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.

We present a new version of a dynamical spectral model for Large Eddy Simulation based on the Eddy Damped Quasi Normal Markovian approximation [1,2]. Three distinct modifications are implemented and tested. On the one hand, whereas in current approaches, a Kolmogorov-like energy spectrum is usually assumed in order to evaluate the nonlocal transfer, in our method the energy spectrum of the subgrid scales adapts itself dynamically to the large-scale resolved spectrum; this first modification allows in particular for a better treatment of transient phases and instabilities, as shown on one specific example. Moreover, the model takes into account the phase relationships of the small-scales, embodied for example in strong localized structures such as vortex filaments. To that effect, phase information is implemented in the treatment of the so-called eddy noise in the closure model. Finally, we also consider the role that helical small scales may play in the evaluation of the transfer of energy and helicity, the two invariants of the primitive equations in the inviscid case; this leads as well to intrinsic variations in the development of helicity spectra. Therefore, our model allows for simulations of flows for a variety of circumstances and a priori at any given Reynolds number. Comparisons with Direct Numerical Simulations of the three-dimensional Navier-Stokes equation are performed on fluids driven by an ABC (Beltrami) flow which is a prototype of fully helical flows. Good agreements are obtained for physical and spectral behavior of the large scales.

We describe a new, original approach to the modelling of the Earth’s magnetic field. The overall objective of this study is to reliably render fast variations of the core field and its secular variation. This method combines a sequential modelling approach, a Kalman filter, and a correlation-based modelling step. Sources that most significantly contribute to the field measured at the surface of the Earth are modelled. Their separation is based on strong prior information on their spatial and temporal behaviours. We obtain a time series of model distributions which display behaviours similar to those of recent models based on more classic approaches, particularly at large temporal and spatial scales. Interesting new features and periodicities are visible in our models at smaller time and spatial scales. An important aspect of our method is to yield reliable error bars for all model parameters. These errors, however, are only as reliable as the description of the different sources and the prior information used are realistic. Finally, we used a slightly different version of our method to produce candidate models for the thirteenth edition of the International Geomagnetic Reference Field.

We present a dynamical spectral model for large-eddy simulation of the incompressible magnetohydrodynamic (MHD) equations based on the eddy damped quasinormal Markovian approximation. This model extends classical spectral large-eddy simulations for the Navier-Stokes equations to incorporate general (non-Kolmogorovian) spectra as well as eddy noise. We derive the model for MHD flows and show that the introduction of an eddy damping time for the dynamics of spectral tensors, in the absence of equipartition between the velocity and magnetic fields, leads to better agreement with direct numerical simulations, an important point for dynamo computations.