1. Page 1 1 of 100, L2 Peer Review, 3/24/2006 Level 2 Algorithm Peer Review Polarization Vijay Natraj

2. Page 2 2 of 100, L2 Peer Review, 3/24/2006 Level 2 Algorithm Peer Review Importance of Polarization Polarization is a result of scattering. The Earth’s atmosphere contains molecules, aerosols and clouds, all of which contribute to scattering. Surfaces can also polarize, in some cases significantly (e.g., ocean). Polarization depends on solar and viewing angles and will therefore introduce spatial biases in X CO2 if unaccounted for. The OCO instrument measures only one component of polarization.

3. Page 3 3 of 100, L2 Peer Review, 3/24/2006 Level 2 Algorithm Peer Review Polarization in the O 2 A Band continuum line core gas absorption od ~ 1 SZA = 10° (solid); 40° (dotted); 70° (dashed)

4. Page 4 4 of 100, L2 Peer Review, 3/24/2006 Level 2 Algorithm Peer Review Proposed Solution: Two Orders of Scattering Approximation Full multiple-scattering vector ARTM codes (e.g. VLIDORT) are too slow to meet large-scale OCO processing requirements. Scalar computation causes two kinds of errors. –polarized component of the Stokes vector is neglected. –correction to intensity due to polarization is neglected. Major contribution to polarization comes from first few orders of scattering (multiple scattering is depolarizing). Single scattering does not account for the correction to intensity due to polarization.

5. Page 5 5 of 100, L2 Peer Review, 3/24/2006 Level 2 Algorithm Peer Review Polarization Approximation Overview X CO2 retrievals will only be applied to optically thin scattering (τ<0.3). Intensity will still be calculated with full multiple scattering scalar model. S = I sca +I cor -Q 2 Fast correction to standard scalar code Exact through second order Simple model, easily implemented Supports analytic Jacobians

6. Page 6 6 of 100, L2 Peer Review, 3/24/2006 Level 2 Algorithm Peer Review Scenarios for Testing Proposed Method SZA: 10°, 40°, 70° VZA: 0° (OCO nadir mode), 35°, 70° Azimuth: 0° (OCO nadir mode), 45°, 90°, 135°, 180° Surface Albedo: 0.01, 0.1, 0.3 Aerosol OD: 0 (Rayleigh), 0.01, 0.1 Dusty continental aerosol (Kahn et al., JGR 106(D16), pp. 18219- 18238, 2001) 45 geometries 9 scenarios

7. Page 7 7 of 100, L2 Peer Review, 3/24/2006 Level 2 Algorithm Peer Review Forward Model Radiance Errors: O 2 A Band Asterisks refer to different geometries; The red triangles refer to OCO nadir viewing geometry. RayleighAerosol OD = 0.01Aerosol OD = 0.1 Increasing Surface Albedo

8. Page 8 8 of 100, L2 Peer Review, 3/24/2006 Level 2 Algorithm Peer Review Forward Model Radiance Errors: 1.61 µm CO 2 Band Asterisks refer to different geometries; The red triangles refer to OCO nadir viewing geometry. RayleighAerosol OD = 0.01Aerosol OD = 0.1 Increasing Surface Albedo

9. Page 9 9 of 100, L2 Peer Review, 3/24/2006 Level 2 Algorithm Peer Review Forward Model Radiance Errors: 2.06 µm CO 2 Band Asterisks refer to different geometries; The red triangles refer to OCO nadir viewing geometry. RayleighAerosol OD = 0.01Aerosol OD = 0.1 Increasing Surface Albedo

10. Page 10 10 of 100, L2 Peer Review, 3/24/2006 Level 2 Algorithm Peer Review Residuals: Best Case Scenario (O 2 A Band) SZA = 10°; VZA = 0°; Azimuth = 0°; Surface Albedo = 0.3; No Aerosol

