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“Heads-Up”

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“Heads-Up”

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  1. Lessons Learned in Developing the USU Kalman GAIMJ. J. Sojka, R. W. Schunk, D. Thompson, and L. Scherliess22 May 2003Presented to CISM TeamLASP, Boulder, Colorado

  2. “Heads-Up” • It’s not a one-step process because . . . • One observation can drive a Kalman if . . . • More is not better since . . . • Observations cannot be assimilated without . . . • Our view of the world is via quirky observations--always!

  3. It’s Not a One-Step Process Because . . . • One has more data types than can be assimilated in the physics model. • Some of these data can improve drivers to get a better first “guess” physics model. • Your first guess needs to be linearly perturbable away from the true answers. For GAIM Model: E, DB, [neutrals], u, modify drivers ne, TEC = ne, UV = ne2 are assimilated

  4. One Observation Can Drive a Kalman If . . . • The physics of the phenomena is reasonably understood and coherence scales are long. • In the ionosphere-thermosphere high latitude storms cause large scale TADs (traveling atmospheric disturbances) and TIDs. • Once detected, one can forecast their structure and velocity. ? ? ? Can a CME or Magnetic Cloud be put into such a category?

  5. 6 Observatories

  6. Observational Data • 6 Stations • Density Perturbations • 50% Noise [Density perturbations ~10% of Ne, noise level of Ne measurements at least 5%]

  7. Comparison

  8. More is Not Better Since . . . • Your problem is represented by a state vector of [n] unknowns. • You always want more resolution. • Storage space increases as [n]2. • CPU time increases as [n]3. • Real time means do a [n] update in minutes not 70 years. GAIM [n] = ne (latitude, longitude, altitude) + n* (GPS receiver biases) and

  9. Hence, The Reason Nobody Does Full Kalman Filters • Types of Kalman Approximations • Don’t recalculate “covariance” matrices each time step. • Use Tri-diagonal “covariance” matrices. • Use reduced “covariance” matrices. • Use some diagonal matrices. • But, remember, the covariance matrices also contain information on uncertainty/quality of the process.

  10. Observations Cannot be Assimilated Without . . .Their Uncertainty Being Specified Kalman Filtering is based upon linear least-squares fitting of a model and observations whose uncertainties are Gaussian!! Weather could be defined as observed real world variability associated with physical processes not included in the model; this is the representation error. Non-Gaussian errors include biases, saturation effects, operational constraints, data handling, . . . “Gaussian” noise of the sensor system. Quirks, things that humans won’t see but the Kalman needs to be protected from them.

  11. GPS Receiver Biases in the State Vector

  12. Ionosonde Frequency Restrictions; Wrong foF2

  13. Ionosonde Frequency Restrictions; Wrong foF2

  14. If there are two (or more) ways of measuring the same parameter at the same place and time, pick one.Don’t look at the others!

  15. LORAAS UV Data Good, but Satellite Pointing WRONG!WRONGhmF2

  16. GPS Observations are used “universally,” hence they are good--NOT!! When the “error” is large, it’s easy to discard. What happens when it is almost okay?

  17. Dynamic Ionospheric Structures Weather: NOT included in Physical Model. Data Representation ERROR > 100%!!