1. Deducing Ionospheric Turbulence Parameters from High-Rate GPS Observations during the COPEX Campaign
Charles S. Carrano, Cesar E. Valladares, Keith M. Groves
Boston College, Chestnut Hill, MA, 02467
2nd Low-Latitude Ionospheric Sensor Network Workshop São José dos Campos  November 2011

2. Overview
Plasma instabilities in the equatorial ionosphere create irregularities in the electron density over a broad range of spatial scales (plasma turbulence).
These irregularities cause scintillations in the amplitude and phase of radio waves that traverse them.
Previous authors have reported on the morphology of GPS scintillations and irregularity zonal drift during the 2002 Conjugate Point Equatorial Experiment (COPEX) in Brazil.
Our focus is to use GPS observations at the three COPEX stations to characterize the turbulent ionospheric medium that produced these scintillations.
We developed a new method called Iterative Parameter Estimation for this purpose. It valid when S4 saturates due to multiple-scatter effects. This is crucial since scintillations during COPEX were too strong for weak scatter theory.
We report on the latitudinal and local time variation of turbulent intensity, spectral index, and irregularity zonal drift velocity. 2

3. Modeling Propagation through the Equatorial Ionosphere
xp (magnetic north)
z (vertical)
yp (magnetic east)   x y L
Transmitter
Scattering Layer
Reception Plane
Receiver
Diffraction Pattern 
We assume the plasma turbulence can be represented by a homogenous scattering layer of thickness L
These irregularities are highly elongated along Earth’s magnetic field
Propagation of radio wave through scattering layer produces a diffraction pattern on the ground t
Receiver detects temporal fluctuations (scintillations)
Our interest is to infer characteristics of scattering layer from the time series of intensity fluctuations 4

4. Ionospheric Turbulence Model (Rino, 1979)
Power law model for 3D spectrum of electron density fluctuations, N:
Correlation function of phase fluctuations, R(), after passage through layer:
Step 1: apply coordinate transformation to account for irregularity anisotropy
Step 2: integrate through the scattering layer along the line of sight
Step 3: apply Fourier Transform in the transverse plane
wavelength
re classical electron radius
spatial separation distance
 Propagation (zenith) angle
p phase spectral index (p=2)
CkL vertically integrated turbulent intensity
q, q0 wavenumber, outer scale wavenumber
K,  modified Bessel function, Gamma function
G geometry enhancement factor
A,B,C propagation and B-field geometry factors 5

5. The Model Intensity Spectrum (Booker and MajidiAhi, 1981)
A solution of the 4th moment equation governing intensity fluctuations following propagation of a plane wave through a thin phase-changing screen.
Define Fresnel parameter:
and two functions that depend on F and the phase correlation function R():
The intensity spectrum at the reception plane is given by:
The S4 index is calculated by integrating spectrum over all wavenumbers: 6

6. Space-to-Time Translation (Rino, 1979)
Spatial wavenumbers translate to temporal frequencies in a model-dependent fashion:
and
Effective scan velocity (Rino, 1979):
where A,B,C are propagation and magnetic field geometry factors
The scan velocity (Vsx,Vsy) of the ray path through the irregularities is given by:
Vpx, Vpy, Vpz are the geomagnetic north, east and down coordinates of the IPP velocity,
and VD is the irregularity zonal drift velocity. 7

7. Iterative Parameter Estimation (IPE)
The independent variables in the ionospheric turbulence model are CkL, p, and VD
All others are calculable from geometry and B field direction except the outer scale, anisotropy ratio, and layer height--we assume L0 = 10 km, a : b = 50, and Hp=350 km.
Define a metric to quantify difference between model and measured intensity spectra:
Integration performed over frequency range fmin and fmax to exclude receiver noise
Solve for 3 unknown parameters iteratively using the Downhill Simplex Method 8

8. Two Examples of IPE Analysis
Weak Scatter Example
Strong Scatter Example 10

9. High-Rate GPS Receivers Operating During COPEX
Three sites located on nearly the same magnetic field line
Alta Floresta at dip equator
Boa Vista and Campo Grande at magnetically conjugate points, close to crests of equatorial anomaly
Three high-rate (10 Hz) Ashtech Z-CGRS receivers operated by AFRL / INPE
Data collected Oct-Dec 2002 under solar max conditions.
We present results for the evening of 1-2 Nov 2002 3