11. Page 11 11 of 100, L2 Peer Review, 3/24/2006 Level 2 Algorithm Peer Review Residuals: Best Case Scenario (1.61 µm CO 2 Band) SZA = 10°; VZA = 0°; Azimuth = 0°; Surface Albedo = 0.3; No Aerosol

12. Page 12 12 of 100, L2 Peer Review, 3/24/2006 Level 2 Algorithm Peer Review Residuals: Best Case Scenario (2.06 µm CO 2 Band) SZA = 10°; VZA = 0°; Azimuth = 0°; Surface Albedo = 0.3; No Aerosol

13. Page 13 13 of 100, L2 Peer Review, 3/24/2006 Level 2 Algorithm Peer Review Residuals: Worst-Case Scenario (O 2 A Band) SZA = 70°; VZA = 70°; Azimuth = 90°; Surface Albedo =0.01; Aerosol OD = 0.1

14. Page 14 14 of 100, L2 Peer Review, 3/24/2006 Level 2 Algorithm Peer Review Residuals: Worst-Case Scenario (1.61 µm CO 2 Band) SZA = 70°; VZA = 70°; Azimuth = 90°; Surface Albedo =0.01; Aerosol OD = 0.1

15. Page 15 15 of 100, L2 Peer Review, 3/24/2006 Level 2 Algorithm Peer Review Residuals: Worst-Case Scenario (2.06 µm CO 2 Band) SZA = 70°; VZA = 70°; Azimuth = 90°; Surface Albedo =0.01; Aerosol OD = 0.1

16. Page 16 16 of 100, L2 Peer Review, 3/24/2006 Level 2 Algorithm Peer Review Timing Results: No Aerosol O 2 A Band1.61 µm CO 2 Band2.06 µm CO 2 Band Vector51609 s22724 s17686 s Scalar1434 s627 s509 s Onescat4 s2 s1.5 s Twoscat1960 s856 s656 s 16 half-space streams for Gaussian quadrature

17. Page 17 17 of 100, L2 Peer Review, 3/24/2006 Level 2 Algorithm Peer Review Timing Results: Aerosol Present O 2 A Band1.61 µm CO 2 Band2.06 µm CO 2 Band Vector401581 s176730 s119845 s Scalar7781 s3545 s2438 s Onescat102 s23 s15 s Twoscat4234 s1678 s1072 s 2 scat approx. adds only 50% to scalar calculation (for simulating 45 geometries). For OCO retrievals, overhead is expected to be around 10%.

18. Page 18 18 of 100, L2 Peer Review, 3/24/2006 Level 2 Algorithm Peer Review Linear Error Analysis G001_A001G001_A01G01_A001G01_A01G03_A001G03_A01 Noise (ppm) 5.4835.8561.2921.2990.5910.611 Smoothing (ppm) 6.1466.1310.7660.8960.4040.421 Polarization (ppm) 0.00060.4580.0030.0760.0070.016 6 scenarios considered –Surface Albedo: 0.01, 0.1, 0.3 –Aerosol OD: 0.01, 0.1 SZA = 45°; VZA = 0°; Azimuth = 0° (OCO Nadir Mode) 8 half-space streams, 11 layers Number of spectral points: 8307 (O2 A band), 3334 (CO2 bands)

19. Page 19 19 of 100, L2 Peer Review, 3/24/2006 Level 2 Algorithm Peer Review Status and Implementation Schedule Offline sensitivity tests for nadir viewing over Lambertian surface: Done Implementation in OCO Level 2 Algorithm: May Testing and implementation of two orders of scattering approximation for glint viewing over ocean: June Modification for spherical geometry, calculation of analytic weighting functions, spectral binning: December

20. Page 20 20 of 100, L2 Peer Review, 3/24/2006 Level 2 Algorithm Peer Review Summary Ignoring polarization could lead to significant (as high as 10 ppm) errors in X CO2 retrievals. A two orders of scattering approach to account for the polarization works very well, giving X CO2 errors that are much smaller than other biases. The approach is two orders of magnitude faster than a full vector calculation. The additional overhead is in the range of 10% of the scalar computation.