1. 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

2. 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?

3. Complex dynamics-simple statistics

4. 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

5. Scaling: basic concepts Building blocks Fluctuations: Scaling Segments: Length depends on scaleStatistics depends on scale self-similarity

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

7. 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

8. Indices and solar wind: SF

9. 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?-

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

11. 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

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