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

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.

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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 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.

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 = Isca+Icor-Q2

• Fast correction to standard scalar code

• Exact through second order

• Simple model, easily implemented

• Supports analytic Jacobians

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 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

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OCO Spectroscopy

O2 A bandClouds/Aerosols, Surface

Pressure

“strong” CO2 bandClouds/Aerosols, H2O,

Temperature

“weak” CO2 bandColumn CO2

• Column-integrated CO2 abundance => Maximum contribution from surface

• High resolution spectroscopic measurements of reflected sunlight in near IR CO2 and O2 bands

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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

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: 2.06 µm CO2 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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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)

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

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Residuals: Best Case Scenario (2.06 µm CO2 Band)

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

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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)

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

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

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

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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%

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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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Further Work

• Glint viewing over ocean

• Spherical geometry

• Analytic computation of weighting functions

• Spectral binning

• Other Trace Gas Retrievals (SCIAMACHY/GOME/…)

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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 .