1. GEM Workshop June 24, 2003 Data Assimilation Workshop Notes Why and What is Data Assimilation? What Data Assimilation is not Key Challenges in Data Assimilation Key Challenges with respect to magnetospheric DA How magnetospheric DA differs from meteorological DA CU/LASP held a data assimilation workshop after Space Weather Week Copies of the talks are available at http://lasp.colorado.edu/cism/Data_Assimilation

2. GEM Workshop June 24, 2003 Lessons Learned Why and What is DA? Purpose of data assimilation is to combine measurements and models to produce best estimate of current and future conditions. Kalman filter often used as a method for data assimilation. It became popular because it is a recursive solution to the optimal estimator problem. (Only last time step of information needs to be stored.) Full implementation of Kalman filter is usually not possible. There is a growing field in the study alternatives. AD ≠ DA (The Assimilation of Data is not necessarily Data Assimilation) Data assimilation does not require a physics-based model.

3. GEM Workshop June 24, 2003 Model Types Model Types Linear: Nonlinear: Physical: Vector X contains all quantities on the grid, S is the external driver, M propagates the state forward

4. GEM Workshop June 24, 2003 Challenges in DA Analyzed field does not match a realizable model state Non-uniform and sparse measurements Observed variables do not match variables predicted by the model Observing systems are diverse and subject to error, sometimes poorly known

5. GEM Workshop June 24, 2003 Challenges For Magnetospheric DA Very sparse measurements Diverse set of both forward and inverse models that are highly specialized and/or are expert in different areas.  How to combine forward models (MHD, particle pushing) with inverse models (empirical, stochastic).  How to integrate data with these models

6. GEM Workshop June 24, 2003 Space Weather Meteorology Graphical to Mathematical Statistical Estimation & Prediction Four- Dimensional Data Assimilation Combine Satellite, Aircraft, & Drift Buoys Continued Improvements Discovery of Radiation Belts Empirical Studies Leading to NASA’s AE / AP Models AMIE CRRES Radiation Belt Models 4DDA in Ionosphere, Thermosphere, and Rad-Belts Physical Modeling Magnetospheric Data Assimilation

7. GEM Workshop June 24, 2003 Magnetospheric Data Assimilation: Baseline Model Considerations Magneto-Hydrodynamic (MHD) and hybrid models are (currently) computationally prohibitive for many space-weather applications. Incomplete physics result in significant scaling problems. The system is strongly driven by poorly sampled boundary conditions. Empirical baseline models provide an excellent interim solution for the radiation belts due to strong global dynamical coherence.

8. GEM Workshop June 24, 2003 Specifying Relativistic Electrons in the Outer Radiation Belt CRRES-ELE used as a baseline model: –Good global coverage (L = 2.5 to ~6.7) –Good energy coverage (0.5 to 6.6 MeV) –Quasi-dynamic (6 geomagnetic activity levels based on Ap15 index) Electron data to be assimilated / validated: –Los Alamos Geostationary Satellites (80, 84, 95) –NOAA GOES Satellites (8, 9) –GPS Satellites (24, 33, 39) Pre-assimilation requirements: –Correct for CRRES-ELE B-field errors and satellite magnetic latitude –Cross-calibrate and normalize sensor data –Interpolate / extrapolate to fill gaps in data coverage –Re-parameterize geomagnetic activity based on GPS electron data

9. GEM Workshop June 24, 2003 Four-Dimensional Data Assimilation

10. GEM Workshop June 24, 2003 Real-time, Optimal Specification of Radiation Belt Electrons Based on AFRL CRRESELE model ORBSAF (Outer Radiation Belt Specification and Forecast) Program [Moorer and Baker, 2000] Utilizes GOES, LANL and GPS data as inputs

11. GEM Workshop June 24, 2003 High Accuracy at Geostationary Orbit

12. GEM Workshop June 24, 2003 Anomaly Analysis—Actual Electron Flux at Spacecraft Location Spacecraft—Brazilsat (A2) Analysis References: Frederickson et al., 1991-92; Weenas, et al., 1979 Electron Flux: Discharges were observed on CRRES for fluxes > 5e5 #/cm 2 /sec for > 10 hours –Flux at Brazilsat location exceeded this threshold for 8 hours before failure Electron Fluence: Discharges were observed at fluences greater than 1.8e10 electrons in a 10-hour period on CRRES –Assuming a nominal leak rate of 2e5 electrons/sec, fluence at Brazilsat location exceeded this figure for 2 hours prior to failure

13. GEM Workshop June 24, 2003 Dynamical Model Identification

14. GEM Workshop June 24, 2003 SISO Impulse Response Operational Forecasts (NOAA REFM) Days Since Solar Wind Impulse Why Linear Prediction Filters?

15. GEM Workshop June 24, 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)

16. GEM Workshop June 24, 2003 Adaptive Single-Input, Single-Output (SISO) Linear Filters EKF-Derived Model Coefficients (w/o Process Noise) EKF-Derived Model Coefficients (with Process Noise)

17. GEM Workshop June 24, 2003 SISO Model Residuals

18. GEM Workshop June 24, 2003 Multiple Input / Output (MIMO)

19. GEM Workshop June 24, 2003 Average Prediction Efficiencies MIMO PEEKF-MIMO PE (w/o process noise) EKF-MIMO PE (with process noise)

20. GEM Workshop June 24, 2003 Alternative Model Structures ARMAX, Box-Jenkins, etc. –Better separation between driven and recurrent dynamics. –Colored noise filters. –True, non-linear dynamic feedback. Combining the State and Model Parameters True data assimilation. –Issues exist with bias and stability of the EKF algorithm. –Ideal for on-line specification and forecast model. –Framework is amenable to physics-based dynamics modules.