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Ionosphere Scintillation Mapping

Beacon Satellite Symposium, Bath, 8 – 12 july 2013

Y. Béniguel, P. Hamel, IEEA, Paris, France

C. Sambou, M. Darces, M. Hélier, UPMC, Paris, France

Contents

• Calculation technique

• Input Data


• Conclusion

• Algorithm

• Examples of results

Calculation Technique

Kriging technique

• Well suited to random data processing


• Accuracy increases with the number of data

• Allows to produce a map and the corresponding error map

Input Data

50 Hz receivers Monitor Project


1 Hz IGS Data

Simulated GISM

Monitor Network50 Hz receivers


Scintillation indices at 50 Hz (top panel)vs 1 Hz (IGS data: bottom panel)


Modelling(GISM) MPS model

Inputs

Geophysical Parameters

Scenario

The model includes an orbit generator (GPS, Glonass, Galileo, …)

Intermediate calculation : LOS, Ionisation along the LOS


Outputs

Intermediate calculation : LOS, Ionisation along the LOS

Scattering function

Time series, Scintillation indices, Correlation Distances

Béniguel Y., P. Hamel, “A Global Ionosphere Scintillation Propagation Model for Equatorial Regions”, Journal of Space Weather Space Climate, 1, (2011), doi: 10.1051/swsc/2011004

0

0.2

0.4

0.6

0.8

1

-40 -20 0 20 40 60 80 100

S4 all satellitesCayenne days 314 to 319 : year 2006

PRN2PRN13PRN10PRN4PRN24PRN28PRN17PRN12PRN8PRN29PRN26PRN9PRN6PRN23

S4

Samples with S4 < 0.2 were ignored (noise level)

Modelling vs Measurements(Intensity)

Measurements


LT

0

0.2

0.4

0.6

0.8

1

18 19 20 21 22 23 24 25

Cayenne day 314 / 2006GISM

132327817284102429226596

S4

LT

Modelling

0

0.2

0.4

0.6

0.8

1

-40 -20 0 20 40 60 80 100

Sigma Phi all satellitesCayenne, days 314 to 319 / year 2006

PRN2PRN13PRN10PRN4PRN24PRN28PRN17PRN12PRN8PRN29PRN26PRN9PRN6PRN23

Sig

ma

Phi

(ra

dian

)

LT

The phase RMS value is slightly lower than the S4 valueSome samples exhibit high

Modelling vs Measurements(Phase)

Measurements


0

0.2

0.4

0.6

0.8

1

18 19 20 21 22 23 24 25

Cayenne day 314 / 2006G ISM

132327817284102429226596

Sig

ma

phi

LT

Some samples exhibit high values (both measurements and modelling) due to the phase jumps

Modelling

Comparison with MeasurementsYear 2011 / Guiana / Novatel Measurements

0.6

0.8

1

S4 Calculated (GISM) in CayenneLatitude 4°8 Longitude 37°6 year 2011

0.7

0.8

0.9

1

S4 Measurement in CayenneLatitude 4°8 Longitude 37°6 year 2011


0.2

0.4

0.6

0 50 100 150 200 250 300Doy

0.2

0.3

0.4

0.5

0.6

0 50 100 150 200 250 300

Doy

Kriging Algorithm


Kriging Algorithm

) , f ( ) f ( m ) , f ( Y ωω Γ+=

Y the observable, f a vector of factors (location, …)

Y is the sum of a mean value and a random part

Kriging Random Variables


) f ( a ) f ( m i

M

1i ϕ∑=

)h ( c ) , f ( ) , f ( ) f , f ( c jiji =ΓΓ= ωω

Covariance function

Covariance Function

� Few data points

� Many data points

Computation of the experimental covariance


� Few data points

Choice of the covariance function among known models.

Kriging Interpolation Technique

) , f ( Y *Y j

N

1 j ωλ∑=

A linear estimator is built with all data points

The outcome at f0 is linear


The estimator gives an exact value at the data points

(Lagrange multipliers)

) f ( Y ) c , f , (f ) f ( *Y N

1jj0 j 0 ∑= λ

Variance Minimization

2

0 Y *Y −• Minimizing the variance

• Taking the inverse of the covariance matrix

Y w ) f ( *Y T=


Y w ) f ( *Y T0 =

• It is an exact interpolator : no errors at data points

• Gives an estimate of the accuracy of the Kriged estimates

2Min

2 Y *Y Min σ=−

Variogram Estimation

0.014

0.016

0.018

0.02

0.022

GISM Variogram (Cayenne input data scenario)

0.016

0.017

0.018

0.019

Variogram using Measurements in Cayenne


r r h ji −=

) r ( Y ) r ( Y )h ( 2

j i −=γ

0.006

0.008

0.01

0.012

0 2000 4000 6000 8000 1 104

Distance (km)

0.012

0.013

0.014

0.015

0 2000 4000 6000 8000 1 104

Distance (km)

Variograms Estimated on a Reduced Time Duration

Experimental variograms based on GISM calculations


S4 variogram variogramϕσ

Covariance Function

)h ( T )h ( C γ−= 4 10 4.7 T −=with


range

T

Reference data Kriged data


Results of S4 data kriging

Reference data

Kriging data

Kriged data

Cut at Latitude 6°


Cut at Latitude - 3°


Cut at Latitude – 3°


Cut at Longitude - 44°


Coupe de SigmaPhi pour

une longitude de -36°



Kriging Over a Whole Year


The covariance function used was

deduced from GISM calculationsLima 2012

Dip Lat. 0°65

Conclusion

Analysis of scintillations using the IGS network

Improve the calculation of the variogram

(Comparison to 50 Hz data)


Improve the calculation of the variogram

(Time as an additionnal factor)

Produce the error maps

Thank you


ionosphere scintillation mapping - ieeaieea.fr/publications/ieea-2013-bss.pdfionosphere...

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