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Inferring Internal Properties of Earth's Core Dynamics and Their Evolution from Surface Observations and a Numerical Geodynamo Model : Volume 18, Issue 5 (12/10/2011)

By Aubert, J.

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Book Id: WPLBN0003974454
Format Type: PDF Article :
File Size: Pages 18
Reproduction Date: 2015

Title: Inferring Internal Properties of Earth's Core Dynamics and Their Evolution from Surface Observations and a Numerical Geodynamo Model : Volume 18, Issue 5 (12/10/2011)  
Author: Aubert, J.
Volume: Vol. 18, Issue 5
Language: English
Subject: Science, Nonlinear, Processes
Collections: Periodicals: Journal and Magazine Collection (Contemporary), Copernicus GmbH
Historic
Publication Date:
2011
Publisher: Copernicus Gmbh, Göttingen, Germany
Member Page: Copernicus Publications

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Aubert, J., & Fournier, A. (2011). Inferring Internal Properties of Earth's Core Dynamics and Their Evolution from Surface Observations and a Numerical Geodynamo Model : Volume 18, Issue 5 (12/10/2011). Retrieved from http://hawaiilibrary.net/


Description
Description: Institut de Physique du Globe de Paris, UMR7154, INSU, CNRS – Université Paris-Diderot, PRES Sorbonne Paris Cité, 1 rue Jussieu, 75238 Paris cedex 5, France. Over the past decades, direct three-dimensional numerical modelling has been successfully used to reproduce the main features of the geodynamo. Here we report on efforts to solve the associated inverse problem, aiming at inferring the underlying properties of the system from the sole knowledge of surface observations and the first principle dynamical equations describing the convective dynamo. To this end we rely on twin experiments. A reference model time sequence is first produced and used to generate synthetic data, restricted here to the large-scale component of the magnetic field and its rate of change at the outer boundary. Starting from a different initial condition, a second sequence is next run and attempts are made to recover the internal magnetic, velocity and buoyancy anomaly fields from the sparse surficial data. In order to reduce the vast underdetermination of this problem, we use stochastic inversion, a linear estimation method determining the most likely internal state compatible with the observations and some prior knowledge, and we also implement a sequential evolution algorithm in order to invert time-dependent surface observations. The prior is the multivariate statistics of the numerical model, which are directly computed from a large number of snapshots stored during a preliminary direct run. The statistics display strong correlation between different harmonic degrees of the surface observations and internal fields, provided they share the same harmonic order, a natural consequence of the linear coupling of the governing dynamical equations and of the leading influence of the Coriolis force. Synthetic experiments performed with a weakly nonlinear model yield an excellent quantitative retrieval of the internal structure. In contrast, the use of a strongly nonlinear (and more realistic) model results in less accurate static estimations, which in turn fail to constrain the unobserved small scales in the time integration of the evolution scheme. Evaluating the quality of forecasts of the system evolution against the reference solution, we show that our scheme can improve predictions based on linear extrapolations on forecast horizons shorter than the system e-folding time. Still, in the perspective of forthcoming data assimilation activities, our study underlines the need of advanced estimation techniques able to cope with the moderate to strong nonlinearities present in the geodynamo.

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

Excerpt
Aubert, J., Aurnou, J., and Wicht, J.: The magnetic structure of convection-driven numerical dynamos, Geophys. J. Int., 172, 945–956, doi:10.1111/j.1365-246X.2007.03693.x, 2008.; Aubert, J., Labrosse, S., and Poitou, C.: Modelling the palaeo-evolution of the geodynamo, Geophys. J. Int., 179, 1414–1428, doi:10.1111/j.1365-246X.2009.04361.x, 2009.; Bloxham, J. and Jackson, A.: Simultaneous stochastic inversion for geomagnetic main field and secular variation, 2, 1820–1980, J. Geophys. Res., 94, 15753–15769, 1989.; Aubert, J., Tarduno, J. A., and Johnson, C. L.: Observations and Models of the Long-Term Evolution of Earth's Magnetic Field, Space. Sci. Rev., 155, 337–370, doi:10.1007/s11214-010-9684-5, 2010.; Braginsky, S. I. and Roberts, P. H.: Equations governing convection in {e}arth's core and the geodynamo, Geophys. Astrophys. Fluid Dyn., 79, 1–97, 1995.; Brasseur, P.: Ocean Data Assimilation using Sequential Methods based on the {K}alman Filter, in: Ocean Weather Forecasting: An Integrated View of Oceanography, edited by: Chassignet, E. and Verron, J., Springer, 271–316, 2006.; Buffett, B. A.: Tidal dissipation and the strength of the Earth's internal magnetic field, Nature, 468, 952–955, doi:10.1038/nature09643, 2010.; Buffett, B. A., Mound, J., and Jackson, A.: Inversion of torsional oscillations for the structure and dynamics of Earth's core, Geophys. J. Int., 177, 878–890, doi:10.1111/j.1365-246X.2009.04129.x, 2009.; Canet, E., Fournier, A., and Jault, D.: Forward and adjoint quasi-geostrophic models of the geomagnetic secular variation, J. Geophys. Res., 114, B11101, doi:10.1029/2008JB006189, 2009.; Christensen, U. and Aubert, J.: Scaling properties of convection-driven dynamos in rotating spherical shells and application to planetary magnetic fields, Geophys. J. Int., 117, 97–114, doi:10.1111/j.1365-246X.2006.03009.x, 2006.; Christensen, U. and Tilgner, A.: Power requirement of the geodynamo from ohmic losses in numerical and laboratory dynamos, Nature, 429, 169–171, doi:10.1038/nature02508, 2004.; Roberts, P. H. and Scott, S.: On the analysis of the secular variation, I. A hydromagnetic constraint: theory., J. Geomag. Geoelectr., 17, 137–151, 1965.; Christensen, U. R.: Geodynamo models: Tools for understanding properties of Earth's magnetic field, Phys. Earth Planet. Int., 187, 157–169, doi:10.1016/j.pepi.2011.03.012, 2011.; Christensen, U. R., Aubert, J., and Hulot, G.: Conditions for Earth-like geodynamo models, Earth. Plan. Sci. Let., 296, 487–496, doi:10.1016/j.epsl.2010.06.009, 2010.; Dormy, E., Cardin, P., and Jault, D.: MHD flow in a slightly differentially rotating spherical shell, with conducting inner core, in a dipolar magnetic field, Earth. Plan. Sci. Let., 160, 15–30, 1998.; Elbern, H., Strunk, A., and Nieradzik, L.: Inverse Modelling and Combined State-Source Estimation for Chemical Weather, in: Data Assimilation, edited by: Lahoz, W., Khattatov, B., and Ménard, R., Springer, Berlin Heidelberg, 491–513, doi:10.1007/978-3-540-74703-119, 2010.; Evensen, G.: Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte-Carlo methods to forecast error stati

 

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