2nd Low-Latitude Ionospheric Sensor Network Workshop

São José dos Campos 7-10 November 2011

Charles S. Carrano, Cesar E. Valladares, Keith M. Groves

Boston College, Chestnut Hill, MA, 02467

Deducing Ionospheric Turbulence Parameters from High-Rate GPS Observations during the COPEX Campaign

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

Modeling Propagation through the Equatorial Ionosphere

Receiver detects temporal fluctuations (scintillations)

These irregularities are highly elongated along

Earth’s magnetic field

t

xp

(magnetic north)

z (vertical)

yp

(magnetic east)

x

y

L

Transmitter

Scattering Layer

Reception Plane

Receiver

Diffraction Pattern

Propagation of radio wave through scattering layer

produces a diffraction pattern on the ground

4

Our interest is to infer characteristics of scattering layer from the time series of intensity

fluctuations

We assume the plasma turbulence can be represented by a

homogenous scattering layer of thickness L

Ionospheric Turbulence Model (Rino, 1979)

5

( 1/2)2 20

( ) sN

Cqq q

121

( 1)/2 02 2

0

( )1000( ) sec2 2 2 [( 1) / 2]

pp

pe k

K qR r GC L

q p

wavelength

re

classical electron radius

spatial separation distance

Propagation (zenith) angle

p phase spectral index (p=2)

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

• Power law model for 3D spectrum of electron density fluctuations, N:

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

• Correlation function of phase fluctuations, R

(), after passage through layer:

The Model Intensity Spectrum (Booker and MajidiAhi, 1981)

6

1/2sec2zF

2 2( , ) 2 ( ) ( ) ( )f k R R kF R kF

( , ) exp (0, ) ( , ) exp (0, )g k f k f k f k

24

0

1 ( )2

S I k dk

• The S4 index is calculated by integrating spectrum over all wavenumbers:

0( ) 2 ( , )cos( )I k g k k d

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:

• A solution of the 4th moment equation governing intensity fluctuations following propagation of a plane wave through a thin phase-changing screen.

Space-to-Time Translation (Rino, 1979)

7

1/22 2

2 / 4sx sx sy sy

eff

CV BV V AVv

AC B

tan( )cos( )

tan( )cos( )

sx px pz

sy D py pz

V V V

V V V V

where A,B,C are propagation and magnetic field geometry factors

Vpx

, Vpy

, Vpz

are the geomagnetic north, east and down coordinates of the IPP velocity,

and VD

is the irregularity zonal drift velocity.

• Effective scan velocity (Rino, 1979):

• The scan velocity (Vsx

,Vsy

) of the ray path through the irregularities is given by:

2effkf v

( ) ( ) / effI f I k v

• Spatial wavenumbers translate to temporal frequencies in a model-dependent fashion:

and

Iterative Parameter Estimation (IPE)

8

max

min

22

max min

2 log ( ; , , ) log ( )f

k D mf

I f C L p V I f dff f

• Define a metric to quantify difference between model and measured intensity spectra:

• The independent variables in the ionospheric turbulence model are CkL, p, and V

D

• Solve for 3 unknown parameters iteratively using the Downhill Simplex Method

Integration performed over frequency range fmin

and fmax

to exclude receiver noise

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.

Two Examples of IPE Analysis

10

Weak Scatter Example Strong Scatter Example

High-Rate GPS Receivers Operating During COPEX

3

• 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

Directly Measured Parameters

11

b)

Vertical TEC

Scintillation Index Decorrelation Time

TECU

S4m

m

(sec)

Measured and Modeled Scintillation Statistics

12

Measured Scintillation Index

Mod

el S

cint

illat

ion

Inde

x

Measured Decorrelation Time (sec)

Mod

el D

ecor

rela

tion

Tim

e (s

ec)

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

Parameters Inferred by IPE Analysis

13

a)

b)

TECU

p VD

(m/s)

Log(CkL)

Vertical TEC Turbulent Intensity

Phase Spectral Index Drift Velocity

Phase Scintillation Parameters inferred from IPE Analysis

14

a)a) 1

2 2 11

2 ( / 2)sec1000 (2 ) [( 1) / 2]

pp

e k effppT r G C L vp

11

1 02 2 2 221000 1

2

( )sec

4 ( )

ppp

e k p

qr G C L

Phase Spectral Strength Phase Variance

2(rad2)T (dB)

• Spectrum of phase fluctuations:

• Variance of phase fluctuations:

/22 20

( ) ,pTP f

f f

Local Time Variation at the Three COPEX Stations

15

b)

Turbulent Intensity

Phase Spectral Index Phase Spectral Strength

Comparison with Spaced-Receiver Drift Measurements

16

b)

Boa Vista

Campo GrandeAlta Floresta

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]

Next Steps – Chains of Receivers from LISN Network

17

a)

b)

• 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!

Latitude (deg)

Long

itude

(deg

)

Conclusions

18

• 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.

• 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

Extra Slides

Determination of Model Parameters CkL, p, and VD

20

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

High-Rate GPS Receivers Operating During COPEX

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Station Geographic GeomagneticLat. 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°

Local Time Variation at the Three COPEX Stations

Scintillation Index

Decorrelation Time

22