1. Page 1 1 of 21, 28th Review of Atmospheric Transmission Models, 6/14/2006 A Two Orders of Scattering Approach to Account for Polarization in Near Infrared Retrievals Vijay Natraj, Hartmut Bösch and Yuk L. Yung

2. Page 2 2 of 21, 28th Review of Atmospheric Transmission Models, 6/14/2006 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 retrieved trace gas column densities if unaccounted for. The satellite instrument could be sensitive to polarization.

3. Page 3 3 of 21, 28th Review of Atmospheric Transmission Models, 6/14/2006 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 21, 28th Review of Atmospheric Transmission Models, 6/14/2006 Proposed Solution: Two Orders of Scattering Approximation Full multiple-scattering vector ARTM codes (e.g. VLIDORT) are too slow to meet large-scale operational 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 21, 28th Review of Atmospheric Transmission Models, 6/14/2006 Polarization Approximation Overview 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 21, 28th Review of Atmospheric Transmission Models, 6/14/2006 Case Study: Orbiting Carbon Observatory (OCO) Mission First global, space-based observations of atmospheric CO 2 –high accuracy, resolution and coverage –geographic distribution of CO 2 sources and sinks and variability High resolution spectroscopic measurements of reflected sunlight – NIR CO 2 and O 2 bands Remote sensing retrieval algorithms –estimates of column-averaged CO 2 dry air mole fraction (X CO2 ) –accuracies near 0.3% (1 ppm) Chemical transport models –spatial distribution of CO 2 sources and sinks

7. Page 7 7 of 21, 28th Review of Atmospheric Transmission Models, 6/14/2006 OCO Spectroscopy O 2 A band Clouds/Aerosols, Surface Pressure “strong” CO 2 band Clouds/Aerosols, H 2 O, Temperature “weak” CO 2 band Column CO 2 Column-integrated CO 2 abundance => Maximum contribution from surface High resolution spectroscopic measurements of reflected sunlight in near IR CO 2 and O 2 bands

8. Page 8 8 of 21, 28th Review of Atmospheric Transmission Models, 6/14/2006 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

9. Page 9 9 of 21, 28th Review of Atmospheric Transmission Models, 6/14/2006 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

10. Page 10 10 of 21, 28th Review of Atmospheric Transmission Models, 6/14/2006 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

11. Page 11 11 of 21, 28th Review of Atmospheric Transmission Models, 6/14/2006 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

12. Page 12 12 of 21, 28th Review of Atmospheric Transmission Models, 6/14/2006 Residuals: Best Case Scenario (O 2 A Band) SZA = 10°; VZA = 0°; Azimuth = 0°; Surface Albedo = 0.3; No Aerosol

13. Page 13 13 of 21, 28th Review of Atmospheric Transmission Models, 6/14/2006 Residuals: Best Case Scenario (1.61 µm CO 2 Band) SZA = 10°; VZA = 0°; Azimuth = 0°; Surface Albedo = 0.3; No Aerosol

14. Page 14 14 of 21, 28th Review of Atmospheric Transmission Models, 6/14/2006 Residuals: Best Case Scenario (2.06 µm CO 2 Band) SZA = 10°; VZA = 0°; Azimuth = 0°; Surface Albedo = 0.3; No Aerosol

15. Page 15 15 of 21, 28th Review of Atmospheric Transmission Models, 6/14/2006 Residuals: Worst-Case Scenario (O 2 A Band) SZA = 70°; VZA = 70°; Azimuth = 90°; Surface Albedo =0.01; Aerosol OD = 0.1

16. Page 16 16 of 21, 28th Review of Atmospheric Transmission Models, 6/14/2006 Residuals: Worst-Case Scenario (1.61 µm CO 2 Band) SZA = 70°; VZA = 70°; Azimuth = 90°; Surface Albedo =0.01; Aerosol OD = 0.1

17. Page 17 17 of 21, 28th Review of Atmospheric Transmission Models, 6/14/2006 Residuals: Worst-Case Scenario (2.06 µm CO 2 Band) SZA = 70°; VZA = 70°; Azimuth = 90°; Surface Albedo =0.01; Aerosol OD = 0.1

18. Page 18 18 of 21, 28th Review of Atmospheric Transmission Models, 6/14/2006 Timing Results Twoscat two orders of magnitude faster than vector calculation 50% overhead to scalar calculation VLIDORT optimized for multiple geometry calculations For real retrievals, overhead expected to be ~ 10%

19. Page 19 19 of 21, 28th Review of Atmospheric Transmission Models, 6/14/2006 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)

20. Page 20 20 of 21, 28th Review of Atmospheric Transmission Models, 6/14/2006 Further Work Glint viewing over ocean Spherical geometry Analytic computation of weighting functions Spectral binning Other Trace Gas Retrievals (SCIAMACHY/GOME/…)

21. Page 21 21 of 21, 28th Review of Atmospheric Transmission Models, 6/14/2006 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.