Modelling complexity in the upper atmosphere using GPS data

1. Modelling complexity in the upper atmosphere using GPS data Chris Budd, Cathryn Mitchell, Paul Spencer Bath Institute for Complex Systems, University of Bath

2. Ground-receiver tomography Instrumentation Have. Networks of GPS receivers at mid-latitudes over continental regions of the Northern Hemisphere Problem: Atmosphere is a highly complex and multi-scale, time-evolving system. It is vital to know the state of all levels for meteorology and navigation

3. Ionospheric Imaging Multi-Instrument Data AnalysiS Measured – relative values of total electron content TEC Find – 3D time-evolving electron density Ne ALTITUDE LATITUDE

4. MIDAS – Northern Hemisphere GPS receivers Acknowledgements: IGS network

6. 6 moving satellites S Ionosphere 1000km Time varying Electron density Ne s 100 receivers R Measure the differential phase change between dual frequency radio signals from S to R at 2 minute intervals over one hour is directly proportional to the total electron content (TEC) of the ionosphere over the path s

7. Ne : electron concentration along the I = 6*100 paths s at the initial time (order 100 G electrons/metre cubed) Set up 3D grid of J = 20 [height] *360*360[angle] voxels, x electron density in each voxel, matrix A of path lengths in each voxel Ill-conditioned .. Use a-priori information to solve

8. MIDAS algorithm [electron density] = [model electron density] [coefficients] The electron density (x) distribution is formed from the weighted (W) sum of orthonormal basis functions,X: 4*50Spherical Harmonics in latitude and longitude and 3 empirical functions Chapman Profilesinheight z

9. Chapman functions z

10. Obtain least squares best fit for W using the regularisedSVD to calculate the generalised inverse Initial estimate of the electron density

11. MIDAS – time-dependent inversion Update this estimate every 2 minutes by assuming small change y in x, cinthe measuredTECb and D in the ray path matrix A. To leading order have Mapping matrix, X, transforms the problem to one for which the unknowns are the linear changes in coefficients G (y = XG) of the orthonormal basis functions Improve with a Kalman filter

12. Horizontal Variation Spherical Harmonics Model (eg IRI) • Graphics options • Vertical profiles of Ne • Horizontal profiles of Ne • TEC maps • Electron concentration images (latitude vs height) at one longitude. • Electron concentration images (longitude vs height) at one latitude. • TEC movies • Electron concentration movies Inversion type 2-D (latitude-height or thin shell) 3-D (2-D with time evolution or latitude-longitude-altitude) 4-D (latitude-longitude- altitude-time) Height profile (to create EOFS) Thin Shell (variable height) Chapman profiles Epstein profiles Models (eg IRI) Co-ordinate frame Geographic Geomagnetic TIME: None Zonal/Meridional Zonal/Meridional & Radial MIDAS algorithm

13. Electron density North America Longitude 70 W Electron density Ne Vertical TEC b

14. Vertical TEC b

17. Observations of mid-latitude ionospheric storms • Near global view of TEC distributions • Observations of storm enhanced density • Uplifts in layer height over Europe and North America • Poleward movement of the anomaly

18. Imaging Issues What is the spatial resolution? What is the temporal resolution? What is the accuracy of the imaged electron density? What scientific information can we derive directly from the images?

19. Verification of the peak height uplift over the USA MIDAS Radar backscatter

20. Combining imaging with first-principle modeling How can we relate the images the underlying physics? • Imaging alone cannot get at the underlying physics • Simply reproducing localized image features with modeling does not uniquely determine the physical drivers • Future aim – develop methods that constrain the physical models with full 4D imaging

21. Acknowledgementsto: GPS RINEX data from SOPAC, IDA3D images from ARLUT, EISCAT Collaboration with Cornell University Support from BAE SYSTEMS, the UK EPSRC, BICS and PPARC

22. MIDAS – Northern Hemisphere

23. Coverage of Input Data ionosonde GPS Polar NIMS

24. TEC over the Northern Hemisphere • Is the TEC movie showing convection? • If so, the plasma over Europe originates from the USA

25. 3 2 1 East-west progression of layer height uplift F2 layer uplifts move horizontally westwards, that is, firstly, in the European sector, then the east coast of the USA, and around an hour later, occurring in the west coast of the USA.

26. Equatorial imaging (with Cornell University)

27. Polar imaging • Observations of patches over ESR • IDA3D imaging appears to show patches convecting from Sondestrom to ESR • Imaging alone cannot show the convection • Combine AMIE convection patterns with trajectory analysis into IDA3D • Provides strong evidence of plasma transport from Sondestrom to ESR

28. Patch IDA3D Ne at 400 km 2005 UT

29. Results from Europe

30. Ionospheric Measurements

31. Observations over ESR Patch at 20 UT