1. The Probability Distribution of Extreme Geomagnetic Events in the Auroral Zone
R.S. Weigel
Space Weather Laboratory Department of Computational and Data Sciences George Mason University, Fairfax Virginia
Chapman Conference on Complexity and Extreme Events in Geosciences, February 16th, 2010; Hyderabad India

2. Outline Overview of system Model prediction error
Input/Output comparison
Characterize unpredictable component
Determine influence of input “complexity” on internal “complexity” and extreme behavior
Chapman Conference on Complexity and Extreme Events in Geosciences, February 16th, 2010; Hyderabad India

3. Overview of System
Chapman Conference on Complexity and Extreme Events in Geosciences, February 16th, 2010; Hyderabad India

4. Large Scale Systems
Chapman Conference on Complexity and Extreme Events in Geosciences, February 16th, 2010; Hyderabad India

5. Large-Scale Structures
Bombay 1859
Lakhina et al. 2005
Chapman Conference on Complexity and Extreme Events in Geosciences, February 16th, 2010; Hyderabad India

6. Small Scale Structures
Chapman Conference on Complexity and Extreme Events in Geosciences, February 16th, 2010; Hyderabad India

7. Prediction
Chapman Conference on Complexity and Extreme Events in Geosciences, February 16th, 2010; Hyderabad India

8. Relative importance of short-time scale changes – model error is often on the order as large scale structure it is predicting.
On short time scales solar wind excites substorms, waves, instability processes, etc. Prediction of timing and amplitude is difficult!
Chapman Conference on Complexity and Extreme Events in Geosciences, February 16th, 2010; Hyderabad India

9. Low pass filter of solar wind input VBs
Chapman Conference on Complexity and Extreme Events in Geosciences, February 16th, 2010; Hyderabad India

10. High dimensional nonlinear filter model
Weigel et al., 2002
Chapman Conference on Complexity and Extreme Events in Geosciences, February 16th, 2010; Hyderabad India

11. Chapman Conference on Complexity and Extreme Events in Geosciences, February 16th, 2010; Hyderabad India
From Spence et al., 2004

12. Input/Output Comparison
Chapman Conference on Complexity and Extreme Events in Geosciences, February 16th, 2010; Hyderabad India

13. Short Time Scale Fluctuation Comparison External or Internal Cause?
Due to way AU computed?
Due to External?
Log(Probability)
Log(Probability)
(de/dt)/σ
(dAU/dt)/σ
External Internal
Hnat et al., 2003
Chapman Conference on Complexity and Extreme Events in Geosciences, February 16th, 2010; Hyderabad India

14. Power spectrum comparisons
External or
internal cause?
External driver
Internal
Internal
c.f., Tsuatrani, 1991.
Chapman Conference on Complexity and Extreme Events in Geosciences, February 16th, 2010; Hyderabad India

15. How does solar wind affect 1-minute geomagnetic variability?
Solar wind has turbulent characteristics – direct driving interpretation would say it is all a manifestation of solar wind.
Need to isolate various influences first.
Eliminate influence of solar wind driver by considering magnetometer fluctuations under very different solar wind conditions.
Eliminate artificial “construction” effects by looking at a single magnetometer
Eliminate spatial effect by partitioning by local time
Then characterize “unpredictable” part.
Chapman Conference on Complexity and Extreme Events in Geosciences, February 16th, 2010; Hyderabad India

16. Data 22 years of 1-minute data 3-years of 1-minute data from 12 sites
Chapman Conference on Complexity and Extreme Events in Geosciences, February 16th, 2010; Hyderabad India

17. Long Time Averages Bx = north-south magnetic field perturbation
Chapman Conference on Complexity and Extreme Events in Geosciences, February 16th, 2010; Hyderabad India

18. Bx = north-south magnetic field perturbation
Long Time Averages
Bx = north-south magnetic field perturbation
Chapman Conference on Complexity and Extreme Events in Geosciences, February 16th, 2010; Hyderabad India

19. A day in the life of a magnetometer
Bx (nT)
dBx/dt (nT/min)
Chapman Conference on Complexity and Extreme Events in Geosciences, February 16th, 2010; Hyderabad India

20. Comparison of Distribution of Short-Time- Scale Fluctuations over 1 Day
Chapman Conference on Complexity and Extreme Events in Geosciences, February 16th, 2010; Hyderabad India

21. Partition by Bz(IMF) Unscaled
Red = Northward Interplanetary Magnetic Field (IMF)
Green = Southward IMF
Chapman Conference on Complexity and Extreme Events in Geosciences, February 16th, 2010; Hyderabad India

22. Partition by Bz(IMF) Scaled
Red = Northward Interplanetary Magnetic Field (IMF)
Green = Southward IMF
Chapman Conference on Complexity and Extreme Events in Geosciences, February 16th, 2010; Hyderabad India

23. Probability (dBx/dt)/σ External Weigel and Baker, 2003
Chapman Conference on Complexity and Extreme Events in Geosciences, February 16th, 2010; Hyderabad India

24. Local time and day-of-year dependence Error in fit
Chapman Conference on Complexity and Extreme Events in Geosciences, February 16th, 2010; Hyderabad India

25. Error in fit
Chapman Conference on Complexity and Extreme Events in Geosciences, February 16th, 2010; Hyderabad India

26. When does PDF invariance break down?
External
External
Probability
(dBx/dt)/σ
(dBx/dt)/σ
Chapman Conference on Complexity and Extreme Events in Geosciences, February 16th, 2010; Hyderabad India

27. When does PDF invariance break down?
External
External
Probability
(dBx/dt)/σ
(dBx/dt)/σ
Chapman Conference on Complexity and Extreme Events in Geosciences, February 16th, 2010; Hyderabad India

28. Paths to a heavy-tail probability distribution
Product of random variables (Lognormal).
Taking maximum of set of random variables. (Frechet)
Gaussian time series with changing variance. (Castaing)
Several possibilities including induction, conductivity, and spatial effects.
Chapman Conference on Complexity and Extreme Events in Geosciences, February 16th, 2010; Hyderabad India

29. Discussion
Importance of short-time scale changes: model error is often on the order as large scale structure it is predicting.
Solar wind driver acts as amplifier of short time scale geomagnetic fluctuations (increases standard deviation of dBx/dt time series).
Strong solar wind forcing decreases complexity of dynamics (PDF becomes more Gaussian).
Why heavy-tail distribution?
Small-scale structures can have significant contributions.
No unique local midnight signature.
Is the system complex, self-organizing, or near a .gphase transition?
Chapman Conference on Complexity and Extreme Events in Geosciences, February 16th, 2010; Hyderabad India

30. Uses Improve modeling of sub-grid physics
Simple parameterization of global models
Probabilistic forecasts
σ depends on Local Time, State of Solar Wind, and Season
Simple rule for computing probability of some amplitude A under different conditions
Chapman Conference on Complexity and Extreme Events in Geosciences, February 16th, 2010; Hyderabad India