GISM Global Ionospheric Scintillation Model

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1 GISM Global Ionospheric Scintillation Model Y. Béniguel, IEEA Béniguel Y., P. Hamel, A Global Ionosphere Scintillation Propagation Model for Equatorial Regions, Journal of Space Weather Space Climate, 1, (11), doi: 1.151/swsc/114 African School on Space Science Kigali, Rwanda 3 june july 14

2 Contents Bias Scintillations Modelling Results vs Measurements Scattering Function Calculation (SAR observations) Conclusion Positioning errors African School on Space Science Kigali, Rwanda 3 june july 14

3 Measurement Campaigns PRIS Béniguel Y., J-P Adam, N. Jakowski, T. Noack, V. Wilken, J-J Valette, M. Cueto, A. Bourdillon, P. Lassudrie-Duchesne, B. Arbesser- Rastburg, Analysis of scintillation recorded during the PRIS measurement campaign, Radio Sci., Vol 44, (9), doi:1.19/8rs49 MONITOR Prieto Cerdeira R., Y. Béniguel, "The MONITOR project: architecture, data and products", Ionospheric Effects Symposium, Alexandria VA, May 11 MONITOR Extension On going; start : 3 june 14 African School on Space Science Kigali, Rwanda 3 june july 14

4 Ionosphere Variability TEC Map S4 map cumulated over 4 hours African School on Space Science Kigali, Rwanda 3 june july 14

5 Mean Errors (ray technique calculation) ( ) ( ) cos Y X 1 sin Y X 1 sin Y 1 X 1 n 1/ + ± = ϑ ϑ ϑ African School on Space Science Kigali, Rwanda 3 june july 14 ω i i k c d t d x = i P P i x d t d k = ω ω ω Haselgrove equations (Simplified) P X ω ω = ω ω b Y =

6 Bias Range error L = λ r e π N T N = z T N e ds 4.3N L = f T Faraday rotation Ψ = e ε c 3 m ω z N e B cosϑ ds Inputs : Ne ; B at any point inside ionosphere African School on Space Science Kigali, Rwanda 3 june july 14

7 Example of results / Solar Flux 15 African School on Space Science Kigali, Rwanda 3 june july 14

8 HF Ground to Ground Propagation (Sky Wave) d x d t i = c k ω i d k d t i = ω p ω ω x p i Etheta (V),8,7,6,5,4,3,, altitude (km) Ray Paths vs Elevation Angles 5 to distance from source (km) HF Antenna Pattern as an input African School on Space Science Kigali, Rwanda 3 june july 14

9 Turbulent Ionosphere (scintillation) African School on Space Science Kigali, Rwanda 3 june july 14

10 Physical Mechanism Satellite signal Drift velocity Receiver level African School on Space Science Kigali, Rwanda 3 june july 14

Medium Radar Observations Observations at

11 Medium Radar Observations Observations at Kwajalen Islands Courtesy K. Groves, AFRL Observations in Brazil Courtesy E. de Paula, INPE The vertical extent may reach hundreds of kilometers African School on Space Science Kigali, Rwanda 3 june july 14

12 Scintillation on Galileo Satellites L1 vs E5a African School on Space Science Kigali, Rwanda 3 june july 14

13 Field Propagation Equation E ( ρ, z, ω, t) = U ( ρ, z, ω) exp ω { j ( t k ( z') dz' )} The field amplitude value U is a solution of the the parabolic equation U( ρ) j k + t U( ρ) + k ε1 ( ρ) U( ρ) = z Method of solution : phase screen technique African School on Space Science Kigali, Rwanda 3 june july 14

14 Field Propagation Equation Solution of the parabolic equation j k z U ( r) + t U ( r) + k ε ( r ) U ( r) = j k z U ( r) + 3 k t U ( r) + j A ( ) U ( r) = 4 Using the phase index autocorrelation function ( z, ) B ρ = ε ( ρ1 ) ε ( ρ ) A ( ρ) ( z, ) dz = B ρ African School on Space Science Kigali, Rwanda 3 june july 14

15 Phase Screen Technique Transmitter Propagation Propagation Scattering Scattering Scattering Receiver Propagation : 1st & 3rd terms ; scattering : nd & 3rd terms African School on Space Science Kigali, Rwanda 3 june july 14

