Stochastic modeling of the AE index and its relation to fluctuations in Bz of the IMF on time scales shorter than substorm duration

[1] We perform a detailed analysis of the auroral electrojet (AE) index on the typical substorm time scales from one minute up to a few hours. Through a systematic test against a model for selfsimilar motion in the form of fractional Levy flights, and against a model for fractional Brownian motion in multifractal time, it is demonstrated that the AE index is better approximated by a multifractal model than by a fractional Levy flight. Standard structure function analysis of the z-component Bz of the interplanetary magnetic field indicates that it is neither selfsimilar nor multifractal, but approximately satisfies a version of extended selfsimilarity. A method to discern an underlying multifractality also in Bz is pointed out.

[1]  J. Rosínski.  Tempering stable processes , 2007 .

[2]  V. Gonchar,et al.  Self and spurious multi-affinity of ordinary Levy motion, and pseudo-Gaussian relations , 2000 .

[3]  George Michailidis,et al.  Simulating sample paths of linear fractional stable motion , 2004, IEEE Transactions on Information Theory.

[4]  V. Anh,et al.  Stochastic modeling of the auroral electrojet index , 2008 .

[5]  Scaling collapse and structure functions: identifying self-affinity in finite length time series , 2005, physics/0504024.

[6]  Solar flare intermittency and the earth's temperature anomalies. , 2003, Physical review letters.

[7]  Masahisa Sugiura,et al.  Auroral electrojet activity index AE and its universal time variations. , 1966 .

[8]  J. Borovsky,et al.  Role of solar wind turbulence in the coupling of the solar wind to the Earth's magnetosphere , 2003 .

[9]  Succi,et al.  Extended self-similarity in turbulent flows. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[10]  C. Meneveau,et al.  Simple multifractal cascade model for fully developed turbulence. , 1987, Physical review letters.

[11]  Scaling and a Fokker-Planck model for fluctuations in geomagnetic indices and comparison with solar wind as seen by Wind and ACE , 2004, physics/0412063.

[12]  Laurent E. Calvet,et al.  A Multifractal Model of Asset Returns , 1997 .

[13]  M. Freeman,et al.  Towards Synthesis of Solar Wind and Geomagnetic Scaling Exponents: A Fractional Lévy Motion Model , 2005 .

[14]  E. Amata,et al.  Intermittency and extended self-similarity in space and fusion plasma: boundary effects , 2008 .

[15]  M. Rypdal,et al.  Testing hypotheses about sun-climate complexity linking. , 2010, Physical review letters.

[16]  Rosario N. Mantegna,et al.  An Introduction to Econophysics: Contents , 1999 .

[17]  J. Takalo,et al.  Correlation dimension and affinity of AE data and bicolored noise , 1993 .

[18]  C. Gardiner.  Handbook of Stochastic Methods , 1983 .

[19]  B. V. Bahr,et al.  Inequalities for the $r$th Absolute Moment of a Sum of Random Variables, $1 \leqq r \leqq 2$ , 1965 .

[20]  C. Heyde,et al.  A Cautionary note on modeling with fractional Lévy flights , 2008 .

[21]  V. Uritsky,et al.  Role of stochastic fluctuations in the magnetosphere‐ionosphere system: A stochastic model for the AE index variations , 2006 .

[22]  Syun-Ichi Akasofu,et al.  A study of geomagnetic storms , 1978 .

[23]  G. P. Pavlos,et al.  SVD analysis of the magnetospheric AE index time series and comparison with low-dimensional chaotic dynamics , 2001 .

[24]  A. Piryatinska,et al.  Fractional- and integer-order moments, and multiscaling for smoothly truncated Lévy flights , 2006 .

[25]  Ioannis A. Koutrouvelis,et al.  Regression-Type Estimation of the Parameters of Stable Laws , 1980 .

[26]  Bernt Øksendal,et al.  Malliavin Calculus for Lévy Processes with Applications to Finance , 2008 .

[27]  Bruce J. West,et al.  Sun-climate complexity linking. , 2008, Physical review letters.

[28]  Karina Weron,et al.  Complete description of all self-similar models driven by Lévy stable noise. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[29]  Karina Weron,et al.  Enigma of Self-Similarity of Fractional Levy Stable Motions , 2003 .

[30]  Stanley,et al.  Stochastic process with ultraslow convergence to a Gaussian: The truncated Lévy flight. , 1994, Physical review letters.

[31]  J. Timonen,et al.  Properties of AE data and bicolored noise , 1994 .

[33]  G. Consolini,et al.  Multifractal structure of auroral electrojet index data. , 1996, Physical review letters.

[34]  J. Timonen,et al.  Characteristic time scale of auroral electrojet data , 1994 .