A STATISTICAL MODEL OF IONOSPHERIC SIGNALS IN LOW-FREQUENCY SAR DATA

1. A STATISTICAL MODEL OF IONOSPHERIC SIGNALS IN LOW-FREQUENCY SAR DATA F.J Meyer1) 2), B. Watkins3) 1)Earth & Planetary Remote Sensing, University of Alaska Fairbanks 2)Alaska Satellite Facility (ASF) 3)Space Physics and Aeronomy, University of Alaska Fairbanks Collaborating Organizations:

2. Ionospheric Artifacts in Radar DataWhat Do They Look Like? Equatorial Regions Phase Distortions Polar Regions 2

3. -7 g [dB] -9 -11 5000 10000 15000 Distance along profile [m] Ionospheric Artifacts in Radar DataWhat Do They Look Like? Image Distortions Rainforest, Brazil South-East Asia

4. Ionospheric Distortions – How to Fix Them? • Signal Correction through Model Inversion: TEC = Total Electron Content of Ionosphere Phase Distortions Image Distortions Measure these! Invert for these! → Image correction & creation of ionospheric maps • Statistical Modeling • If mathematical modeling fails, statistical modeling mitigates effects on final target parameters • Realistic modeling of the accuracy and correlation of data

5. Power Law Model of Ionospheric Turbulence • Most small scale ionospheric turbulence 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

6. Power Law Model of Ionospheric Turbulence • On the convenience of power spectra: • Power Law models can be converted to covariance functions through cosine Fourier Transformation • Spectral slopes can be converted to fractal dimensions D → Basis for signal analysis, statistical modeling, signal representation, and simulation

7. Predicting Ionospheric Power Spectra • Representative power spectrum parameters are derived from global ionospheric scintillation model WBMOD (WideBand MODel) • WBMOD capable to simulate scintillation effects on user-defined system based on solar activity and system parameters • Prediction of power spectrum parameter for wide range of systems and ionospheric conditions Power Spectra

8. IP-STATS: A System for Describing and Simulating the Ionosphere • Workflow of the Ionospheric Phase Statistics Simulator (IP-STATS) Power Spectra Signal Simulation Covariance Matrix Covariance Function 8

9. Relationship between Power Spectrum, Covariance Matrix, and Simulated Phase Screen Spectral power: 2.9 rad2; Spectral Slope: 2.7 Spectral power: 2.9 rad2; Spectral Slope: 3.7 Covariance Matrix Covariance Matrix Location: Alaska Date: 4/1/07 Phase Simulation Phase Simulation 9

10. Significance • 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

11. Simulating Ionospheric Conditions for a 10-Year Time Series of SAR Acquisitions over the North Slope of Alaska • Data point every 46 days • Real PALSAR orbit and acquisition parameters Statistical Ionospheric Descriptors Test Site Geophysical Input Parameters Sample Covariance Function Sample Covariance Matrix Sample Phase Simulation 11

12. 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 Signal Variance s(f) Faraday Rotation from Full-Pol SAR S CovarianceC(r) 12

13. Validation of IP-STATS in Polar Regions • Validation of Signal Variances(f): Model Prediction Case Study 1: Turbulent Ionosphere Measured Signal Variance Case Study 2: Quiet Ionosphere At High Latitudes:Predicted and Measured Signal Variance Matches Well!! 13

14. Validation of IP-STATS in Polar Regions • Validation of Covariance FunctionC(r) : • Measured Covariance: Isotropic signal assumed • Simulated Covariance: Derived from jsim Orbit: 6305; Frame: 1330 Orbit: 6305; Frame: 1390 At High Latitudes: Predicted and Measured Covariance Functions match reasonably well! 14

15. Conclusions • Spaceborne imaging radars are affected by the ionosphere, in particular at times of high ionospheric turbulence • Small scale ionospheric turbulence can be modeled statistically using power spectra, covariance functions, and fractal dimensions • IP-STATS, a system for predicting statistical properties of ionospheric phase delay signals was presented • First validations for Polar Regions show good performance of predicting variance and co-variance parameters • Further validation is required, and anisotropy needs to be incorporated PALSAR Interferogram Amazon area, Ionospheric Disturbances 15

16. Acknowledgments: • 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) PALSAR Interferogram Amazon area, Ionospheric Disturbances 16

17. 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