1. 0 www.ieea.fr 7th ESWW, Bruges, 19-11-2011 Ionospheric Scintillations Propagation Model Y. Béniguel, J-P Adam IEEA, Courbevoie, France

2. 1 www.ieea.fr 7th ESWW, Bruges, 19-11-2011 Outline Overview Practical use Transmitted field calculation Scattering function calculation (SAR observations)

3. 2 www.ieea.fr 7th ESWW, Bruges, 19-11-2011 Disturbed Ionospheric Regions Affected by Scintillation SATCOM AURORAL IRREGULARITIES GPS PLASMA BUBBLES GPS SATCOM MAGNETIC EQUATOR DAYNIGHT EQUATORIAL F LAYER ANOMALIES SBR POLAR CAP PAT CHE S

4. 3 www.ieea.fr 7th ESWW, Bruges, 19-11-2011 GPS / Galileo signal Receiver level Drift velocity Physical Mechanism

5. 4 www.ieea.fr 7th ESWW, Bruges, 19-11-2011 Medium Radar Observations The vertical extent may reach hundreds of kilometers Observations at Kwajalen Islands Courtesy K. Groves, AFRL Observations in Brazil Courtesy E. de Paula, INPE

6. 5 www.ieea.fr 7th ESWW, Bruges, 19-11-2011 Development of Inhomogeneities (Modelling) Solving momentum and continuity equation small scale model Allows estimating dimensions and temporal behaviour t = 20 s.t = 200 s.

7. 6 www.ieea.fr 7th ESWW, Bruges, 19-11-2011 Signal at receiver level (Measurements) IntensityPhase

8. 7 www.ieea.fr 7th ESWW, Bruges, 19-11-2011 Scintillations Parameters S4 and   S4 and   are statistical variables computed over a “reasonable” time period that satisfies both good statistics and stationarity, as follows “Reasonable Time” depends primarily on the effective velocity of the satellite raypath; varies from 10 to 100 seconds; the phase is derived from detrended time series These quantities depend on the density fluctuations in the medium

9. 8 www.ieea.fr 7th ESWW, Bruges, 19-11-2011 Seasonal Dependency Seasonal : peak at equinoxes : march & october

10. 9 www.ieea.fr 7th ESWW, Bruges, 19-11-2011 Local Time Dependency Local time : post sunset hours

11. 10 www.ieea.fr 7th ESWW, Bruges, 19-11-2011 Field received at ground level Solution of the parabolic equation

12. 11 www.ieea.fr 7th ESWW, Bruges, 19-11-2011 Field Propagation Equation Solution of the parabolic equation Using the phase index autocorrelation function

13. 12 www.ieea.fr 7th ESWW, Bruges, 19-11-2011 Algorithm Phase Screen Technique Propagation : 1st and 3rd terms (Space domain) Diffraction : 1st and 2 nd terms (Transform domain)

14. 13 www.ieea.fr 7th ESWW, Bruges, 19-11-2011 Phase Screen Technique Scattering Propagation Receiver Transmitter

15. 14 www.ieea.fr 7th ESWW, Bruges, 19-11-2011 3 parameters : Medium’s Characterisation 5 days RINEX files in Cayenne considered in the analysis S4 > 0.2 & sigma phi < 2 (filter convergence)

16. 15 www.ieea.fr 7th ESWW, Bruges, 19-11-2011 2D Analysis : Isotropic transverse medium LOS

17. 16 www.ieea.fr 7th ESWW, Bruges, 19-11-2011 Anisotropic vs Isotropic Additional geometric factor with respect to the 2D case a, b ellipses axes A, B, C trigonometric terms resulting from rotations related to variable changes LOS B field

18. 17 www.ieea.fr 7th ESWW, Bruges, 19-11-2011 How many screens When it converges matched to the electron density profile As many screens as discretisation points along the LOS Current option : one point every 15 km On average : 7 screens

19. 18 www.ieea.fr 7th ESWW, Bruges, 19-11-2011 Signal at receiver level Modelling IntensityPhase

20. 19 www.ieea.fr 7th ESWW, Bruges, 19-11-2011 Spectrum

21. 20 www.ieea.fr 7th ESWW, Bruges, 19-11-2011 Space step along the LOS = 5 km Space step along the LOS = 15 km Space step along the LOS = 30 km Space step along the LOS = 100 km CPU Time*23’7’303’2650’’ Convergence of Results

22. 21 www.ieea.fr 7th ESWW, Bruges, 19-11-2011 Global Maps TEC Map ModellingScintillation Map Modelling

23. 22 www.ieea.fr 7th ESWW, Bruges, 19-11-2011 Comparison with Measurements Upper decile slant S4 index at Marak Parak during September 2000. The dashed line indicates the magnetic equator. GISM Result

24. 23 www.ieea.fr 7th ESWW, Bruges, 19-11-2011 Radar Observations Medium Scattering Function

25. 24 www.ieea.fr 7th ESWW, Bruges, 19-11-2011 Two Points - Two Frequencies Coherence Function Same process than previously : propagation 1st & 3rd terms ; diffraction : 1st & 2nd The structure function is quadratic with respect to the distance Using the parabolic equation

26. 25 www.ieea.fr 7th ESWW, Bruges, 19-11-2011 Propagation 1st & 3rd terms

27. 26 www.ieea.fr 7th ESWW, Bruges, 19-11-2011 One screen ; distance = 500 km ; drift velocity = 100 m / s. ;   = 0.8 F = 400 MHzF = 1.5 GHz Medium Scattering Function The Doppler spreading is related to the drift velocity which can vary with the screen altitude

28. 27 www.ieea.fr 7th ESWW, Bruges, 19-11-2011 Including a particular waveform Field intensity Medium’s scattering function

29. 28 www.ieea.fr 7th ESWW, Bruges, 19-11-2011 Practical use of the model (GISM)

30. 29 www.ieea.fr 7th ESWW, Bruges, 19-11-2011 Medium Characterisation Mean Effects (Sub Models) Scintillations (Fluctuating medium) NeQuick, Terrestrial Magnetic Field (NOAA) Geophysical Parameters SSN, Drift Velocity Spectrum slope (p), BubblesRMS, OuterScale (L 0 ) Anisotropy ratio

31. 30 www.ieea.fr 7th ESWW, Bruges, 19-11-2011 Numerical Implementation Inputs Outputs Scintillation indices Correlation Distances (Time & Space) Medium Characterisation Geophysical Parameters Scenario The model includes an orbit generator (GPS, Glonass, Galileo, …) Intermediate calculation : LOS, Ionisation along the LOS Scattering function

32. 31 www.ieea.fr 7th ESWW, Bruges, 19-11-2011 Conclusion The geometry (LOS) with respect to the bubbles orientation is arbitrary The model allows calculating the transmitted field at receiver level the scattering function for radar observations A 1D algorithm applies to all cases