N. Gillet

International Geomagnetic Reference Field: the 12th generation

The 12th generation of the International Geomagnetic Reference Field (IGRF) was adopted in December 2014 by the Working Group V-MOD appointed by the International Association of Geomagnetism and Aeronomy (IAGA). It updates the previous IGRF generation with a definitive main field model for epoch 2010.0, a main field model for epoch 2015.0, and a linear annual predictive secular variation model for 2015.0-2020.0. Here, we present the equations defining the IGRF model, provide the spherical harmonic coefficients, and provide maps of the magnetic declination, inclination, and total intensity for epoch 2015.0 and their predicted rates of change for 2015.0-2020.0. We also update the magnetic pole positions and discuss briefly the latest changes and possible future trends of the Earth’s magnetic field.

Fast torsional waves and strong magnetic field within the Earth’s core

The magnetic field inside the Earth’s fluid and electrically conducting outer core cannot be directly probed. The root-mean-squared (r.m.s.) intensity for the resolved part of the radial magnetic field at the core–mantle boundary is 0.3 mT, but further assumptions are needed to infer the strength of the field inside the core. Recent diagnostics obtained from numerical geodynamo models indicate that the magnitude of the dipole field at the surface of a fluid dynamo is about ten times weaker than the r.m.s. field strength in its interior, which would yield an intensity of the order of several millitesla within the Earth’s core. However, a 60-year signal found in the variation in the length of day has long been associated with magneto-hydrodynamic torsional waves carried by a much weaker internal field. According to these studies, the r.m.s. strength of the field in the cylindrical radial direction (calculated for all length scales) is only 0.2 mT, a figure even smaller than the r.m.s. strength of the large-scale (spherical harmonic degree n ≤ 13) field visible at the core–mantle boundary. Here we reconcile numerical geodynamo models with studies of geostrophic motions in the Earth’s core that rely on geomagnetic data. From an ensemble inversion of core flow models, we find a torsional wave recurring every six years, the angular momentum of which accounts well for both the phase and the amplitude of the six-year signal for change in length of day detected over the second half of the twentieth century. It takes about four years for the wave to propagate throughout the fluid outer core, and this travel time translates into a slowness for Alfvén waves that corresponds to a r.m.s. field strength in the cylindrical radial direction of approximately 2 mT. Assuming isotropy, this yields a r.m.s. field strength of 4 mT inside the Earth’s core.

Ensemble inversion of time‐dependent core flow models

Quasi-geostrophic core flow models are built from two secular variation models spanning the periods 1960–2002 and 1997–2008. We rely on an ensemble method to account for the contributions of the unresolved small-scale magnetic field interacting with core surface flows to the observed magnetic field changes. The different core flow members of the ensemble solution agree up to spherical harmonic degree l ≃ 10, and this resolved component varies only weakly with regularization. Taking into account the finite correlation time of the small-scale concealed magnetic field, we find that the time variations of the magnetic field occurring over short time scales, such as the geomagnetic jerks, can be accounted for by the resolved (large-scale) part of the flow to a large extent. Residuals from our flow models are 30% smaller for recent epochs, after 1995. This result is attributed to an improvement in the quality of geomagnetic data. The magnetic field models show little frozen flux violation for the most recent epochs, within our estimate of the apparent magnetic flux changes at the core-mantle boundary arising from spatial resolution errors. We associate the more important flux changes detected at earlier epochs with uncertainties in the field models at large harmonic degrees. Our core flow models show, at all epochs, an eccentric and planetary-scale anticyclonic gyre circling around the cylindrical surface tangent to the inner core, at approximately 30 and 60 latitude under the Indian and Pacific oceans, respectively. They account well for the changes in core angular momentum for the most recent epochs.

