An Introduction to Data Assimilation and Predictability in Geomagnetism

Abstract

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

Inferring internal properties of Earth's core dynamics and their evolution from surface observations and a numerical geodynamo model

“…In both cases it is usually referred to as stochastic inversion, but we also note that it is formally identical to one of the Kalman filter equations (e.g. Fournier et al, 2010). The stochastic inversion will be more efficient when P contains strong correlations between the observed and unobserved parts of the state vector.…”

“…Fournier et al, 2010). Our assimilation scheme loses this property because of its imperfections: a timeindependent covariance matrix is used and a part of the solution length scales spectrum (for l and m above l p max ) is left untouched at analysis time and remains only determined by the dynamics.…”

“…The problem of determining core flow then becomes an inverse problem where an initial condition is sought, the evolution of which will subsequently explain and predict the observations at various points in time, hereby all dynamically connected together. Along these lines, the now expanding field of geomagnetic data assimilation aims at optimally combining physical laws and observations of Earth's core dynamics (see Fournier et al, 2010, for a recent review). This expansion capitalizes on the progress made over the last twenty years by data assimilation techniques in other fields of research, most importantly (from the viewpoint of core dynamics), atmospheric dynamics and physical oceanography.…”

Assimilating Data Into an Αω Dynamo Model of the Sun: A Variational Approach

“…A next step could be to use a nonlinear dynamo model that is sensitive to the initial conditions and which uses polar coordinates rather than Cartesian ones. Finally, we could also introduce a so-called background term in the cost function, which limits the departure from an a priori estimate of the state vector (see Fournier et al 2010, for further details). This allows to introduce data that is not contained in the observations such as information on the smoothness of the physical parameters (like the function α for example).…”

Testing IGRF-11 candidate models against CHAMP data and quasi-definitive observatory data

“…This parameterization reflects our currently limited forecasting capability. Despite recent progress in data assimilation and other forecasting techniques applied to geomagnetism (e.g., Fournier et al, 2010), we cannot accurately forecast the secular variation over more than a few months to a year. This can be seen on Fig.…”