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. Data Assimilation Workshop Notes.
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What Data Assimilation is not
Key Challenges in Data Assimilation
Key Challenges with respect to magnetospheric DA
How magnetospheric DA differs from meteorological DAData Assimilation Workshop Notes
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.Lessons LearnedWhy and What is DA?
Model Types models to produce best estimate of current and future conditions.
Vector X contains all quantities on the grid, S is the external driver, M propagates the state forward
Very models to produce best estimate of current and future conditions.sparse measurements
Diverse set of both forward and inverse models that are highly specialized and/or are expert in different areas.Challenges For Magnetospheric DA
Meteorology models to produce best estimate of current and future conditions.
& Drift Buoys
1940 1950 1960 1970 1980 1990 2000 2010
Leading to NASA’s
AE / AP Models
Magnetospheric Data Assimilation
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.Magnetospheric Data Assimilation: Baseline Model Considerations
CRRES-ELE used as a baseline model: computationally prohibitive for many space-weather applications.
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)
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 dataSpecifying Relativistic Electrons in the Outer Radiation Belt
Four-Dimensional Data Assimilation computationally prohibitive for many space-weather applications.
Based on AFRL computationally prohibitive for many space-weather applications.
ORBSAF (Outer Radiation Belt Specification and Forecast) Program [Moorer and Baker, 2000]
Utilizes GOES, LANL and GPS data as inputsReal-time, Optimal Specification of Radiation Belt Electrons
High Accuracy at Geostationary Orbit computationally prohibitive for many space-weather applications.
Spacecraft—Brazilsat (A2) computationally prohibitive for many space-weather applications.
References: Frederickson et al., 1991-92; Weenas, et al., 1979
Electron Flux: Discharges were observed on CRRES for fluxes > 5e5 #/cm2/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 failureAnomaly Analysis—Actual Electron Flux at Spacecraft Location
Days Since Solar Wind Impulse computationally prohibitive for many space-weather applications.Why Linear Prediction Filters?
SISO Impulse Response
Model parameters can be incorporated into a computationally prohibitive for many space-weather applications.state-space configuration.
Process noise (vt) describes time-varying parameters as a random walk.
Observation error noise (et) measures confidence in the measurements.
Provides a more flexible and robust identification algorithm than RLS.Extended Kalman Filter (EKF)
EKF-Derived Model Coefficients (w/o Process Noise)
EKF-Derived Model Coefficients (with Process Noise)
EKF-MIMO PE (w/o process noise)
EKF-MIMO PE (with process noise)
ARMAX, Box-Jenkins, etc. computationally prohibitive for many space-weather applications.
Better separation between driven and recurrent dynamics.
Colored noise filters.
True, non-linear dynamic feedback.Alternative Model Structures
Combining the State and Model Parameters