Wenmo Chang Leung Tsang Department of Electrical Engineering University of Washington

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 3rd and 4th 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 3rd and 4th 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 Incident angle=55° ε0=1, air 20° 60.2° Large slope ε1=1.8, dense snow Critical angle=58.2° 15° ε2=1.3, less dense snow • Phase shifts of v- and h-pol are different • Non-zero U and V are generated Total internal reflection

10. Scattering physics: results based on Maxwell equations • Air to snow • Ɵi=55 deg • ɸi=30 deg • εrsnow =1.8 • εrunder =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 unknowns Continuity 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 At upper rough boundary At lower flat subsurface Matrices formed by the numerical bistatic coefficients

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

20. Outline • Motivations • Scattering physics • Electromagnetic methodology • Results and discussion

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

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

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 3rd and 4th Stokes parameters up to -15 K / 10 K • Less fluctuations • Both 10.7 GHz and 18.7 GHz show up to 15K

24. Thank You for Your Attention!