Scaling of the geomagnetic indices and solar wind

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Scaling of the geomagnetic indices and solar wind: a Fokker-Planck approach Bogdan A. Hnat

Scaling of the geomagnetic indices and solar wind: a Fokker-Planck approach Bogdan A. Hnat Collaborators: S. C. Chapman and G. Rowlands; University of Warwick N. W. Watkins and M. P. Freeman; British Antarctic Survey

Complex magnetosphere General features: Non-equilibrium, non-linear system Driven by variable solar wind Dissipation via

Complex magnetosphere General features: Non-equilibrium, non-linear system Driven by variable solar wind Dissipation via complex current systems Specific issues: Coupling to solar wind essential part of description How to distinguish between features of the driver and the system?

Complex dynamics-simple statistics

Complex dynamics-simple statistics

Stochastic approach Differenced quantities are easier to study Fluctuations treated as stochastic variables Scaling,

Stochastic approach Differenced quantities are easier to study Fluctuations treated as stochastic variables Scaling, derived directly from data, can simplify description If mono-scaling found the Fokker-Planck approach can be used to model statistics

Scaling: basic concepts Building blocks Fluctuations: Scaling Length depends on scale Statistics depends on

Scaling: basic concepts Building blocks Fluctuations: Scaling Length depends on scale Statistics depends on scale Segments: self-similarity

How to determine scaling Fluctuations: Generalized Structure Functions: PDF rescaling: Conditioning: consider events <

How to determine scaling Fluctuations: Generalized Structure Functions: PDF rescaling: Conditioning: consider events < 10 σ(τ)

Indices and solar wind data Solar wind driver represented by Akasofu’s ε: 2 years

Indices and solar wind data Solar wind driver represented by Akasofu’s ε: 2 years of WIND, ACE data used to compute ε Geomagnetic indices: ~10 stations in auroral region AU-strength of E-ward electrojet AL-strength of W-ward electrojet Dates different than ε Indices definition-extreme events

Indices and solar wind: SF

Indices and solar wind: SF

Solar min-max comparison Results: Scaling of δ(AL) nearly insensitive to solar cycle Scaling of

Solar min-max comparison Results: Scaling of δ(AL) nearly insensitive to solar cycle Scaling of δ(AU) follows the trend of δε All scaling exponent are different Constant conversion rate? -

Fokker-Planck equation for PDF Assume: Look for self-similar solutions:

Fokker-Planck equation for PDF Assume: Look for self-similar solutions:

Conclusions Scaling led to full characterise statistics of fluctuations up to 10σ Mono-scaling allowed

Conclusions Scaling led to full characterise statistics of fluctuations up to 10σ Mono-scaling allowed direct comparison of solar wind driver and AE indices Coupling between solar wind and different region of the magnetosphere can be studied Applications: Sub-grid modelling of complex systems Constrains on numerical models and theoretical predictions Predictive power in statistical sense

Post seminar material Conditioning plays important role in establishing scaling – why?

Post seminar material Conditioning plays important role in establishing scaling – why?