16 Medium Characterization Index Spectral Density African School on Space Science Kigali, Rwanda 3 june july 14

17 Medium s Phase Spectrum Power densities Phase Amplitude ( λ r ) frequency (Hz) e L CS σne CP γ Φ ( Κ) = = p / p / ( Κ + q ) ( Κ + q ) 3 parameters : σ Ne ; q ; p African School on Space Science Kigali, Rwanda 3 june july 14

18 One Sample : Intensity Sample characteristics : S4 =.51, sigma phi =.11 African School on Space Science Kigali, Rwanda 3 june july 14

19 One Sample : Phase Sample characteristics : S4 =.51, sigma phi =.11 African School on Space Science Kigali, Rwanda 3 june july 14

20 Spectrum Parameters 5 days RINEX files considered in the analysis S4 >. & sigma phi < (filter convergence) parameters to define the spectrum : T (1 Hz value) & p African School on Space Science Kigali, Rwanda 3 june july 14

21 Slope spectrum vs time after sunset 5 slope Power spectrum 5 slope phase spectrum p p Time after sunset Time after sunset African School on Space Science Kigali, Rwanda 3 june july 14

22 Phase variance Time domain vs frequency domain σphi p+ 1 p f T PSD( f ) df = T f df = T = p 1 p+ 1 ( p 1) fc fc fc = fc (if p > 1) Slope set to.8 African School on Space Science Kigali, Rwanda 3 june july 14

23 Medium Characterization (Correlation Function) Isotropic 1D Anisotropic African School on Space Science Kigali, Rwanda 3 june july 14

24 D Analysis : Isotropic Medium LOS CP BΦ ( ρ) ( π) γ = Φ ( Κ) exp( jκ. ρ ) dκ [ B ( ρ) ] Φ iso = (p 4) / σ Γ Φ ((p ) / ) ( (p / ) ( ρ q ) ) K ( ρ q ) ( (p ) / ) σ B () = Φ = Φ ( λ r ) e L L σ Ne African School on Space Science Kigali, Rwanda 3 june july 14

25 1D Analysis Isotropic Medium LOS B Φ ( ρ) C P = γ Φ (k) exp( jk ρ ) π dk [ B ( ρ) ] Φ 1D = C P π ( p 3)/ π Γ ( p / ) q 1 p (p 1)/ ( ρ q ) K ( ρ q ) ( p 1)/ African School on Space Science Kigali, Rwanda 3 june july 14

26 1D vs Isotropic Slope p p - 1 Multiplicative factor Γ π ( ( p 1) / ) Γ( p / ) African School on Space Science Kigali, Rwanda 3 june july 14

27 Anisotropic vs Isotropic LOS γ Φ ( λ r ) e L CS σ ( Κ) = p / ( q + q ) Ne a b B field γ Φ a b CP ( Κ) = p / ( ) + q ( A K + BK q + CK ) x x y y Additional geometric factor with respect to the D case G = ab ( A C B / ) 4 1/ a, b ellipses axes A, B, C trigonometric terms resulting from rotations related to variable changes African School on Space Science Kigali, Rwanda 3 june july 14

28 Phase Synthesis (1D) Φ ( ρ) = FFT 1 ( FFT (u) * γ (k) ) Φ u random number with a uniform spectral density Done at each successive layer African School on Space Science Kigali, Rwanda 3 june july 14

29 Numerical Constraints Frequency band P 45 MHz Medium parameters (1) L = 5m. Phase variance () Aliasing (3) Propagation z λ σφ σφ = ( λ re ) zl σne L > L x z < L λ = σ Φ 1.41 L > 8 m. N = 1 3 e 1 el/ m ( σ Φ = 1.19 ) z = ; σ 1 Φ = RMS = % z < 5km L = 5m. x = 3.3m. L 1.5 GHz L = 5m. N = 1 e 1 el/ m RMS = % 3 = σ Φ σ Φ =.1.36 ( ) z L > 85 m ; σ = 1 = Φ z < 1km L = 5m. x = 4.88 m. (FFT :14 pts) S.5 GHz L = 5m. N = 1 e 1 el/ m RMS = % 3 σ Φ σ Φ = =.5. ( ) z L > 51 m. = Φ ; σ = 1 z < 3km L = 5m. x = 4.88 m. (FFT :14 pts) African School on Space Science Kigali, Rwanda 3 june july 14

30 Sub Models (1 / ) Seasonal Dependency (Low Latitude Scintillations) African School on Space Science Kigali, Rwanda 3 june july 14

