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ABSTRACT: To constrain the forecast horizon of geomagnetic data assimilation, it is of interest to quantify the range of predictability of the geodynamo. Following earlier work in the field of dynamic meteorology, we investigate the sensitivity of numerical dynamos to various perturbations applied to the magnetic, velocity and temperature fields. These perturbations result in some errors, which affect all fields in the same relative way, and grow at the same exponential rate λ=τ−1e, independent of the type and the amplitude of perturbation. Errors produced by the limited resolution of numerical dynamos are also shown to produce a similar amplification, with the same exponential rate. Exploring various possible scaling laws, we demonstrate that the growth rate is mainly proportional to an advection timescale. To better understand the mechanism responsible for the error amplification, we next compare these growth rates with two other dynamo outputs which display a similar dependence on advection: the inverse τ−1SV of the secular-variation timescale, characterizing the secular variation of the observable field produced by these dynamos; and the inverse (τmagdiss)−1 of the magnetic dissipation time, characterizing the rate at which magnetic energy is produced to compensate for Ohmic dissipation in these dynamos. The possible role of viscous dissipation is also discussed via the inverse (τkindiss)−1 of the analogous viscous dissipation time, characterizing the rate at which kinetic energy is produced to compensate for viscous dissipation. We conclude that τe tends to equate τmagdiss for dynamos operating in a turbulent regime with low enough Ekman number, and such that τmagdiss < τkindiss. As these conditions are met in the Earth's outer core, we suggest that τe is controlled by magnetic dissipation, leading to a value τe=τmagdiss≈ 30 yr. We finally discuss the consequences of our results for the practical limit of predictability of the geodynamo.
Geophysical Journal International 07/2011; 186(2):492 - 508. · 2.42 Impact Factor
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ABSTRACT: We show how a 3-D, self-consistent numerical model of the geodynamo can be used as the subjective prior information for the determination of Earth's core surface flows from the geomagnetic field and its secular variation. This is achieved by estimating those parts of the numerical model state vector hidden from the observations, through a standard Kalman filtering (or stochastic inverse) procedure, where the Kalman gain matrix is based on the multivariate statistics of the geodynamo model. To allow for a direct comparison with observations, the field variables entering these statistics are scaled following two of the scaling laws that have recently come to the fore in numerical dynamo modelling, which express the dependency of the secular variation timescale and the magnetic energy density on their respective control parameters. We perform test experiments with noisy synthetic data, showing good to excellent recovery of the hidden parts of the state vector. A geomagnetic field model parent to a candidate model to the 2010 release of IGRF is then used for a core surface flow estimation. The estimated flow confirms the presence of convective columns underneath America, whereas exhibiting a high level of equatorial symmetry. We suggest that the discrete state estimation problem considered here (in connection with the classical core flow problem) could be used generically as a means to assess the degree of geophysical realism of a given geodynamo model. More generally, this study opens the way to using scaling laws and multivariate statistics from numerical models in the broader context of geomagnetic data assimilation.
Geophysical Journal International 06/2011; 186(1):118 - 136. · 2.42 Impact Factor
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ABSTRACT: The knowledge of the spatial power spectra of the main geomagnetic field and of its secular variation makes it possible to define typical timescales tau(n) for each spherical harmonic degree n. Investigating both observations and numerical dynamos, we show that a one-parameter law of the form tau(n) = tau(SV)/n is satisfied for the non-dipole field, given the statistical way the observed tau(n) are expected to fluctuate. Consequently, we determine the corresponding secular-variation timescale tau(SV) from either instantaneous or time-averaged spectra, leading to a value of 415 +/-(55)(45) yr for recent satellite field models. In the broader context of geomagnetic data assimilation, tau(SV) could provide a sensible and convenient means to rescale the time axis of dynamo simulations. Citation: Lhuillier, F., A. Fournier, G. Hulot, and J. Aubert (2011), The geomagnetic secular-variation timescale in observations and numerical dynamo models, Geophys. Res. Lett., 38, L09306, doi: 10.1029/2011GL047356.
Geophysical Research Letters 01/2011; 38. · 3.79 Impact Factor
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ABSTRACT: Data 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.
Space Science Reviews 01/2010; 155:247-291. · 3.61 Impact Factor
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Geophysical Research Letters 01/2010; · 3.79 Impact Factor
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ABSTRACT: Seismic waves sampling the top 100 km of the Earth's inner core reveal that the eastern hemisphere (40 degrees E-180 degrees E) is seismically faster, more isotropic and more attenuating than the western hemisphere. The origin of this hemispherical dichotomy is a challenging problem for our understanding of the Earth as a system of dynamically coupled layers. Previously, laboratory experiments have established that thermal control from the lower mantle can drastically affect fluid flow in the outer core, which in turn can induce textural heterogeneity on the inner core solidification front. The resulting texture should be consistent with other expected manifestations of thermal mantle control on the geodynamo, specifically magnetic flux concentrations in the time-average palaeomagnetic field over the past 5 Myr, and preferred eddy locations in flows imaged below the core-mantle boundary by the analysis of historical geomagnetic secular variation. Here we show that a single model of thermochemical convection and dynamo action can account for all these effects by producing a large-scale, long-term outer core flow that couples the heterogeneity of the inner core with that of the lower mantle. The main feature of this thermochemical 'wind' is a cyclonic circulation below Asia, which concentrates magnetic field on the core-mantle boundary at the observed location and locally agrees with core flow images. This wind also causes anomalously high rates of light element release in the eastern hemisphere of the inner core boundary, suggesting that lateral seismic anomalies at the top of the inner core result from mantle-induced variations in its freezing rate.
