Polarization Vijay Natraj

1 of 100, L2 Peer Review, 3/24/2006

Level 2 Algorithm Peer Review

Polarization

Vijay Natraj

2 of 100, L2 Peer Review, 3/24/2006


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 XCO2 if unaccounted for.

• The OCO instrument measures only one component of polarization.

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Polarization in the O2 A Band

continuum

line core

gas absorption od ~ 1

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

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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.

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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

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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

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Forward Model Radiance Errors: O2 A Band

Asterisks refer to different geometries; The red triangles refer to OCO nadir viewing geometry.

Rayleigh Aerosol OD = 0.01 Aerosol OD = 0.1

Increasing Surface Albedo

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Forward Model Radiance Errors: 1.61 µm CO2 Band




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Forward Model Radiance Errors: 2.06 µm CO2 Band




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Residuals: Best Case Scenario (O2 A Band)

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

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Residuals: Best Case Scenario (1.61 µm CO2 Band)


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Residuals: Best Case Scenario (2.06 µm CO2 Band)


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Residuals: Worst-Case Scenario (O2 A Band)

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

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Residuals: Worst-Case Scenario (1.61 µm CO2 Band)


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Residuals: Worst-Case Scenario (2.06 µm CO2 Band)


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Timing Results: No Aerosol

O2 A Band 1.61 µm CO2 Band 2.06 µm CO2 Band

Vector 51609 s 22724 s 17686 s

Scalar 1434 s 627 s 509 s

Onescat 4 s 2 s 1.5 s

Twoscat 1960 s 856 s 656 s

16 half-space streams for Gaussian quadrature

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Timing Results: Aerosol Present

O2 A Band 1.61 µm CO2 Band 2.06 µm CO2 Band

Vector 401581 s 176730 s 119845 s

Scalar 7781 s 3545 s 2438 s

Onescat 102 s 23 s 15 s

Twoscat 4234 s 1678 s 1072 s

2 scat approx. adds only 50% to scalar calculation (for simulating 45 geometries). For OCO retrievals, overhead is expected to be around 10%.

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Linear Error Analysis

G001_A001 G001_A01 G01_A001 G01_A01 G03_A001 G03_A01

Noise (ppm)

5.483 5.856 1.292 1.299 0.591 0.611

Smoothing

(ppm)

6.146 6.131 0.766 0.896 0.404 0.421

Polarization

(ppm)

0.0006 0.458 0.003 0.076 0.007 0.016

• 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)

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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

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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 .

Polarization Vijay Natraj

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