31 Scintillation Events Histograms African School on Space Science Kigali, Rwanda 3 june july 14

32 Scintillation Events / Lima 1 S4 vs Day of year 1 Lima S Doy African School on Space Science Kigali, Rwanda 3 june july 14

33 Measurements in Malindi, Kenya African School on Space Science Kigali, Rwanda 3 june july 14

34 Measurements in Burkina Fasso 1 Koudougou (Burkina Fasso) Geographic Latitude : 1 15 / Magnetic Latitude : Number of Events weak strong medium year African School on Space Science Kigali, Rwanda 3 june july 14

35 Sub Models ( / ) Local Time Dependency (Low Latitude Scintillations) African School on Space Science Kigali, Rwanda 3 june july 14

36 One week of measurements in Guiana S Intensity standard deviation (S4) all satellites: week 1/11/6 to 15/11/ S4 all satellites days 314 to 319 / year 6 PRN PRN13 PRN1 PRN4 PRN4 PRN8 PRN17 PRN1 PRN8 PRN9 PRN6 PRN9 PRN6 PRN Local Time (hours) GPS Week Time (hours) Local time : post sunset hours (CLS measurements, PRIS Campaign) African School on Space Science Kigali, Rwanda 3 june july 14

37 Checking Results Indices Inter frequency correlation Probability of intensity Fades distribution Loss of Lock African School on Space Science Kigali, Rwanda 3 june july 14

38 Medium Characterisation Mean Effects (Sub Models) NeQuick, Terrestrial Magnetic Field (NOAA) Geophysical Parameters SSN, Medium Drift Velocity LT & Seasonal dependency Scintillations (Fluctuating medium) Spectrum slope (p), BubblesRMS, OuterScale (L ) Anisotropy ratio African School on Space Science Kigali, Rwanda 3 june july 14

39 Numerical Implementation The model includes an orbit generator (GPS, Glonass, Galileo, ) Inputs Medium Characterisation Geophysical Parameters Scenario Intermediate calculation : LOS, Ionisation along the LOS Outputs Scintillation indices Correlation Distances (Time & Space) Scattering function African School on Space Science Kigali, Rwanda 3 june july 14

40 Signal at receiver level African School on Space Science Kigali, Rwanda 3 june july 14

41 Modelling vs Measurements (Intensity) S4 all satellites Cayenne days 314 to 319 : year 6 1 S PRN PRN13 PRN1 PRN4 PRN4 PRN8 PRN17 PRN1 PRN8 PRN9 PRN6 Measurements. PRN LT Modelling S PRN6 PRN3 Cayenne day 314 / 6 GISM LT African School on Space Science Kigali, Rwanda 3 june july 14

42 Modelling vs Measurements (Phase) Sigma Phi (radian) Sigm a Phi all satellites Cayenne, days 314 to 319 / year LT Modelling Some samples exhibit high values (both measurements and modelling) due to the phase jumps Sigma phi PRN PRN13 PRN1 PRN4 PRN4 PRN8 PRN17 PRN1 PRN8 PRN9 PRN6 PRN9 PRN6 PRN3 The phase RMS value is slightly lower than the S4 value Cayenne day 314 / 6 G ISM African School on Space Science Kigali, Rwanda 3 june july 14 Measurements LT

43 Scintillation Modelling vs Measurements S4 Measurement in Cayenne Latitude 4 8 Longitude 37 6 year Doy S4 Calculated (GISM) in Cayenne Latitude 4 8 Longitude 37 6 year Doy Measurements Modelling African School on Space Science Kigali, Rwanda 3 june july 14

44 Scintillation Index Dependency on Frequency 1.4 Galileo satellites 1 Inter Frequency Correlation L1 vs L (Modelling --> GISM) 1..9 S4 (E5a) S4 (L) S4 (L1) S4 (L1) using Yuma files African School on Space Science Kigali, Rwanda 3 june july 14

45 Global Maps TEC Map Modelling Scintillation Map Modelling African School on Space Science Kigali, Rwanda 3 june july 14

46 Inter Frequency Correlation African School on Space Science Kigali, Rwanda 3 june july 14

47 Weak scintillations vs strong scintillations 4 Tahiti Galileo N 1 doy 85 / 13 S4 (L1) =.1 ; S4 (E5a) =.36 L1 E5a 15 1 Tahiti Galileo N 1 doy 85 / 13 S4(L1) =.59 ; S4(E5a) = 1.36 L1 E5a db Time (s.) db Time (s.) African School on Space Science Kigali, Rwanda 3 june july 14

