A case for variational geomagnetic data assimilation: insights from a one-dimensional, nonlinear, and sparsely observed MHD system

Secular variations of the geomagnetic field have been measured with a continuously improving accuracy during the last few hundred years, culminating nowadays with satellite data. It is however well known that the dynamics of the magnetic field is linked to that of the velocity field in the core and any attempt to model secular variations will involve a coupled dynamical system for magnetic field and core velocity. Unfortunately, there is no direct observation of the velocity. Independently of the exact nature of the above-mentioned coupled system -- some version being currently under construction -- the question is debated in this paper whether good knowledge of the magnetic field can be translated into good knowledge of core dynamics. Furthermore, what will be the impact of the most recent and precise geomagnetic data on our knowledge of the geomagnetic field of the past and future? These questions are cast into the language of variational data assimilation, while the dynamical system considered in this paper consists in a set of two oversimplified one-dimensional equations for magnetic and velocity fields. This toy model retains important features inherited from the induction and Navier-Stokes equations: non-linear magnetic and momentum terms are present and its linear response to small disturbances contains Alfvén waves. It is concluded that variational data assimilation is indeed appropriate in principle, even though the velocity field remains hidden at all times; it allows us to recover the entire evolution of both fields from partial and irregularly distributed information on the magnetic field. This work constitutes a first step on the way toward the reassimilation of historical geomagnetic data and geomagnetic forecast

Etude des mouvements à la surface du noyau terrestre : du 17ème au 21ème siècle

Composition du jury :C. Jaupart (président), P. Cardin (rapporteur), D. Gibert (rapporteur), A. Tangborn (examinateur), G. Hulot (directeur)In order to study the dynamics of the Earth's outer core, we compute core surface flows from observations of the main magnetic field. The relevance of these computations is confirmed by the similarities of the flows obtained with two independent methods and the results of different synthetic tests. Two different kind of observations are used: ground-based observations for the time period 1590-1990 and recent high-resolution satellite observations. We thus obtain a time series of the historical flows as well as a detailed model of the present flow. The evaluation of errors associated to these flows enable us to identify their reliable features. The velocity fields we obtain are in good agreement with different phenomena appearing in 3D-simulations of core dynamics. We also show that geomagnetic jerks have an explicit signature incore surface dynamics. In the last chapter, a variational data assimilation method for the study of the Earth's core is introduced.Afin d'étudier la dynamique du noyau terrestre, nous reconstruisons les mouvements à la surface du noyau liquide compatibles avec les observations du champ magnétique. La similitude des mouvements obtenus par deux méthodes indépendantes et les résultats de tests synthétiques confirment la pertinence de ces reconstructions. Deux types d'observations sont utilisées : des observations terrestres couvrant la période 1590-1990 et des observations satellitaires haute-résolution récentes. Une série temporelle des mouvementshistoriques et un modèle détaillé des mouvements actuels sont obtenus. L'estimation des marges d'erreurs associées permet d'identifier les structures fiables. Nos reconstructions sont en accord avec différents phénomènes mis en évidence par des modélisations 3D du noyau. Nous montrons aussi que les jerks géomagnétiques ont une signature dynamique très nette. Enfin, nous posons les bases d'une méthode d'assimilation variationnelle de données adaptée à l'étude du noyau

On core surface flows inferred from satellite magnetic data

International audienceSatellite-data allows the magnetic field produced by the dynamo within the Earth's core to be imaged with much more accuracy than previously possible with only ground-based data. Changes in this magnetic field can in turn be used to make some inferences about the core surface flow responsible for them. In this paper, we investigate the improvement brought to core flow computation by new satellite-data based core magnetic field models. It is shown that the main limitation now encountered is no longer the (now high) accuracy of those models, but the “non-modelled secular variation” produced by interaction of the non-resolvable small scales of the core flow with the core field, and by interaction of the (partly) resolvable large scales of the core flow with the small scales of the core field unfortunately masked by the crustal field. We show how this non-modelled secular variation can be taken into account to recover the largest scales of the core flow in a consistent way. We also investigate the uncertainties this introduces in core flows computed with the help of the frozen-flux and tangentially geostrophic assumptions. It turns out that flows with much more medium and small scales than previously thought are needed to explain the satellite-data-based core magnetic field models. It also turns out that a significant fraction of this flow unfortunately happens to be non-recoverable (being either “non-resolvable” because too small-scale, or “invisible”, because in the kernel of the inverse method) even though it produces the detectable “non-modelled secular variation”. Applying this to the Magsat (1980) to Ørsted (2000) field changes leads us to conclude that a flow involving at least strong retrograde vortices below the Atlantic Hemisphere, some less-resolved prograde vortices below the Pacific Hemisphere, and some poorly resolved (and partly non-resolvable) polar vortices, is needed to explain the 1980-2000 satellite-era average secular variation. The characteristics of the fraction of the secular variation left unexplained by this flow are also discussed

Small-scale structure of the geodynamo inferred from Ørsted and Magsat satellite data

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