A Two Orders of Scattering Approach to Account for Polarization in Near Infrared Retrievals

1. A Two Orders of Scattering Approach to Account for Polarization in Near Infrared Retrievals Vijay Natraj, Hartmut Bösch and Yuk L. Yung

2. 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. Polarization in the O2A Band SZA = 10° (solid); 40° (dotted); 70° (dashed) continuum gas absorption od ~ 1 line core

4. 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. 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 = Isca+Icor-Q2 • Fast correction to standard scalar code • Exact through second order • Simple model, easily implemented • Supports analytic Jacobians

6. Case Study: Orbiting Carbon Observatory (OCO) Mission • First global, space-based observations of atmospheric CO2 • high accuracy, resolution and coverage • geographic distribution of CO2 sources and sinks and variability • High resolution spectroscopic measurements of reflected sunlight • NIR CO2 and O2 bands • Remote sensing retrieval algorithms • estimates of column-averaged CO2 dry air mole fraction (XCO2) • accuracies near 0.3% (1 ppm) • Chemical transport models • spatial distribution of CO2 sources and sinks

7. OCO Spectroscopy • Column-integrated CO2 abundance => Maximum contribution from surface • High resolution spectroscopic measurements of reflected sunlight in near IR CO2 and O2 bands O2A band Clouds/Aerosols, Surface Pressure “weak” CO2 band Column CO2 “strong” CO2 band Clouds/Aerosols, H2O, Temperature

8. 45 geometries 9 scenarios 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)

9. Rayleigh Aerosol OD = 0.01 Aerosol OD = 0.1 Increasing Surface Albedo Forward Model Radiance Errors: O2A Band Asterisks refer to different geometries; The red triangles refer to OCO nadir viewing geometry.

10. Rayleigh Aerosol OD = 0.01 Aerosol OD = 0.1 Increasing Surface Albedo Forward Model Radiance Errors: 1.61 µm CO2 Band Asterisks refer to different geometries; The red triangles refer to OCO nadir viewing geometry.

11. Rayleigh Aerosol OD = 0.01 Aerosol OD = 0.1 Increasing Surface Albedo Forward Model Radiance Errors: 2.06 µm CO2 Band Asterisks refer to different geometries; The red triangles refer to OCO nadir viewing geometry.

12. Residuals: Best Case Scenario (O2A Band) SZA = 10°; VZA = 0°; Azimuth = 0°; Surface Albedo = 0.3; No Aerosol

13. Residuals: Best Case Scenario (1.61 µm CO2 Band) SZA = 10°; VZA = 0°; Azimuth = 0°; Surface Albedo = 0.3; No Aerosol

14. Residuals: Best Case Scenario (2.06 µm CO2 Band) SZA = 10°; VZA = 0°; Azimuth = 0°; Surface Albedo = 0.3; No Aerosol

15. Residuals: Worst-Case Scenario (O2A Band) SZA = 70°; VZA = 70°; Azimuth = 90°; Surface Albedo =0.01; Aerosol OD = 0.1

16. Residuals: Worst-Case Scenario (1.61 µm CO2 Band) SZA = 70°; VZA = 70°; Azimuth = 90°; Surface Albedo =0.01; Aerosol OD = 0.1

17. Residuals: Worst-Case Scenario (2.06 µm CO2 Band) SZA = 70°; VZA = 70°; Azimuth = 90°; Surface Albedo =0.01; Aerosol OD = 0.1

18. 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. Linear Error Analysis • 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. Further Work • Glint viewing over ocean • Spherical geometry • Analytic computation of weighting functions • Spectral binning • Other Trace Gas Retrievals (SCIAMACHY/GOME/…)

21. Summary • Ignoring polarization could lead to significant (as high as 10 ppm) errors in XCO2 retrievals. • A two orders of scattering approach to account for the polarization works very well, giving XCO2 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 .