GJI Geomagnetism, rock magnetism and palaeomagnetism Earth's dynamo limit of predictability controlled by magnetic dissipation

SUMMARY 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.

[1]  Gauthier Hulot,et al.  Earth's dynamo limit of predictability , 2010 .

[2]  E. Lorenz.  A study of the predictability of a 28-variable atmospheric model , 1965 .

[3]  Gauthier Hulot,et al.  Can core‐surface flow models be used to improve the forecast of the Earth's main magnetic field? , 2008 .

[4]  Alexandre Fournier,et al.  A case for variational geomagnetic data assimilation: insights from a one-dimensional, nonlinear, and sparsely observed MHD system , 2007, 0705.1777.

[5]  Nils Olsen,et al.  FAST TRACK PAPER: Crustal concealing of small-scale core-field secular variation , 2009 .

[6]  Gauthier Hulot,et al.  A statistical approach to the Earth's main magnetic field , 1994 .

[7]  S. Maus,et al.  On the possibility of extending the IGRF predictive secular variation model to a higher SH degree , 2010 .

[8]  Don Liu,et al.  Observing system simulation experiments in geomagnetic data assimilation , 2006 .

[9]  A. Chulliat,et al.  International Geomagnetic Reference Field: the eleventh generation , 2010 .

[10]  Mioara Mandea,et al.  The Magnetic Field of Planet Earth , 2010 .

[11]  E. Lorenz.  Deterministic nonperiodic flow , 1963 .

[12]  Paul H. Roberts,et al.  A three-dimensional self-consistent computer simulation of a geomagnetic field reversal , 1995, Nature.

[13]  G. Hulot,et al.  The geomagnetic secular‐variation timescale in observations and numerical dynamo models , 2011 .

[14]  Edward N. Lorenz,et al.  SECTION OF PLANETARY SCIENCES: THE PREDICTABILITY OF HYDRODYNAMIC FLOW*,† , 1963 .

[15]  U. Christensen,et al.  Dipole moment scaling for convection-driven planetary dynamos , 2005 .

[16]  G. Glatzmaier,et al.  A three-dimensional convective dynamo solution with rotating and finitely conducting inner core and mantle , 1995 .

[17]  Jonathan M. Aurnou,et al.  The magnetic structure of convection-driven numerical dynamos , 2008 .

[18]  G. Hulot,et al.  Swarm: A constellation to study the Earth’s magnetic field , 2006 .

[19]  T. Petroliagis,et al.  Error growth and estimates of predictability from the ECMWF forecasting system , 1995 .

[20]  Ulrich R. Christensen,et al.  Numerical Dynamo Simulations , 2007 .

[21]  Zhibin Sun,et al.  MoSST-DAS: The First Generation Geomagnetic Data Assimilation Framework , 2008 .

[22]  Kathy Whaler,et al.  Forecasting change of the magnetic field using core surface flows and ensemble Kalman filtering , 2009 .

[23]  Gauthier Hulot,et al.  Conditions for Earth-like geodynamo models , 2010 .

[24]  Matthew R. Walker,et al.  Four centuries of geomagnetic secular variation from historical records , 2000, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[25]  E. Kalnay.  Atmospheric modeling, data assimilation and predictability: Atmospheric predictability and ensemble forecasting , 2002 .

[26]  Catherine Constable,et al.  Continuous geomagnetic field models for the past 7 millennia: 2. CALS7K , 2005 .

[27]  Ulrich R. Christensen,et al.  Numerical modelling of the geodynamo: a systematic parameter study , 1999 .

[28]  Akira Kageyama,et al.  Computer simulation of a magnetohydrodynamic dynamo. II , 1994 .

[29]  U. Christensen,et al.  Scaling properties of convection-driven dynamos in rotating spherical shells and application to planetary magnetic fields , 2006 .

[30]  Joseph Smagorinsky,et al.  problems and promises of deterministic extended range forecasting , 1969 .

[31]  J. Smagorinsky,et al.  GENERAL CIRCULATION EXPERIMENTS WITH THE PRIMITIVE EQUATIONS , 1963 .

[32]  Ulrich R. Christensen,et al.  Power requirement of the geodynamo from ohmic losses in numerical and laboratory dynamos , 2004, Nature.

[33]  Vincent Lesur,et al.  Geomagnetic Core Field Secular Variation Models , 2010 .

[34]  E. Al,et al.  The feasibility of a global observation and analysis experiment , 1966 .

[35]  Carsten Kutzner,et al.  From stable dipolar towards reversing numerical dynamos , 2002 .

[36]  U. Christensen,et al.  8.08 – Numerical Dynamo Simulations , 2007 .

[37]  U. R. Christensena,et al.  A numerical dynamo benchmark , 2001 .

[38]  Gauthier Hulot,et al.  An Introduction to Data Assimilation and Predictability in Geomagnetism , 2010 .