Estimating Model Parameters from Ionospheric Reverse Engineering (EMPIRE)

1. Estimating Model Parameters from Ionospheric Reverse Engineering (EMPIRE) G. S. Bust and G. Crowley UTSA S. Datta-Barua ASTRA

2. Outline • Description of IDA4D Reverse Engineering • EMPIRE results • Planned Future Work

3. Direct Estimation of Ionospheric Drivers • Use continuity equation to directly estimate driver terms: Production, loss, diffusion, winds, ExB • Actually estimate low-dimension parameter corrections to “model” estimates • Take advantage of fact that most driver terms do not vary with same spatial-temporal variation as electron density • Once we have correction estimates to these “drivers we can do several things • Complementary to more complex Ensemble Kalman filtering methods • Get estimates of winds , densities and use them to better understand impacts of the Kalman filter.

4. EMPIRE Approach • Ionospheric Imaging • Copious amounts of measurements related to electron density available • Organize into 4D maps of electron density: IDA4D • Use 4D maps + error to estimate driver terms in continuity equation • Estimation Equation • Formulate the electron density continuity equation as y = Mx + a. • Assume a functional form of drivers to estimate, with coefficients xi. • Model some terms, estimate others • Estimated parameters: x • Modeled parameters: a • Matrix M relates the coefficients of the neutral wind function xi to the observations yj. • Least squares estimate of x. • In following we focus on only estimating field aligned winds

5. Example IDA4D Image

6. “Reverse-Engineering” the Ionosphere Electron Density Neutral winds and other drivers Physics of the ionosphere Ionospheric measurements TEC, etc. Estimating Model Parameters from Ionospheric Reverse Engineering (EMPIRE) Electron Density Estimate Neutral wind estimate Ionospheric Data Assimilation 4D (IDA4D) Production, loss, etc., corrections

7. Electron Density Continuity Equation • Continuity Equation for electron density N: • Split electron velocity v into components along magnetic field and perpendicular to it.

8. Electron Velocity and Neutral Wind Velocity • Kirchengast [1996] model for parallel component v||. • Electron velocity v depends on neutral wind u. • Model neutral wind u|| as a power series:

9. Setting Parameters • Choose a range of latitudes and heights at a given longitude whose electron densities will be fed. • -10 to 10 degrees magnetic latitude. • 200 to 500 km. • Choose a time period of interest over which we expect u to be constant. • Estimate u over each hour using Ne data at 15-minute cadence. • Choose a functional form of u. • In the case of a power series in R, theta, must choose maximum order of series kmax and lmax.

10. Algorithm Validation • Case: November 10, 2004 Storm • Equatorial latitudes • Jicamarca longitudes • Use the ASPEN (TIMEGCM) physical model of Ne to estimate the neutral wind for a single longitude and range of latitudes and altitudes. • ASPEN provides ExB, neutral values input to modeled terms • Feed Ne into EMPIRE, get neutral wind speed u. • Compare u to the ASPEN “truth” values of field-aligned neutral wind speeds. • RMS errors in u over time.

11. Case 1 Baseline Test • Order of wind expansion: k=0,l=1 • Region of data: • +/- 10 deg mlat • 200-500km (same for all cases shown) • timespan per fit: 1 hour EMPIRE Estimate ASPEN “Truth”

12. Case 1 2D histogram and RMSE correlation = 0.62

13. Case 2:Only Noon-Sunset • As Case 1: • k=0, l=1 • +/-10 deg mlat • timespan = 1 • Only compute for 15-22 UT

14. Case 2 2D histogram Correlation is 0.83.

15. Wind Comparison at ~18 UT

16. EMPIRE Status • Simulations have validated method and also illustrated issues that need to be improved • Next step will be running same time period using IDA4D data • EMPIRE Issues/ improvements • Hard to separate wind effects from diffusion and gravity • Estimate total field aligned velocity then try to separate • Corrections to ion-neutral collision frequency, plasma temperature • Boundary conditions at edge of grid in estimation • Corrections to other terms – production, loss • Zonal drift velocities • Different functional forms beyond power series • Experimental validation • Mid-latitudes: Arecibo, MH ISR, F-P winds (J. Makela) • High latitudes: Winds (M. Conde), PFISR, Sondrestrom, EISCAT (M. Rietveld)

17. Nadir: Future Plans • Year 2: 2005 EMPIRE Studies • Mid-latitudes • assume no ExB drifting • Correct for neutral density, solar flux, winds • High latitudes • Take in AMIE ExB Drifts • Estimate corrections to drifts • And high latitude winds • Possibly precipitation • EMPIRE comparisons against • Arecibo (M. nicolls) • Nighttime wind measurements (Illinois Fabret-Perot measurements -J. Makela • High latitude winds (M. Conde) • EISCAT (M. Rietveld) • Year 3: • Full estimation of corrections in all drivers • Ability to choose different functional forms and number of parameters estimated • Complete validation against independent measurements

18. Nadir: Future Plans (Cont.) • Year 4: • Self consistent forward model in IDA4D • Continuous estimation of parameters with data assimilation • Estimate of errors on driver retrievals • Year 5: • Comparisons with Kalman Filter Methods, EOF Methods • Correlation of neutral estimates with solar drivers, high latitudes, waves from lower atmosphere • Addition of neutral data to IDA4D