1. CEDAR Workshop, Boulder CO June 20-25, 2010 Statistical Analysis of COSMIC Derived Abel Profiles Jet Propulsion Laboratory California Institute of Technology M/S 238-600 4800 Oak Grove Drive Pasadena CA 91109 Philip Stephens, Attila Komjathy, Brian Wilson, Xiaoqing Pi and Anthony J. Mannucci

2. CEDAR Workshop, Boulder CO June 20-25, 2010 Outline Introduction Motivation for this study Analysis Framework Results Summary

3. CEDAR Workshop, Boulder CO June 20-25, 2010 Abel Inversion With F(y) the integrate line-of-site TEC and f(r) the altitude dependent density the Abel inversion is defined as Major assumption: For occultation measurements we have no horizontal gradients –This is obviously false in reality –What is the impact of this assumption for real data? The Abel is extremely useful, however, as it provides some estimate of 3d structure from the data alone

4. CEDAR Workshop, Boulder CO June 20-25, 2010 Motivation for Study An effort was made to try use Abel profiles to develop a climatology Found important structure was ‘smeared’ no matter what averaging methods were used Hypothesis was the spherical symmetry of Abel inversion assumption would be broken in many cases Can we define some filter which can effectively provide a subset of potentially bad Abel inversions, with the members not in the subset all good inversions?

5. CEDAR Workshop, Boulder CO June 20-25, 2010 Analysis Framework Built database of Abel Profiles for 05/01/2010 Derived from 1 second TEC data, ~1400 profiles Ap: 3.0, Kp: 1-  very little solar activity Linked to database profiles generated by assimilation of COSMIC data into JPL/USC GAIM Used 30 second data for these results Linked to database VTEC generated by GIM 3-shell model Ground data only Slice profiles according to three criteria Low/Med/High Magnetic Latitude (±20, ±50, >50) Dawn/Midday/Dusk/Midnight (3-9 LT, 9-15 LT, 15-21 LT, 21-24/0-3 LT) Length of arc, measured by with short/medium/long (±5, ±30,>30) Computed Pearson Coefficient (r) and slope of line of best fit (m) Hypothesis: Abel will break down most often when spherical symmetry breaks down – large gradients and long spatial tracks

6. CEDAR Workshop, Boulder CO June 20-25, 2010 Filtering Arcs by Magnetic Latitude Low lat (<20 degrees) Mid lat (20<x<50 degrees) High lat (>50 degrees)

7. CEDAR Workshop, Boulder CO June 20-25, 2010 Nmf2 and Hmf2 Correlation Plots

8. CEDAR Workshop, Boulder CO June 20-25, 2010 VTEC at High Latitude, Pearson Coefficient

9. CEDAR Workshop, Boulder CO June 20-25, 2010 Correlation Plots High Latitude Long-arc, high lat, dusk Long-arc, high lat, midday Medium-arc, high lat, midnight 2 2 1 1 3 3

10. CEDAR Workshop, Boulder CO June 20-25, 2010 High Lat Correlations, Nmf2, Hmf2

11. CEDAR Workshop, Boulder CO June 20-25, 2010 Case 1: Long arc, High Lat, Dusk

12. CEDAR Workshop, Boulder CO June 20-25, 2010 Case 2: Long arc, High Latitude, Midday

13. CEDAR Workshop, Boulder CO June 20-25, 2010 Case 3: High lat, medium arc, midnight

14. CEDAR Workshop, Boulder CO June 20-25, 2010 Mid Latitude VTEC, Pearson Coefficient

15. CEDAR Workshop, Boulder CO June 20-25, 2010 Mid Latitude Correlation Plots Mid latitude, midnight long arcs, only 5 points though 4 4 4 4

16. CEDAR Workshop, Boulder CO June 20-25, 2010 Case 4: Mid Lat, Long Arc, Midnight

17. CEDAR Workshop, Boulder CO June 20-25, 2010 Low Latitude VTEC, Pearson Coefficient

18. CEDAR Workshop, Boulder CO June 20-25, 2010 Correlation Plots Low Latitude Long-arc, low lat, dusk Long-arc, low lat, midday 66 5 5

19. CEDAR Workshop, Boulder CO June 20-25, 2010 Low Lat Correlation Plots, Hmf2, Nmf2

20. CEDAR Workshop, Boulder CO June 20-25, 2010 Case 5: Long arc, Low lat, Dawn

21. CEDAR Workshop, Boulder CO June 20-25, 2010 Case 6: Long arc, Low lat, Midday

22. CEDAR Workshop, Boulder CO June 20-25, 2010 Conclusions It does appear there is significantly more variability in comparing Abel profiles versus GAIM profiles in cases where spherical symmetry approximation is likely to breakdown This study was a test case of a very calm day Expect more variability for more active days Still to do: Extend study to multiple days with different conditions Develop a measure of ‘physicality’ of profiles and apply to Abel and GAIM profiles under different filters –Possibly using fits to Vary-Chapman function Measure effectiveness of suggested filters –E.g. what percentage of ‘bad’ profiles are captured by filters Important note: vast majority of profiles appear to correlate well to GIM VTEC and GAIM 3d structure

23. CEDAR Workshop, Boulder CO June 20-25, 2010 Backup slides

24. CEDAR Workshop, Boulder CO June 20-25, 2010 High Lat NmF2, Pearson Coefficient

25. CEDAR Workshop, Boulder CO June 20-25, 2010 Mid Lat, Nmf2, Pearson Coefficient

26. CEDAR Workshop, Boulder CO June 20-25, 2010 Low Lat Nmf2, Pearson Coefficient

27. CEDAR Workshop, Boulder CO June 20-25, 2010 Hmf2 High Lat, Pearson Coefficient

28. CEDAR Workshop, Boulder CO June 20-25, 2010 Hmf2 Mid latitude, Pearson Coefficient

29. CEDAR Workshop, Boulder CO June 20-25, 2010 Hmf2 low lat, Pearson Coefficient