48 Inter Frequency Correlation Time Using 1 week of measurements in Tahiti African School on Space Science Kigali, Rwanda 3 june july 14

49 Frequency Correlation (Modelling) Inter Frequency Correlation Frequency correlation predicted by GISM 3 S4 (L1) =.18 S4 (L) = db -1 - db Time (s.) -15 S4(L1) =.7 S4(L) = Time (s.) Weak scintillations Strong scintillations African School on Space Science Kigali, Rwanda 3 june july 14

50 Loss of Lock African School on Space Science Kigali, Rwanda 3 june july 14

51 Probability of Loss of Lock Loss of Lock when σ φ > threshold value probability of intensity Theoretical (Nakagami distribution) vs Measurements S4 =. S4 =.3 S4 =.4 S4 =.5 S4 =. S4 =.3 S4 =.4 S4 =.5 σ The phase noise is related to the Intensity of the received signal Φ T = B n (c / n ) I η (c / n ) p(i) Nakagami distributed I db Probability of Loss of Lock is p(σ φ ) > threshold value African School on Space Science Kigali, Rwanda 3 june july 14

52 Loss of Lock (Measurements in Tahiti) Loss of Locks L / strong scintillations 1 L1 L 5 Intensity (db) S4 (L1) =.44 S4 (L) =.69 S4 (L1) =.5 S4 (L) = 1.6 S4 (L1) =.68 S4 (L) =.68 S4 (L1) =.49 S4 (L) =.87 S4 (L1) =.55 S4 (L) =.76 S4 (L1) =.55 S4 (L) = Time (s.) African School on Space Science Kigali, Rwanda 3 june july 14

53 Loss of Lock Measurements vs Modelling 1 1 Number of Loss of Lock on L (Measurements).3. 5 C / N = 4 d B C / N = 3 7 d B C / N = 3 d B C / N = 8 d B Modeling P ro b a b ility o f lo s s o f lo c k S4 (L) s 4 3 days of analysis in Tahiti African School on Space Science Kigali, Rwanda 3 june july 14

54 Geographical Extent Simultaneous Scintillation African School on Space Science Kigali, Rwanda 3 june july 14

55 Number of Satellites Simultaneously Corrupted by Scintillation Number of Satellites weak medium strong Lima 1 Number of satellites Lima 1 weak medium strong Day number Day number African School on Space Science Kigali, Rwanda 3 june july 14

56 Probability of intensity / Modelling 1 intensity fluctuations s4 =.73 1, probability of intensity fluctuations s4 = , ,1 db - -3,1,1 numerical Nakagami -4,1 s. db GISM output m A Γ ( m ) m -1 Nakagami law p ( A) = exp ( - m A ) m with m = 1 / S 4 African School on Space Science Kigali, Rwanda 3 june july 14

57 Fades Statistics Example of equatorial scintillation in Ascension Island, in solarmax conditions (1) 1.Real data 5 4 mc fading duration histogram mc mi fading times histogram experimental theoretical experimental theoretical GISM simulation African School on Space Science Kigali, Rwanda 3 june july 14

58 Probability of intensity / Modelling Nakagami vs measurements African School on Space Science Kigali, Rwanda 3 june july 14

59 Radar Observations Mutual Coherence Function African School on Space Science Kigali, Rwanda 3 june july 14

60 Correlation distance vs LSAR L e Synthetic Aperture Length 1 km African School on Space Science Kigali, Rwanda 3 june july 14

61 Ionosphere Effects Free Space Resolution x y SAR Ionosphere Effects x ' Pulse broadening (dispersion) y ' L y ' Turbulence Effect y L Group Delay x' x African School on Space Science Kigali, Rwanda 3 june july 14

62 Two Points - Two Frequencies Coherence Function ), k z, ( U ), k z, ( U ),, k, k z, ( * ρ ρ ρ ρ = Γ ) z,, k ( ) ( D ) ( A k k k 8 k k k j z d d 4 p d d = Γ + + ρ ρ ξ ξ Using the parabolic equation African School on Space Science Kigali, Rwanda 3 june july 14 k k 8 k z Same process than previously : propagation 1st & 3rd terms ; Diffraction : nd & 3rd terms [ ] ) B ( ) ( B ) (z, D ρ ρ Φ Φ Φ = The structure function is quadratic with respect to the distance

