Page 1 1 of 100, L2 Peer Review, 3/24/2006 Level 2 Algorithm Peer Review Polarization Vijay Natraj
Dec 21, 2015
Page 1 1 of 100, L2 Peer Review, 3/24/2006
Level 2 Algorithm Peer Review
Polarization
Vijay Natraj
Page 2 2 of 100, L2 Peer Review, 3/24/2006
Level 2 Algorithm Peer Review
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.
Page 3 3 of 100, L2 Peer Review, 3/24/2006
Level 2 Algorithm Peer Review
Polarization in the O2 A Band
continuum
line core
gas absorption od ~ 1
SZA = 10° (solid); 40° (dotted); 70° (dashed)
Page 4 4 of 100, L2 Peer Review, 3/24/2006
Level 2 Algorithm Peer Review
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.
Page 5 5 of 100, L2 Peer Review, 3/24/2006
Level 2 Algorithm Peer Review
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
Page 6 6 of 100, L2 Peer Review, 3/24/2006
Level 2 Algorithm Peer Review
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
Page 7 7 of 100, L2 Peer Review, 3/24/2006
Level 2 Algorithm Peer Review
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
Page 8 8 of 100, L2 Peer Review, 3/24/2006
Level 2 Algorithm Peer Review
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
Page 9 9 of 100, L2 Peer Review, 3/24/2006
Level 2 Algorithm Peer Review
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
Page 10 10 of 100, L2 Peer Review, 3/24/2006
Level 2 Algorithm Peer Review
Residuals: Best Case Scenario (O2 A Band)
SZA = 10°; VZA = 0°; Azimuth = 0°; Surface Albedo = 0.3; No Aerosol
Page 11 11 of 100, L2 Peer Review, 3/24/2006
Level 2 Algorithm Peer Review
Residuals: Best Case Scenario (1.61 µm CO2 Band)
SZA = 10°; VZA = 0°; Azimuth = 0°; Surface Albedo = 0.3; No Aerosol
Page 12 12 of 100, L2 Peer Review, 3/24/2006
Level 2 Algorithm Peer Review
Residuals: Best Case Scenario (2.06 µm CO2 Band)
SZA = 10°; VZA = 0°; Azimuth = 0°; Surface Albedo = 0.3; No Aerosol
Page 13 13 of 100, L2 Peer Review, 3/24/2006
Level 2 Algorithm Peer Review
Residuals: Worst-Case Scenario (O2 A Band)
SZA = 70°; VZA = 70°; Azimuth = 90°; Surface Albedo =0.01; Aerosol OD = 0.1
Page 14 14 of 100, L2 Peer Review, 3/24/2006
Level 2 Algorithm Peer Review
Residuals: Worst-Case Scenario (1.61 µm CO2 Band)
SZA = 70°; VZA = 70°; Azimuth = 90°; Surface Albedo =0.01; Aerosol OD = 0.1
Page 15 15 of 100, L2 Peer Review, 3/24/2006
Level 2 Algorithm Peer Review
Residuals: Worst-Case Scenario (2.06 µm CO2 Band)
SZA = 70°; VZA = 70°; Azimuth = 90°; Surface Albedo =0.01; Aerosol OD = 0.1
Page 16 16 of 100, L2 Peer Review, 3/24/2006
Level 2 Algorithm Peer Review
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
Page 17 17 of 100, L2 Peer Review, 3/24/2006
Level 2 Algorithm Peer Review
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%.
Page 18 18 of 100, L2 Peer Review, 3/24/2006
Level 2 Algorithm Peer Review
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)
Page 19 19 of 100, L2 Peer Review, 3/24/2006
Level 2 Algorithm Peer Review
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
Page 20 20 of 100, L2 Peer Review, 3/24/2006
Level 2 Algorithm Peer Review
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 .