Data assimilation in a sparsely observed one-dimensional modeled MHD system

A one dimensional non-linear magneto-hydrodynamic (MHD) system has been introduced to test a sequential optimal interpolation assimilation technique that uses a Monte-Carlo method to calculate the forecast error covariance. An ensemble of 100 model runs with perturbed initial conditions are used to construct the covariance, and the assimilation algorithm is tested using Observation Simulation Experiments (OSE's). The system is run with a variety of observation types (magnetic and/or velocity fields) and a range of observation densities. The impact of cross covariances between velocity and magnetic fields is investigated by running the assimilation with and without these terms. Sets of twin experiments show that while observing both velocity and magnetic fields has the greatest positive impact on the system, observing the magnetic field alone can also effectively constrain the system. Observations of the velocity field are ineffective as a constraint on the magnetic field, even when observations are made at every point. The implications for geomagnetic data assimilation are discussed.

[1]  S. I. Braginskiy.  Magnetic Waves in the Earth's Core , 1967 .

[2]  Nils Olsen,et al.  A comprehensive model of the quiet‐time, near‐Earth magnetic field: phase 3 , 2002 .

[3]  P. Roberts,et al.  $alpha$-EFFECT DYNAMOS, BY THE BULLARD--GELLMAN FORMALISM. , 1972 .

[4]  Jeremy Bloxham,et al.  Geomagnetic secular variation , 1989, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[5]  S. Cohn,et al.  An Introduction to Estimation Theory , 1997 .

[6]  C. Johnson,et al.  Global geomagnetic field models for the past 3000 years: transient or permanent flux lobes? , 2000, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[7]  Jean-Pierre Valet,et al.  Global changes in intensity of the Earth's magnetic field during the past 800 kyr , 1999, Nature.

[8]  M. Richards,et al.  Mantle–circulation models with sequential data assimilation: inferring present–day mantle structure from plate–motion histories , 2002, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[9]  Masaru Kono,et al.  RECENT GEODYNAMO SIMULATIONS AND OBSERVATIONS OF THE GEOMAGNETIC FIELD , 2002 .

[10]  Robert N. Miller,et al.  Data assimilation into nonlinear stochastic models , 1999 .

[11]  M. Fang,et al.  Understanding Time-variable Gravity due to Core Dynamical Processes with Numerical Geodynamo Modeling , 2007 .

[12]  A. Tangborn.  Wavelet approximation of error covariance propagation in data assimilation , 2004 .

[13]  P. Roberts,et al.  A three-dimensional kinematic dynamo , 1975, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[14]  S. I. Braginskii.  Torsional Magnetohydrodynamic Vibrations in the Earth's Core and Variations in Day Length , 1970 .

[15]  S. Cohn,et al.  Ooce Note Series on Global Modeling and Data Assimilation Construction of Correlation Functions in Two and Three Dimensions and Convolution Covariance Functions , 2022 .

[16]  G. Evensen.  Sequential data assimilation with a nonlinear quasi‐geostrophic model using Monte Carlo methods to forecast error statistics , 1994 .

[17]  J. Larmor.  17. How Could a Rotating Body such as the Sun Become a Magnet , 1979 .

[18]  S. Braginsky.  Magnetic waves in the core of the earth. II , 1979 .