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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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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

Data Assimilation Workshop Notes
  • CU/LASP held a data assimilation workshop after Space Weather Week
  • Copies of the talks are available at
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.

Lessons LearnedWhy and What is DA?
  • AD ≠ DA (The Assimilation of Data is not necessarily Data Assimilation)
  • Data assimilation does not require a physics-based model.

Model Types

Vector X contains all quantities on the grid, S is the external driver, M propagates the state forward

  • Linear:
  • Nonlinear:
  • Physical:
challenges in da
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
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.

Challenges For Magnetospheric DA
  • How to combine forward models (MHD, particle pushing) with inverse models (empirical, stochastic).
  • How to integrate data with these models







Satellite, Aircraft,

& Drift Buoys

Continued Improvements

Graphical to



Estimation &


Physical Modeling

1940 1950 1960 1970 1980 1990 2000 2010

Physical Modeling




4DDA in



and Rad-Belts

Discovery of



Empirical Studies

Leading to NASA’s

AE / AP Models


Radiation Belt


Magnetospheric Data Assimilation

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.

Magnetospheric Data Assimilation: Baseline Model Considerations
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

Specifying Relativistic Electrons in the Outer Radiation Belt
real time optimal specification of radiation belt electrons
Based on AFRL


ORBSAF (Outer Radiation Belt Specification and Forecast) Program [Moorer and Baker, 2000]

Utilizes GOES, LANL and GPS data as inputs

Real-time, Optimal Specification of Radiation Belt Electrons
anomaly analysis actual electron flux at spacecraft location
Spacecraft—Brazilsat (A2)


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

Anomaly Analysis—Actual Electron Flux at Spacecraft Location
why linear prediction filters

Days Since Solar Wind Impulse

Why Linear Prediction Filters?

SISO Impulse Response

Operational Forecasts


extended kalman filter ekf
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.

Extended Kalman Filter (EKF)
adaptive single input single output siso linear filters
Adaptive Single-Input, Single-Output (SISO) Linear Filters

EKF-Derived Model Coefficients (w/o Process Noise)

EKF-Derived Model Coefficients (with Process Noise)

average prediction efficiencies
Average Prediction Efficiencies


EKF-MIMO PE (w/o process noise)

EKF-MIMO PE (with process noise)

alternative model structures
ARMAX, Box-Jenkins, etc.

Better separation between driven and recurrent dynamics.

Colored noise filters.

True, non-linear dynamic feedback.

Alternative Model Structures

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.