63 Two Points - Two Frequencies Coherence Function * Γ ( z, k1, k, ρ 1, ρ ) = U1 ( z, k1, ρ1 ) U ( z, k, ρ ) African School on Space Science Kigali, Rwanda 3 june july 14

64 Solution (one single screen) Scattering constants B = σ Φ ω S = σ Φ Log ( L ( L1 ) 6 L / l i ) Propagation 1 constant P = 1 c k L L 1 L 1 * Nickisch, RS 9, Knepp & Nickisch, RS, 1 African School on Space Science Kigali, Rwanda 3 june july 14

65 One Single Screen Analytical solution K x τ and K x Γ ( τ, K x, z ) = z B S exp z K 4 S x exp ( τ z K P) + 4 B x African School on Space Science Kigali, Rwanda 3 june july 14

66 Spreading Extent K = τ1 = A B K = KMax τ = 4 S P A Spread factor Q = τ τ = 1 A B S P τ K = K African School on Space Science Kigali, Rwanda 3 june july 14

Spreading Extent 1 MHz Very large value of

ionospheric scattering on VHF and UHF radar

67 Spreading Extent 1 MHz Very large value of Q 1 MHz Large value of Q 435 MHz Q around 1 Rogers, N., P. Cannon, and K. Groves, Measurements and simulations of ionospheric scattering on VHF and UHF radar signals: Channel scattering function, Radio Sci., 44, RSA33, DOI: 1.19/8RS433, 9. African School on Space Science Kigali, Rwanda 3 june july 14

68 Analytic vs Numerical African School on Space Science Kigali, Rwanda 3 june july 14

69 Several Screens Refined Analysis The algorithm can easily be generalized Different statistical properties may be assigned to the different layers Numerical FFT (1D) shall be performed to get the coherence function African School on Space Science Kigali, Rwanda 3 june july 14

70 Ambiguity Function * χ ( r, r ) = g n ( t, rn ) f n ( t, r n n ) dt g n is the received signal and f n is the matched filter ( j ( ω ω ) Φ ( ω ω ) ) d ω 1 χ n rn, r n ) = exp ( j Φ ) exp 1 Φ 4 π r ( ( ) n Value of Coherent field received ( σ ) ( σ ) exp Le / ρ Φ exp Φ χ ( r, r ) = exp j k r d in c ρ e Le / ( 4 r ) ρ s π + = r ( 4π r ) ( k L / r ) An attenuation factor on the coherent component is included African School on Space Science Kigali, Rwanda 3 june july 14

71 Coherent Length ( ) It is given by function Γ ( ω, ρ, r ) = exp B ω D ( ρ / r ) d Phase Standard Deviation and related Coherent Length in the case of strong fluctuations (red lines) & very strong fluctuations (blue lines) D S d 6 Sigma Phi Coh Length (m.) Sigma Phi Coh Length (m.) 5 8 Sigma Phi (radians) Coh Length (m.) 1,5 1 1,5,5 f (GHz) African School on Space Science Kigali, Rwanda 3 june july 14

72 Positioning Errors African School on Space Science Kigali, Rwanda 3 june july 14

73 Modelling S4 measured for each tracked satellite σ τ is calculated taking the thermal noise as the main contribution Range error calculated assuming a gaussian distribution GPS constellation simulated with a yuma file African School on Space Science Kigali, Rwanda 3 june july 14

74 GPS Positioning Errors African School on Space Science Kigali, Rwanda 3 june july 14

75 s4moy s4max 1,4 1, 1,8,6,4, Positioning errors from Measurements in Brazil in nbsat Longitude error Latitude error degrees,6,4, , -,4 -,6 utc (hour) African School on Space Science Kigali, Rwanda 3 june july 14

76 Conclusion Reasonable agreement between modelling (GISM) and measurements Positioning errors due to scintillations may reach values up to 5 meters The azimuthal resolution of a SAR may be significantly decreased All results will be updated taking measurements campaign data into account African School on Space Science Kigali, Rwanda 3 june july 14

Scintillation Nowcasting with GNSS Radio Occultation Data

Scintillation Nowcasting with GNSS Radio Occultation Data Keith Groves, Charles Carrano, Charles Rino and John Retterer Institute for Scientific Research, Boston College Paul Straus Aerospace Corporation