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Polarization Vijay Natraj. 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).

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Polarization

Vijay Natraj


Importance of polarization
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 XCO2 if unaccounted for.

  • The OCO instrument measures only one component of polarization.


Polarization in the o 2 a band
Polarization in the O2A Band

SZA = 10° (solid); 40° (dotted); 70° (dashed)

continuum

gas absorption od ~ 1

line core


Proposed solution two orders of scattering approximation
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.


Polarization approximation overview
Polarization Approximation Overview

  • XCO2 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


Scenarios for testing proposed method

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)


Forward model radiance errors o 2 a band

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.


Forward model radiance errors 1 61 m co 2 band

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.


Forward model radiance errors 2 06 m co 2 band

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.


Residuals best case scenario o 2 a band
Residuals: Best Case Scenario (O2A Band)

SZA = 10°; VZA = 0°; Azimuth = 0°; Surface Albedo = 0.3; No Aerosol


Residuals best case scenario 1 61 m co 2 band
Residuals: Best Case Scenario (1.61 µm CO2 Band)

SZA = 10°; VZA = 0°; Azimuth = 0°; Surface Albedo = 0.3; No Aerosol


Residuals best case scenario 2 06 m co 2 band
Residuals: Best Case Scenario (2.06 µm CO2 Band)

SZA = 10°; VZA = 0°; Azimuth = 0°; Surface Albedo = 0.3; No Aerosol


Residuals worst case scenario o 2 a band
Residuals: Worst-Case Scenario (O2A Band)

SZA = 70°; VZA = 70°; Azimuth = 90°; Surface Albedo =0.01; Aerosol OD = 0.1


Residuals worst case scenario 1 61 m co 2 band
Residuals: Worst-Case Scenario (1.61 µm CO2 Band)

SZA = 70°; VZA = 70°; Azimuth = 90°; Surface Albedo =0.01; Aerosol OD = 0.1


Residuals worst case scenario 2 06 m co 2 band
Residuals: Worst-Case Scenario (2.06 µm CO2 Band)

SZA = 70°; VZA = 70°; Azimuth = 90°; Surface Albedo =0.01; Aerosol OD = 0.1


Timing results no aerosol
Timing Results: No Aerosol

16 half-space streams for Gaussian quadrature


Timing results aerosol present
Timing Results: Aerosol Present

2 scat approx. adds only 50% to scalar calculation (for simulating 45 geometries).

For OCO retrievals, overhead is expected to be around 10%.


Linear error analysis
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)


Status and implementation schedule
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


Summary
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 .


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