F.J Meyer1) 2), B. Watkins3) , J.S. Kim4) , K. Papathanassiou4)

1)Earth & Planetary Remote Sensing, University of Alaska Fairbanks 2)Alaska Satellite Facility (ASF)

3)Space Physics and Aeronomy, University of Alaska Fairbanks 4)High Frequency and Radar Institute, German Aerospace Center (DLR), Germany

RECENT ADVANCES IN THE CORRECTION OF IONOSPHERIC EFFECTS IN LOW-FREQUENCY SAR

DATA

Collaborating Organizations:

F. Meyer et al. CEOS’11, Fairbanks, AK 2

Methods for Ionospheric Correction of SAR

• Ionosphere causes range of effects especially in low-frequency SAR systems

Ionosphere (TEC)

Faraday Rotation

Azimuth Shift

Range Shift

Interferometric phase (differential)

Dispersion

Ionospheric Artifacts in Radar Data

3

Am

plitu

de D

isto

rtion

s

Phase D

istortions

Rainforest, Brazil

F. Meyer et al. CEOS’11, Fairbanks, AK 4

Ionospheric Distortions – How to Fix Them?

1. Mathematical Modeling and Inversion:

( ) ( )2

0300

020000

28.40428.40428.404 ffTECfc

ffTECfc

TECfc

−⋅−−⋅+−=∆πππψ

Phase Distortions Image Distortions

Measure these!

TEC TEC TEC

Invert for these!

2. Statistical Modeling If mathematical modeling fails, statistical modeling mitigates effects on final target parameters Realistic modeling of the accuracy and correlation of data

→ Image correction & creation of ionospheric maps

TEC = Total Electron Content of Ionosphere

Mathematical Modeling and Inversion

Faraday Rotation (FR) Based Inversion (Freeman, 2004; Quegan, 2010; Nicoll & Meyer, 2008)

Range Split-Spectrum Based Inversion (Rosen, 2010; Papathanassiou, 2009; Meyer & Bamler, 2005; Brcic & Meyer, 2010)

Transmitted ground level Ω

Azimuth Autofocus Based Inversion (Papathanassiou, 2008; Meyer & Nicoll, 2008; Meyer, 2010)

Hybrid Methods (Meyer, 2005; Meyer, 2010; Meyer & Liu, 2011)

F. Meyer et al. CEOS’11, Fairbanks, AK 5

F. Meyer et al. CEOS’11, Fairbanks, AK 6

Advances in Optimizing Mapping Performance

Method 1

Method 2

Method 3

Method 5

Method 6

Method 7

∫

∫

∫

F. Meyer et al. CEOS’11, Fairbanks, AK 7

• Mitigation of ionospheric effects from Faraday Rotation and azimuth- shit estimates → reduced phase distortion and

improved coherence

Optimizing Ionospheric Correction C

oher

ence

com

paris

on:

Bef

ore

and

afte

r cor

rect

ion

Before correction

FR correction

Original phase Corrected phase

7

Cou

rtesy

of J

un S

u K

im, D

LR

FR & Az. shifts

In Case Signal Correction Fails:

• Statistical Modeling: • Statistical modeling mitigates effects on final target parameters through

realistic modeling of the accuracy and correlation of data

F. Meyer et al. CEOS’11, Fairbanks, AK 8

• Most small scale variations of ionospheric delay can be described as featureless, scale invariant noise like signals

• Convenient Descriptor: Power Law Functions

• Indicates:

– Total power of signal – Distribution of power over spatial scales

• Spectral Slope v: – Steep → smooth signal – Shallow → noisy signal

• Spectral slopes between ~2 and ~5 have been observed

Power Law Model of Small-Scale Ionospheric Signals

( ) vkkP −∝ϕ

F. Meyer et al. CEOS’11, Fairbanks, AK 9

Power Law Model of Small-Scale Ionospheric Signals

• On the convenience of power spectra: 1. Power Law models can be converted to covariance functions through cosine

Fourier Transformation

2. Spectral slopes can be converted to fractal dimensions D

( ) ( ) ( )∫= dffPfrrC ϕϕ π2cos

Dv 27 −=

→ Basis for signal analysis, statistical modeling, signal representation, and simulation

F. Meyer et al. CEOS’11, Fairbanks, AK 10

• Representative power spectrum parameters are derived from global ionospheric scintillation model WBMOD (WideBand MODel) – WBMOD capable to simulate statistical properties of scintillation effects on

user-defined system based on solar activity and system parameters

– Prediction of single-regime power spectrum parameters for wide range of systems and ionospheric conditions

Power Spectra

Predicting Ionospheric Power Spectra

E.J. Fremouw & J.A. Secan (1984): Modeling and Scientific Application of Scintillation Results, Radio Science, 19(3), pp 687 – 694.

