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.
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
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.
Vector X contains all quantities on the grid, S is the external driver, M propagates the state forward
Very sparse measurements
Diverse set of both forward and inverse models that are highly specialized and/or are expert in different areas.
& Drift Buoys
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.
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)
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
Four-Dimensional Data Assimilation
Based on AFRL
ORBSAF (Outer Radiation Belt Specification and Forecast) Program [Moorer and Baker, 2000]
Utilizes GOES, LANL and GPS data as inputs
High Accuracy at Geostationary Orbit
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 failure
Days Since Solar Wind Impulse
SISO Impulse Response
Model parameters can be incorporated into a 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.
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.
Better separation between driven and recurrent dynamics.
Colored noise filters.
True, non-linear dynamic feedback.
Combining the State and Model Parameters