1. CONICAL ELECTROMAGNETIC WAVES DIFFRACTION FROM SASTRUGI TYPE SURFACES OF LAYERED SNOW DUNES ON GREENLAND ICE SHEETS IN PASSIVE MICROWAVE REMOTE SENSING Wenmo Chang Leung Tsang Department of Electrical Engineering University of Washington

2. Outline Motivation – Observations in passive microwave remote sensing – Large 3 rd and 4 th Stokes parameters Scattering physics – Rough surfaces : Large slope and large height – Total internal reflection in layered media Electromagnetic methodology – Maxwell equations for rough surface – Radiative transfer theory for layered media Results and discussion

3. Greenland’s snow profile Wind induced – Sastrugi surface Large RMS height – 20 cm – 7 wavelengths @ 10.7 GHz – 12 wavelengths @ 18.7 GHz Large slope Photo courtesy of Quintin Lake www.quintinlake.com

4. Four Stokes parameters in passive microwave remote sensing Microwave polarimetric signatures

5. Observations WindSat data over the Summit site Large 3 rd and 4 th Stokes parameters Up to 15 K for 10.7 GHz, 18.7 GHz and 37 GHz Li, L.; Gaiser, P.; Twarog, E.; Long, D.; Albert, M.;, "WindSat Polarimetric View of Greenland," Geoscience and Remote Sensing Symposium, 2006. IGARSS 2006. IEEE International Conference on, vol., no., pp.3824-3827, July 31 2006-Aug. 4 2006

6. Outline Motivations Scattering physics Electromagnetic methodology Results and discussion

7. Physical model Large height and large slope coupled with subsurface total internal reflection 1-D roughness: azimuthal asymmetry

8. Computer generation of Sastrugi surfaces Statistical data needed for Sastrugi profile Photo courtesy of Quintin Lake www.quintinlake.com

9. Large angle transmission 20° 15° 60.2° Incident angle=55° Total internal reflection ε 1 =1.8, dense snow ε 2 =1.3, less dense snow ε 0 =1, air Critical angle=58.2° Large slope Phase shifts of v- and h-pol are different Non-zero U and V are generated

10. Scattering physics: results based on Maxwell equations Air to snow – Ɵ i =55 deg – ɸ i =30 deg – ε r snow =1.8 – ε r under =1.3 Two peaks in transmission Specular transmission angle in snow: 37.6 deg A secondary peak: around 60.4 deg Critical angle between snow and underlying layers: 58.2 deg The 60.4-deg transmission will have total internal reflection

11. Outline Motivations Scattering physics Electromagnetic methodology Results and discussion

12. Challenges in electromagnetic model Height of profile – Past: small to moderate height – New: large height up to 7 wavelengths Fluctuations of microwave signatures in simulations – Past coherent 3-D MoM (Tsang et al., 2008) Fluctuations due to roughness Fluctuations due to coherent multiple reflections of layering – Present model has less fluctuations

13. Present hybrid model Previous 3D MoM coherent model (Tsang et al., 2008) for comparisons (1) Maxwell equations for rough surface scattering to numerically derive rough surface’s bistatic coefficients (2) Radiative transfer theory for layered media Combine (1) and (2) : rough surface’s bistatic coefficients from Maxwell equations used as boundary conditions for radiative transfer

14. Rough surface’s boundary conditions Numerical methods to solve Maxwell equations (integral equations) – Conical diffraction – Field components obtained Four types of surface unknownsContinuity boundary conditions

15. Numerical solutions Numerical methods to solve Maxwell equations (integral equations) – Conical diffraction – Field components obtained

16. Numerical requirements Physical Parameters – RMS height: 20 cm 7.1 wavelengths @ 10.7 GHz 12.4 wavelengths @ 18.7 GHz Numerical parameters – Surface length: 4 m 142 wavelengths @ 10.7 GHz 249 wavelengths @ 18.7 GHz Number of surface unknowns: up to 20,000 Linear solver – Direct solver based on LU decomposition – In the future: multi-level UV

17. Bistatic coefficients Bistatic scattering and transmission coefficients

18. Boundary conditions for radiative transfer ‘Boundary condition’ for radiative transfer of layered media Multiple reflection – Iterative scheme Solid angle integral Matrices formed by the numerical bistatic coefficients At upper rough boundary At lower flat subsurface

19. Periodic profile Single realization Hybrid model compared with coherent 3-D MoM Geometry

20. Outline Motivations Scattering physics Electromagnetic methodology Results and discussion

21. Sastrugi surface at 10.7 GHz Averaging over 5 realizations Geometry 3 rd and 4 th Stokes parameters up to -15 K / +10 K

22. Sastrugi surface at 18.7 GHz Averaging over 5 realizations 3 rd and 4 th Stokes parameters up to -2 K / +10 K Geometry

23. Summary Hybrid model – 2-D MoM for rough surface – Radiative transfer for layer media – Combine rough surface boundary conditions with radiative transfer Numerical results of the model – Large 3 rd and 4 th Stokes parameters up to -15 K / 10 K – Less fluctuations – Both 10.7 GHz and 18.7 GHz show up to 15K

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