The Probability Distribution of Extreme Geomagnetic Events in the Auroral Zone R.S. Weigel Space Weather Laboratory Department of Computational and Data.

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Presentation transcript:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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