Abstract

We have extended the Wang–Gordon [Appl. Opt. 32, 4598–4609 (1993)] and Gordon–Zhang [Appl. Opt. 34, 5552–5555 (1995)] algorithms for retrieval of ω0 P(Θ, where ω0 is the aerosol single-scattering albedo and P(Θ) is the aerosol phase function for scattering through an angle Θ, from measurement of the radiances exiting the top and the bottom of the atmosphere over the ocean, to include polarization. This permits derivation of the P11(Θ) and P12(Θ) elements of the Mueller scattering phase matrix P(Θ) from measurement of the linear polarization portion of the Stokes vectors associated with the radiance exiting the top and the bottom of the atmosphere. Simulations show that good retrievals are possible for aerosol optical thicknesses as large as 2; however, the atmosphere is required to be horizontally homogeneous. We study the influence of the elements of P(Θ) that cannot be determined in this manner. It is shown that including surface measurements of the linear polarization of the sky radiance improves the estimation of the radiance simultaneously exiting the top of the atmosphere (TOA) and also allows reasonably accurate estimates of the TOA polarization. This is important for in-orbit calibration of ocean-color sensors.

© 1997 Optical Society of America

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References

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  1. M. Wang, H. R. Gordon, “Retrieval of the columnar aerosol phase function and single-scattering albedo from sky radiance over the ocean: simulations,” Appl. Opt. 32, 4598–4609 (1993).
    [CrossRef] [PubMed]
  2. H. R. Gordon, T. Zhang, “Columnar aerosol properties over oceans by combining surface and aircraft measurements: simulations,” Appl. Opt. 34, 5552–5555 (1995).
    [CrossRef] [PubMed]
  3. T. Zhang, H. R. Gordon, “Columnar aerosol properties over oceans by combining surface and aircraft measurements: sensitivity analysis,” Appl. Opt. 36, 2650–2662 (1997).
    [CrossRef] [PubMed]
  4. H. R. Gordon, T. Zhang, “How well can radiance reflected from the ocean-atmosphere system be predicted from measurements at the sea surface?” Appl. Opt. 35, 6527–6543 (1996).
    [CrossRef] [PubMed]
  5. H. R. Gordon, “A preliminary assessment of the Nimbus-7 CZCS atmospheric correction algorithm in a horizontally inhomogeneous atmosphere,” in Oceanography from Space, J. R. F. Gower, ed. (Plenum, New York, 1981) pp. 257–266.
    [CrossRef]
  6. H. R. Gordon, “Reduction of error introduced in the processing of coastal zone color scanner-type imagery resulting from sensor calibration and solar irradiance uncertainty,” Appl. Opt. 20, 207–210 (1981).
    [CrossRef] [PubMed]
  7. P. Koepke, “Vicarious satellite calibration in the solar spectral range by means of calculated radiances and its application to Meteosat,” Appl. Opt. 21, 2845–2854 (1982).
    [CrossRef] [PubMed]
  8. M. Viollier, “Radiance calibration of the Coastal Zone Color Scanner on Nimbus 7: a proposed adjustment,” Appl. Opt. 21, 1142–1145 (1982).
    [CrossRef] [PubMed]
  9. H. R. Gordon, D. K. Clark, J. W. Brown, O. B. Brown, R. H. Evans, W. W. Broenkow, “Phytoplankton pigment concentrations in the Middle Atlantic Bight: comparison of ship determinations and CZCS estimates,” Appl. Opt. 22, 20–36 (1983).
    [CrossRef] [PubMed]
  10. H. R. Gordon, J. W. Brown, O. B. Brown, R. H. Evans, D. K. Clark, “Nimbus 7 CZCS: reduction of its radiometric sensitivity with time,” Appl. Opt. 22, 3929–3931 (1983).
    [CrossRef] [PubMed]
  11. W. A. Hovis, J. S. Knoll, G. R. Smith, “Aircraft measurements for calibration of an orbiting spacecraft sensor,” Appl. Opt. 24, 407–410 (1985).
    [CrossRef] [PubMed]
  12. R. S. Fraser, Y. J. Kaufman, “Calibration of satellite sensors after launch,” Appl. Opt. 25, 1177–1185 (1986).
    [CrossRef] [PubMed]
  13. P. N. Slater, S. F. Biggar, R. G. Holm, R. D. Jackson, Y. Mao, M. S. Moran, J. M. Palmer, B. Yuan, “Reflectance- and radiance-based methods for the in-flight absolute calibration of multispectral sensors,” Remote Sensing Environ. 22, 11–37 (1987).
    [CrossRef]
  14. R. Frouin, C. Gautier, “Calibration of NOAA-7 AVHRR, GOES-5, and GOES-6 VISSR/VAS solar channels,” Remote Sensing Environ. 22, 73–101 (1987).
    [CrossRef]
  15. Y. J. Kaufman, B. N. Holben, “Calibration of the AVHRR visible and near-IR bands by atmospheric scattering, ocean glint, and desert reflection,” Int. J. Remote Sensing 14, 21–52 (1993).
    [CrossRef]
  16. S. F. Biggar, P. N. Slater, D. I. Gellman, “Uncertainties in the in-flight calibration of sensors with reference to measured ground sites in the 0.4 to 1.1 µm range,” Remote Sensing Environ. 48, 245–252 (1994).
    [CrossRef]
  17. P. Y. Deschamps, F. M. Bréon, M. Leroy, A. Podaire, A. Bricaud, J. C. Buriez, G. Sèze, “The POLDER mission: instrument characteristics and scientific objectives,” IEEE Trans. Geosci. Remote Sensing 32, 598–615 (1994).
    [CrossRef]
  18. Y. Sasano, E. V. Browell, “Light scattering characteristics of various aerosol types derived from multiple wavelength lidar observations,” Appl. Opt. 28, 1670–1679 (1989).
    [CrossRef] [PubMed]
  19. E. P. Shettle, R. W. Fenn, “Models for the aerosols of the lower atmosphere and the effects of humidity variations on their optical properties, (U.S. Air Force Geophysics Laboratory, Hanscomb Air Force Base, Mass. 01731, 1979).
  20. K. J. Voss, Y. Liu, “Polarized radiance distribution measurements of skylight. 1: system description and characterization,” Appl. Opt. 36, 0000–0000 (1997).
    [CrossRef]
  21. M. I. Mishchenko, L. D. Travis, “Light scattering by polydispersions of randomly oriented spheroids with sizes comparable to wavelengths of observation,” Appl. Opt. 33, 7206–7225 (1994).
    [CrossRef] [PubMed]