F. Meyer et al. CEOS’11, Fairbanks, AK 11

• Workflow of the Ionospheric Phase Statistics Simulator (IP-STATS)

IP-STATS: A System for Describing and Simulating the Ionosphere

Power Spectra

Covariance Function

Covariance Matrix

Signal Simulation

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F. Meyer et al. CEOS’11, Fairbanks, AK 12

Potential Significance of IP-STATS

• Only dependent on quantifiable ionospheric and system parameters and no requirement for real observations

• Covariance Functions and Matrices: – Can support realistic statistical models to be used in parameter estimation

• Phase Simulations: – Sensitivity analysis of spaceborne radar systems – Useful in System design analysis – Selection of best suited radar system for an application

F. Meyer et al. CEOS’11, Fairbanks, AK 13

Geophysical Input Parameters

• Data point every 46 days

• Real PALSAR orbit and acquisition parameters

Simulating Ionospheric Conditions for a 10-Year Time Series of SAR Acquisitions over the North Slope of Alaska

Test Site

Statistical Ionospheric Descriptors

Sample Covariance Function Sample Covariance Matrix Sample Phase Simulation

13

F. Meyer et al. CEOS’11, Fairbanks, AK 14

Validation of IP-STATS in Polar Regions

• Real data processing:

• IP-STATS: • Ionospheric phase statistics parameter from SAR system parameters,

observation geometry, and solar parameters at acquisition time

• COMPARISON: • Validation for Auroral Zone conditions

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Σ Signal Variance σ(φ)

Covariance C(r)

Faraday Rotation from Quad-Pol SAR

F. Meyer et al. CEOS’11, Fairbanks, AK 15

Validation of IP-STATS in Polar Regions

• Validation of Signal Variance σ(φ):

15

At High Latitudes: Predicted and Measured Signal Variance Matches Well!!

F. Meyer et al. CEOS’11, Fairbanks, AK 16

• Validation of Covariance Function C(r) : • Measured Covariance: Isotropic signal assumed

• Simulated Covariance: Derived from ϕsim

Validation of IP-STATS in Polar Regions

16

At High Latitudes: Predicted and Measured Covariance Functions match reasonably well!

Orbit: 6305; Frame: 1330 Orbit: 6305; Frame: 1390

Problem: Isotropic signal assumed Most observed ionospheric signals are NOT isotropic

F. Meyer et al. CEOS’11, Fairbanks, AK 17

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Anisotropy Model in IP-STATS

• Current approach – extract information from WBMOD • Anisotropy approximated by “Correlation Ellipse”:

– Shape: axial ratios a and b (length of axes of correlation ellipse relative to vertical layer thickness thin layer approximation is used)

– Orientation: angle δ relative to local ionospheric L-shell

L-Shells

5 4 3

2

1.5

• a = 10; b = 1; δ = 0 Rod-like oriented roughly east-west

• a = 10; b = 10; δ = 0 Sheet-like

• Examples:

D.G. Singleton (1970): Dependence of Satellite Scintillations on Zenith Angle and Azimuth, Journal of Atmospheric and Terrestrial Physics, 32, pp 789 – 803.

F. Meyer et al. CEOS’11, Fairbanks, AK 18

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Anisotropy Model in IP-STATS

• a = 3; b = 1; δ = 0 Rod-like oriented roughly east-west

• April 1, 2007:

WBMOD Estimate

Observed SAR Phase distortions on April 1, 2007

F. Meyer et al. CEOS’11, Fairbanks, AK 19

• We have shown recent work:

– Advanced (combined) analytical correction methods show promise

– IP-STATS system models statistical properties of small scale ionospheric irregularities based on power spectra, covariance functions, and fractal dimensions

– First validations for Polar Regions show good performance of predicting variance and co-variance parameters

• Next steps: – Combination of more than two detection methods

– Further validation and incorporation of anisotropy in statistical model – Investigation of multi-scale power spectra for statistical model

Conclusions

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Open Three Year PhD Position starting fall 2011 / spring 2012 for a radar remote sensing research project at the Geophysical

Institute of the University of Alaska Fairbanks on

Theoretical Investigations into the Impact and Mitigation of Ionospheric Effects on Low-Frequency SAR and InSAR Data

Research Focus:

• Investigation of spatial and temporal properties of ionospheric effects in SAR data

• Development of statistical signal models

• Design of optimized methods for ionospheric correction

More information: Dr. Franz Meyer (fmeyer@gi.alaska.edu) and at: www.insar.alaska.edu

F. Meyer et al. CEOS’11, Fairbanks, AK 21

• Funding was provided by: – NASA EPSCoR Research Initiation Grant “Structural and Statistical

Properties of Ionospheric Effects in Space‐based L‐Band SAR Data” – NASA ROSES 2009 “Remote Sensing Theory” Grant “Collaborative

Research: Theoretical Investigations into the Impact and Mitigation of Ionospheric Effects on Low-Frequency SAR and InSAR”

• The ionospheric model WBMOD was provided by Northwest Research

Associates (NWRA)

• ALOS PALSAR data were provided by the Alaska Satellite Facility (ASF) and the Japanese Aerospace Exploration Agency (JAXA)

Acknowledgments:

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