10. Directly Measured Parameters
Vertical TEC
TECU
Scintillation Index
Decorrelation Time b)
S4m
m (sec) 11

11. Measured and Modeled Scintillation Statistics
Measured Scintillation Index
Model Scintillation Index
Measured Decorrelation Time (sec)
Model Decorrelation Time (sec)
IPE results accurately reproduce …
S4 (depth of fading)
decorrelation time,  (rate of fading)
This is makes sense, since S4 and  can be inferred from the intensity spectrum
Previous modeling efforts have tried to reproduce either S4, or both S4 and . IPE reproduces the entire intensity spectrum 12

12. Parameters Inferred by IPE Analysis
Vertical TEC
Turbulent Intensity a)
TECU
Log(CkL)
Phase Spectral Index
Drift Velocity b) p
VD (m/s) 13

13. Phase Scintillation Parameters inferred from IPE Analysis
Spectrum of phase fluctuations: a) a)
Variance of phase fluctuations:
Phase Spectral Strength
Phase Variance
T (dB)
2(rad2) 14

14. Local Time Variation at the Three COPEX Stations
Turbulent Intensity
Phase Spectral Index
Phase Spectral Strength b) 15

15. Comparison with Spaced-Receiver Drift Measurements
Boa Vista
VHF east link (channels 3-4)
VHF west link (channels 1-2)
GPS spaced-receivers
IPE analysis
VHF spaced-receiver drift provided by Robert Livingston (SCION Associates)
GPS spaced-receiver drift provided by Marcio Muella et al. [2008]
Alta Floresta
Campo Grande b) 16

16. Next Steps – Chains of Receivers from LISN Network
Apply analysis to observations from meridional chain of GPS receivers:
Can provide latitudinal and local time morphology of ionospheric turbulence responsible for scintillations at low latitudes.
Apply analysis to observations from longitudinal chain of GPS receivers:
Can provide evolution of turbulence within individual bubbles (i.e. in a coordinate system that follows the bubbles).
These GPS receivers are already operating—let’s extract the most information from them as possible! a)
Longitude (deg) b)
Latitude (deg) 17

17. Conclusions
We developed the IPE technique to characterize the turbulent ionospheric medium that produced GPS scintillations during the 2002 COPEX experiment in Brazil.
Our analysis of data collected on 1-2 Nov 2002 provides the latitudinal and local time variation of turbulent intensity, phase spectral index, and zonal drift.
The strength of turbulence tends to be largest where the TEC is largest (qualitatively)
The phase spectral index increases with local time from 2.5 to 4.5, we conjecture this is due erosion (decay) of small scale irregularities in the turbulence.
Our estimates of the zonal irregularity drift are consistent with those provided by the spaced GPS receiver technique (but our technique requires only 1 receiver)
Our drift estimates are similar at the three stations, unlike those provided by the VHF spaced-receiver technique which are larger at Campo Grande than at Boa Vista.
Next steps: Apply to LISN GPS receivers arranged in meridional/longitudinal chains
Reference: Carrano, C. S., C. E. Valladares, K. M. Groves, Latitudinal and Local Time Variation of Ionospheric Turbulence Parameters during the Conjugate Point Equatorial Experiment (COPEX) in Brazil, submitted to International Journal of Geophysics, 2011. 18

18. Extra Slides

19. Determination of Model Parameters CkL, p, and VD
5.0x1034
1.0x1035
5.0x1035
1.0x1036
2.5
3.0
3.5
4.0
75 m/s
150 m/s
300 m/s
400 m/s
2.3x1035
3.6
212 m/s
Varying CkL
Varying p
Varying VD 20

20. High-Rate GPS Receivers Operating During COPEX
Station
Geographic
Geomagnetic
Lat.
Lon.
Dip Angle
Inclination
Declination
Boa Vista
2.8°N
60.7°W
22.1°N
22.1°
-13.0°
Alta Floresta
9.9°S
56.1°W
3.38°S
-3.2°
-14.6°
Campo Grande
20.5°S
54.7°W
22.3°S
-21.8°
-13.8° 21

21. Local Time Variation at the Three COPEX Stations
Scintillation Index
Decorrelation Time 22