[1] The knowledge of the spatial power spectra of the main geomagnetic field and of its secular variation makes it possible to define typical timescales t n for each spherical harmonic degree n. Investigating both observations and numerical dynamos, we show that a one-parameter law of the form t n = t SV /n is satisfied for the non-dipole field, given the statistical way the observed t n are expected to fluctuate. Consequently, we determine the corresponding secularvariation timescale t SV from either instantaneous or timeaveraged spectra, leading to a value of 415 ± 45 55 yr for recent satellite field models. In the broader context of geomagnetic data assimilation, t SV could provide a sensible and convenient means to rescale the time axis of dynamo simulations.

International audienceData assimilation in geomagnetism designates the set of inverse methods for geomagnetic data analysis which rely on an underlying prognostic numerical model of core dynamics. Within that framework, the time-dependency of the magnetohydrodynamic state of the core need no longer be parameterized: The model trajectory (and the secular variation it generates at the surface of the Earth) is controlled by the initial condition, and possibly some other static control parameters. The primary goal of geomagnetic data assimilation is then to combine in an optimal fashion the information contained in the database of geomagnetic observations and in the dynamical model, by adjusting the model trajectory in order to provide an adequate fit to the data. The recent developments in that emerging field of research are motivated mostly by the increase in data quality and quantity during the last decade, owing to the ongoing era of magnetic observation of the Earth from space, and by the concurrent progress in the numerical description of core dynamics. In this article we review briefly the current status of our knowledge of core dynamics, and elaborate on the reasons which motivate geomagnetic data assimilation studies, most notably (a) the prospect to propagate the current quality of data backward in time to construct dynamically consistent historical core field and flow models, (b) the possibility to improve the forecast of the secular variation, and (c) on a more fundamental level, the will to identify unambiguously the physical mechanisms governing the secular variation. We then present the fundamentals of data assimilation (in its sequential and variational forms) and summarize the observations at hand for data assimilation practice. We present next two approaches to geomagnetic data assimilation: The first relies on a three-dimensional model of the geodynamo, and the second on a quasi-geostrophic approximation. We also provide an estimate of the limit of the predictability of the geomagnetic secular variation based upon a suite of three-dimensional dynamo models. We finish by discussing possible directions for future research, in particular the assimilation of laboratory observations of liquid metal analogs of Earth's core