Recent geomagnetic secular variation from Swarm and ground observatories as estimated in the CHAOS-6 geomagnetic field model

We use more than 2 years of magnetic data from the Swarm mission, and monthly means from 160 ground observatories as available in March 2016, to update the CHAOS time-dependent geomagnetic field model. The new model, CHAOS-6, provides information on time variations of the core-generated part of the Earth’s magnetic field between 1999.0 and 2016.5. We present details of the secular variation (SV) and secular acceleration (SA) from CHAOS-6 at Earth’s surface and downward continued to the core surface. At Earth’s surface, we find evidence for positive acceleration of the field intensity in 2015 over a broad area around longitude 90°E that is also seen at ground observatories such as Novosibirsk. At the core surface, we are able to map the SV up to at least degree 16. The radial field SA at the core surface in 2015 is found to be largest at low latitudes under the India–South-East Asia region, under the region of northern South America, and at high northern latitudes under Alaska and Siberia. Surprisingly, there is also evidence for significant SA in the central Pacific region, for example near Hawaii where radial field SA is observed on either side of a jerk in 2014. On the other hand, little SV or SA has occurred over the past 17 years in the southern polar region. Inverting for a quasi-geostrophic core flow that accounts for this SV, we obtain a prominent planetary-scale, anti-cyclonic, gyre centred on the Atlantic hemisphere. We also find oscillations of non-axisymmetric, azimuthal, jets at low latitudes, for example close to 40°W, that may be responsible for localized SA oscillations. In addition to scalar data from Ørsted, CHAMP, SAC-C and Swarm, and vector data from Ørsted, CHAMP and Swarm, CHAOS-6 benefits from the inclusion of along-track differences of scalar and vector field data from both CHAMP and the three Swarm satellites, as well as east–west differences between the lower pair of Swarm satellites, Alpha and Charlie. Moreover, ground observatory SV estimates are fit to a Huber-weighted rms level of 3.1 nT/year for the eastward components and 3.8 and 3.7 nT/year for the vertical and southward components. We also present an update of the CHAOS high-degree lithospheric field, making use of along-track differences of CHAMP scalar and vector field data to produce a new static field model that agrees well with the MF7 field model out to degree 110.

Planetary gyre, time‐dependent eddies, torsional waves, and equatorial jets at the Earth's core surface

We report a calculation of time-dependent quasi-geostrophic core flows for 1940-2010. Inverting recursively for an ensemble of solutions, we evaluate the main source of uncertainties, namely the model errors arising from interactions between unresolved core surface motions and magnetic fields. Temporal correlations of these uncertainties are accounted for. The covariance matrix for the flow coefficients is also obtained recursively from the dispersion of an ensemble of solutions. Maps of the flow at the core surface show, upon a planetary-scale gyre, time-dependent large-scale eddies at mid-latitudes and vigorous azimuthal jets in the equatorial belt. The stationary part of the flow predominates on all the spatial scales that we can resolve. We retrieve torsional waves that explain the length-of-day changes at 4 to 9.5 years periods. These waves may be triggered by the nonlinear interaction between the magnetic field and sub-decadal non-zonal motions within the fluid outer core. Both the zonal and the more energetic non-zonal interannual motions were particularly intense close to the equator (below 10 degrees latitude) between 1995 and 2010. We revise down the amplitude of the decade fluctuations of the planetary scale circulation and find that electromagnetic core-mantle coupling is not the main mechanism for angular momentum exchanges on decadal time scales if mantle conductance is 3 10 8 S or lower.

Gyre-driven decay of the Earth's magnetic dipole

Direct observations indicate that the magnitude of the Earths magnetic axial dipole has decreased over the past 175 years; it is now 9% weaker than it was in 1840. Here we show how the rate of dipole decay may be controlled by a planetary-scale gyre in the liquid metal outer core. The gyres meridional limbs on average transport normal polarity magnetic flux equatorward and reverse polarity flux poleward. Asymmetry in the geomagnetic field, due to the South Atlantic Anomaly, is essential to the proposed mechanism. We find that meridional flux advection accounts for the majority of the dipole decay since 1840, especially during times of rapid decline, with magnetic diffusion making an almost steady contribution generally of smaller magnitude. Based on the morphology of the present field, and the persistent nature of the gyre, the current episode of dipole decay looks set to continue, at least for the next few decades.

