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## “Heads-Up”

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**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**“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!**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**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?**Observational Data**• 6 Stations • Density Perturbations • 50% Noise [Density perturbations ~10% of Ne, noise level of Ne measurements at least 5%]**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**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.**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.**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!**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?**Dynamic Ionospheric Structures**Weather: NOT included in Physical Model. Data Representation ERROR > 100%!!