1. GAII.05 8 July 2003 Data Assimilation Methods for Characterizing Radiation Belt Dynamics E.J. Rigler 1, D.N. Baker 1, D. Vassiliadis 2, R.S. Weigel 1 (1) Laboratory for Atmospheric and Space Physics University of Colorado at Boulder (2) Universities Space Research Association NASA / Goddard Space Flight Center

2. GAII.05 8 July 2003 Using Data Assimilation (DA) algorithms for identification of empirical dynamical systems Finite Impulse Response (FIR) linear prediction filters –Intuitive model structure –Robust and proven predictive capabilities Adaptive System Identification (RLS vs. EKF) –Weighted least squares estimates of model parameters –Tracking non-linear systems with adaptive linear models Better Model Structures: –Multiple input, multiple output (MIMO) models –Dynamic feedback and noise models (ARMAX, Box-Jenkins) –Combining RB state with dynamical model parameters Introduction and Outline

3. GAII.05 8 July 2003 Dynamic Model Identification

4. GAII.05 8 July 2003 SISO Impulse Response Operational Forecasts (NOAA REFM) Why Linear Prediction Filters? Days Since Solar Wind Impulse Electron Flux Response

5. GAII.05 8 July 2003 Recursive System Identification RLS minimizes least-squares criterion recursively. –Forgetting factor (λ) allows tracking of non-time-stationary dynamic processes. –Weighting factor (q) (de)emphasizes certain observations.

6. GAII.05 8 July 2003 Model parameters can be incorporated into a state- space configuration. Process noise (v t ) describes time-varying parameters as a random walk. Observation error noise (e t ) measures confidence in the measurements. Provides a more flexible and robust identification algorithm than RLS. Extended Kalman Filter (EKF)

7. GAII.05 8 July 2003 Adaptive Single-Input, Single-Output (SISO) Linear Filters EKF-Derived Model Coefficients (w/o Process Noise) EKF-Derived Model Coefficients (with Process Noise)

8. GAII.05 8 July 2003 SISO Model Residuals EKF-FIR Residuals (with Process Noise) EKF-FIR Residuals (w/o Process Noise) FIR Residuals Auto-covariance Lagged Days

9. GAII.05 8 July 2003 Multiple Input / Output (MIMO)

10. GAII.05 8 July 2003 Average Prediction Efficiencies MIMO PEEKF-MIMO PE (w/o process noise) EKF-MIMO PE (with process noise)

11. GAII.05 8 July 2003 Alternative Model Structures ARMAX, Box-Jenkins, etc. –Adaptive colored noise filters. –True dynamic feedback.  Better separation between driven and recurrent dynamics. Combining the State and Model Parameters True data assimilation: –Ideal for on-line, real-time RB specification and forecasting. –Framework is easily adapted to incorporate semi-empirical or physics-based dynamics modules.

12. GAII.05 8 July 2003 Acknowledgements Special thanks are extended to Drs. Scot Elkington and Alex Klimas for their valuable time and feedback. The data used for this study was generously provided by the National Space Science Data Center (NSSDC) OmniWeb project and the SAMPEX data team. This work was supported by the NSF Space Weather Program (grant ATM-0208341), and the NASA Graduate Student Research Program (GSRP, grant NGT5-132).

13. GAII.05 8 July 2003