduced model mimic models derived from primitive equations at decadal and longer periods, and complement by construction their too low power at high frequencies. We implement the derived stochastic model into a data assimilation algorithm and present a re-analysis of geomagnetic records over the observatory and satellite eras.

We will discuss progress in the theory of 4D variational data assimilation for the core. Data assimilation holds the prospect of learning about the interior properties of the core such as functions of magnetic field strength and perhaps buoyancy. Such a scheme requires a predictive model (dynamical core) that generates a trajectory of the magnetic field from an initial state. At the present time a dynamical core that is suitable for short time scale dynamics does not exist, and it is a community challenge to develop an appropriate model.

Our focus will be on models for the dynamical core. We will show our success in a proof of concept where the dynamical model contains most forces thought to be relevant in the core, with the proviso that the role played by viscosity is too large (as is commonly the case). When data are given for several thousand years, we can demonstrate recovery of some properties of the core magnetic field. We will discuss recent progress in the development of a completely inviscid model of the core’s dynamics that has been developed for very long (centennial) time scales and beyond, and is designed to suitably represent the dynamo process. This model is not suitable for a dynamical core on sub-decadal time scales, but illustrates what can be achieved. Finally we will discuss some of the progress and pitfalls that apply to an inviscid short-timescale model that is under development and that might be suitable for data assimilation using several decades of satellite data. The model is based on the quasi-geostrophic approximation that prescribes a leading role to the axial invariance of horizontal fluid motions as a consequence of the Coriolis force. Our present work focuses on taking into account the presence of Lorentz (magnetic) forces, and possibly the effects of buoyancy.

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.
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.
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.