Nature 09/2008; 454(7205):758-61. · 36.28 Impact Factor
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ABSTRACT: 1] The use of a quasigeostrophic, two-dimensional approximation in the problem of convection in a rapidly rotating spherical shell has been limited so far to investigations of the qualitative behavior of the solution. In this study, we build a quasigeostrophic model that agrees quantitatively with full three-dimensional solutions of the onset of convection in the case of differential heating. Reducing the dimensionality of the problem also permits the simulation of finite amplitude regimes of convection, up to quasigeostrophic turbulence. The nonlinear behavior of the system is studied in detail and compared to ultrasonic Doppler velocimetry measurements performed in a convecting, rapidly rotating spherical shell filled with water and liquid gallium. The results are quantitatively satisfactory and open the way to less computer-demanding, and still accurate, simulations of the geodynamo. Components: 8168 words, 13 figures, 1 table, 2 dynamic content.
Geochem. Geophys. Geosyst. 01/1052; 4.
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ABSTRACT: For many published dynamo models an Earth-like magnetic field has been claimed. However, it has also been noted that as the Ekman number (viscosity) is lowered to less unrealistic values, the magnetic field tends to become less Earth-like. Here we define quantitative criteria for the degree of semblance of a model field with the geomagnetic field, based on the field morphology at the core–mantle boundary. We consider the ratio of the power in the axial dipole component to that in the rest if the field, the ratios between equatorially symmetric and antisymmetric and between zonal and non-zonal non-dipole components, and a measure for the degree of spatial concentration of magnetic flux at the core surface. We also briefly discuss shortcomings of possible other criteria for an Earth-like model. We test the compliance with our criteria for a large number of dynamo models driven by imposed temperatures at their inner and outer boundaries that cover the accessible parameter space. We order models according to their magnetic Reynolds number Rm (ratio of advection to diffusion of magnetic field) and magnetic Ekman number Eη (ratio between rotation period and magnetic diffusion time). Requirements for an Earth-like field morphology are that Eη < 10− 4 and that Rm falls into a limited range that depends on Eη. Higher values of Rm are required at low values of Eη. Extrapolating the boundaries of compliant dynamos in this parameter space to the Earth's value of Eη suggests that Earth-like dynamos exist all the way between present model values and parameter values of the geodynamo. We also study a more limited set of dynamo models with flux boundary conditions. The nature of the boundary condition and the distribution of sources and sinks of buoyancy have a secondary influence on the field morphology.
Earth and Planetary Science Letters.
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Kupka, F.; Roxburgh, I. W.; Chan, K. L.: Convection in Astrophysics, Proceedings IAU Symposium No. 239, 2006, International Astronomical Union, 188-195 (2007).
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ABSTRACT: The impact of the heterogeneous lower mantle on the geomagnetic field is under debate, especially the question of whether high‐latitude intense geomagnetic flux patches currently observed at the core surface are stationary, oscillating, or drifting on longer time scales. While the correlation between the location of these patches with that of similar patches found in the time‐averaged paleomagnetic field may suggest stationary behavior, their variability over archaeomagnetic time scales together with their weaker signature in the average paleomagnetic field relative to the present geomagnetic field precludes such a scenario. Here we use numerical dynamos with an imposed heat flux boundary condition based on lower mantle tomography to study the behavior of such intense magnetic flux patches. We design an algorithm to detect centers of intense flux patches and track their time evolution. We find that the time‐dependent nature of those patches comprises oscillatory motion about statistically preferred locations imposed by mantle control, with episodic drift from one preferred location to the other corresponding to an azimuthal migration of fluid downwelling structures that concentrate surface magnetic flux. This statistical behavior provides a possible explanation for both the observed variability of high‐latitude patches on the archaeomagnetic time scale and the similar locations of the current patches and the weaker patches seen in the paleomagnetic field. Our simulations also show that the patches exhibit more time dependence and less coherency in the southern hemisphere, leading to a weaker time‐averaged patch signature in that hemisphere.
Journal of Geophysical Research. Solid Earth.
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ABSTRACT: The geomagnetic field and secular variation exhibit asymmetrical spatial features which are possibly originating from an heterogeneous thermal control of the Earth's lower mantle on the core. The identification of this control in magnetic data is subject to several difficulties, some of which can be alleviated by the use of core surface flow models. Using numerical dynamos driven by heterogeneous boundary heat flux, we confirm that within the parameter space accessible to simulations, time average surface flows obey a simple thermal wind equilibrium between the Coriolis and buoyancy forces, the Lorentz, inertial and viscous forces playing only a secondary role, even for Elsasser numbers significantly larger than 1. Furthermore, we average the models over the duration of three vortex turnovers, and correlate them with a longer time average which fully reveals the signature of boundary heterogeneity. This allows us to quantify the possibility of observing mantle control in core surface flows averaged over a short time period. A scaling analysis is performed in order to apply the results to the Earth's core. We find that three vortex turnovers could represent between 100 and 360 years of Earth time, and that the heat flux heterogeneity at the core-mantle boundary could be large enough to yield an observable signature of thermal mantle control in a time average core surface flow within reach of the available geomagnetic data.
Physics of the Earth and Planetary Interiors.
