0 7th ESWW, Bruges, Ionospheric Scintillations Propagation Model Y. Béniguel, J-P Adam IEEA, Courbevoie, France

1 7th ESWW, Bruges, Outline Overview Practical use Transmitted field calculation Scattering function calculation (SAR observations)

2 7th ESWW, Bruges, 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

3 7th ESWW, Bruges, GPS / Galileo signal Receiver level Drift velocity Physical Mechanism

4 7th ESWW, Bruges, 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

5 7th ESWW, Bruges, Development of Inhomogeneities (Modelling) Solving momentum and continuity equation small scale model Allows estimating dimensions and temporal behaviour t = 20 s.t = 200 s.

6 7th ESWW, Bruges, Signal at receiver level (Measurements) IntensityPhase

7 7th ESWW, Bruges, 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

8 7th ESWW, Bruges, Seasonal Dependency Seasonal : peak at equinoxes : march & october

9 7th ESWW, Bruges, Local Time Dependency Local time : post sunset hours

10 7th ESWW, Bruges, Field received at ground level Solution of the parabolic equation

11 7th ESWW, Bruges, Field Propagation Equation Solution of the parabolic equation Using the phase index autocorrelation function

12 7th ESWW, Bruges, Algorithm Phase Screen Technique Propagation : 1st and 3rd terms (Space domain) Diffraction : 1st and 2 nd terms (Transform domain)

13 7th ESWW, Bruges, Phase Screen Technique Scattering Propagation Receiver Transmitter

14 7th ESWW, Bruges, parameters : Medium’s Characterisation 5 days RINEX files in Cayenne considered in the analysis S4 > 0.2 & sigma phi < 2 (filter convergence)

15 7th ESWW, Bruges, D Analysis : Isotropic transverse medium LOS

16 7th ESWW, Bruges, 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

17 7th ESWW, Bruges, 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

18 7th ESWW, Bruges, Signal at receiver level Modelling IntensityPhase

19 7th ESWW, Bruges, Spectrum

20 7th ESWW, Bruges, 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

21 7th ESWW, Bruges, Global Maps TEC Map ModellingScintillation Map Modelling

22 7th ESWW, Bruges, Comparison with Measurements Upper decile slant S4 index at Marak Parak during September The dashed line indicates the magnetic equator. GISM Result

23 7th ESWW, Bruges, Radar Observations Medium Scattering Function

24 7th ESWW, Bruges, 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

25 7th ESWW, Bruges, Propagation 1st & 3rd terms

26 7th ESWW, Bruges, 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

27 7th ESWW, Bruges, Including a particular waveform Field intensity Medium’s scattering function

28 7th ESWW, Bruges, Practical use of the model (GISM)

29 7th ESWW, Bruges, 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

30 7th ESWW, Bruges, 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

31 7th ESWW, Bruges, 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