Stochastic forecasting of the geomagnetic field from the COV-OBS.x1 geomagnetic field model, and candidate models for IGRF-12

We present the geomagnetic field model COV-OBS.x1, covering 1840 to 2020, from which have been derived candidate models for the IGRF-12. Towards the most recent epochs, it is primarily constrained by first differences of observatory annual means and measurements from the Oersted, Champ, and Swarm satellite missions. Stochastic information derived from the temporal spectra of geomagnetic series is used to construct the a priori model covariance matrix that complements the constraint brought by the data. This approach makes it possible the use of a posteriori model errors, for instance, to measure the ‘observations’ uncertainties in data assimilation schemes for the study of the outer core dynamics.We also present and illustrate a stochastic algorithm designed to forecast the geomagnetic field. The radial field at the outer core surface is advected by core motions governed by an auto-regressive process of order 1. This particular choice is motivated by the slope observed for the power spectral density of geomagnetic series. Accounting for time-correlated model errors (subgrid processes associated with the unresolved magnetic field) is made possible thanks to the use of an augmented state ensemble Kalman filter algorithm. We show that the envelope of forecasts includes the observed secular variation of the geomagnetic field over 5-year intervals, even in the case of rapid changes. In a purpose of testing hypotheses about the core dynamics, this prototype method could be implemented to build the ‘state zero’ of the ability to forecast the geomagnetic field, by measuring what can be predicted when no deterministic physics is incorporated into the dynamical model.

On magnetostrophic inertia-less waves in quasi-geostrophic models of planetary cores

We investigate quasi-geostrophic waves in a rotating spherical shell permeated by an imposed magnetic field . A projection of the momentum equation onto a well chosen class of velocity fields results in a quasi-geostrophic reduced model where, in contrast with previous such models, the evolution of the velocity is not prescribed by an equation for the axial vorticity. We consider fields that may be longitudinally dependent. Increasing the angular rotation frequency, we find that the non-axisymmetric Alfvén waves that are present at low rotation morph into inertial waves, torsional Alfvén waves and low frequency magnetostrophic waves that satisfy Taylor’s constraint (i.e. vanishing acceleration of the geostrophic cylinders by the magnetic forces).

Stochastic modelling of regional archaeomagnetic series

SUMMARY We report a new method to infer continuous time series of the declination, inclination and intensity of the magnetic field from archeomagnetic data. Adopting a Bayesian perspective, we need to specify a priori knowledge about the time evolution of the magnetic field. It consists in a time correlation function that we choose to be compatible with present knowledge about the geomagnetic time spectra. The results are presented as distributions of possible values for the declination, inclination or intensity. We find that the methodology can be adapted to account for the age uncertainties of archeological artefacts and we use Markov Chain Monte Carlo to explore the possible dates of observations. We apply the method to intensity datasets from Mari, Syria and to intensity and directional datasets from Paris, France. Our reconstructions display more rapid variations than previous studies and we find that the possible values of geomagnetic field elements are not necessarily normally distributed. Another output of the model is better age estimates of archeological artefacts.

Geomagnetic observatory monthly series, 1930 to 2010: empirical analysis and unmodeled signal estimation

Ground-based magnetic observatory series are the main source of information for constructing time-dependent spherical harmonic geomagnetic field models from sub-annual to pluri-decadal time scales. Assessing the reliability of such models requires accurate estimation of the data errors. We propose an analysis of observatory monthly means over the period 1930 to 2010, where we sequentially isolate (i) a stochastic regression for the main field at every site, performed in the framework of Gaussian processes, (ii) a local fit to annual and semiannual signals, (iii) a month by month estimate of global, large length-scale external and induced fields. We then estimate the unmodeled signal level (UMSL, which refers to the instrumental noise plus extra signals not captured by the above data treatment) from the standard deviation of the residuals to the sequential analysis. This may be used to estimate data error covariances in future field modeling studies. Mainly a function of the geomagnetic latitude, the UMSL is larger towards auroral regions and carries the temporal signature of solar activity. While the UMSL shows rather similar magnitudes in all three components in recent epochs (typically a few nT), a significant decrease is found in the downward component of the field around 1960, which correlates with the introduction of proton magnetometers. We detail the geographic distribution of the periodic signals and confirm the variation of their amplitude at pluri-decadal time scales. From the spherical harmonic description of horizontal and vertical fields, we isolate the main patterns of the inducing field in Z. These are dominated by a zonal structure of degree 1 (and to a lesser extent, of degree 3) in dipole coordinates. We nevertheless isolate secondary, non-zonal sources that are most active during the 1960s and around 1990, periods of particularly large solar activity, denoting an unusual morphology of the inducing field.