1997 (2)

T. Zhang, H. R. Gordon, “Columnar aerosol properties over oceans by combining surface and aircraft measurements: sensitivity analysis,” Appl. Opt. 36, 2650–2662 (1997).
[CrossRef] [PubMed]

K. J. Voss, Y. Liu, “Polarized radiance distribution measurements of skylight. 1: system description and characterization,” Appl. Opt. 36, 0000–0000 (1997).
[CrossRef]

1996 (1)

1995 (1)

1994 (3)

M. I. Mishchenko, L. D. Travis, “Light scattering by polydispersions of randomly oriented spheroids with sizes comparable to wavelengths of observation,” Appl. Opt. 33, 7206–7225 (1994).
[CrossRef] [PubMed]

S. F. Biggar, P. N. Slater, D. I. Gellman, “Uncertainties in the in-flight calibration of sensors with reference to measured ground sites in the 0.4 to 1.1 µm range,” Remote Sensing Environ. 48, 245–252 (1994).
[CrossRef]

P. Y. Deschamps, F. M. Bréon, M. Leroy, A. Podaire, A. Bricaud, J. C. Buriez, G. Sèze, “The POLDER mission: instrument characteristics and scientific objectives,” IEEE Trans. Geosci. Remote Sensing 32, 598–615 (1994).
[CrossRef]

1993 (2)

M. Wang, H. R. Gordon, “Retrieval of the columnar aerosol phase function and single-scattering albedo from sky radiance over the ocean: simulations,” Appl. Opt. 32, 4598–4609 (1993).
[CrossRef] [PubMed]

Y. J. Kaufman, B. N. Holben, “Calibration of the AVHRR visible and near-IR bands by atmospheric scattering, ocean glint, and desert reflection,” Int. J. Remote Sensing 14, 21–52 (1993).
[CrossRef]

1989 (1)

1987 (2)

P. N. Slater, S. F. Biggar, R. G. Holm, R. D. Jackson, Y. Mao, M. S. Moran, J. M. Palmer, B. Yuan, “Reflectance- and radiance-based methods for the in-flight absolute calibration of multispectral sensors,” Remote Sensing Environ. 22, 11–37 (1987).
[CrossRef]

R. Frouin, C. Gautier, “Calibration of NOAA-7 AVHRR, GOES-5, and GOES-6 VISSR/VAS solar channels,” Remote Sensing Environ. 22, 73–101 (1987).
[CrossRef]

1986 (1)

1985 (1)

1983 (2)

1982 (2)

1981 (1)

Biggar, S. F.

S. F. Biggar, P. N. Slater, D. I. Gellman, “Uncertainties in the in-flight calibration of sensors with reference to measured ground sites in the 0.4 to 1.1 µm range,” Remote Sensing Environ. 48, 245–252 (1994).
[CrossRef]

P. N. Slater, S. F. Biggar, R. G. Holm, R. D. Jackson, Y. Mao, M. S. Moran, J. M. Palmer, B. Yuan, “Reflectance- and radiance-based methods for the in-flight absolute calibration of multispectral sensors,” Remote Sensing Environ. 22, 11–37 (1987).
[CrossRef]

Bréon, F. M.

P. Y. Deschamps, F. M. Bréon, M. Leroy, A. Podaire, A. Bricaud, J. C. Buriez, G. Sèze, “The POLDER mission: instrument characteristics and scientific objectives,” IEEE Trans. Geosci. Remote Sensing 32, 598–615 (1994).
[CrossRef]

Bricaud, A.

P. Y. Deschamps, F. M. Bréon, M. Leroy, A. Podaire, A. Bricaud, J. C. Buriez, G. Sèze, “The POLDER mission: instrument characteristics and scientific objectives,” IEEE Trans. Geosci. Remote Sensing 32, 598–615 (1994).
[CrossRef]

Broenkow, W. W.

Browell, E. V.

Brown, J. W.

Brown, O. B.

Buriez, J. C.

P. Y. Deschamps, F. M. Bréon, M. Leroy, A. Podaire, A. Bricaud, J. C. Buriez, G. Sèze, “The POLDER mission: instrument characteristics and scientific objectives,” IEEE Trans. Geosci. Remote Sensing 32, 598–615 (1994).
[CrossRef]

Clark, D. K.

Deschamps, P. Y.

P. Y. Deschamps, F. M. Bréon, M. Leroy, A. Podaire, A. Bricaud, J. C. Buriez, G. Sèze, “The POLDER mission: instrument characteristics and scientific objectives,” IEEE Trans. Geosci. Remote Sensing 32, 598–615 (1994).
[CrossRef]

Evans, R. H.

Fenn, R. W.

E. P. Shettle, R. W. Fenn, “Models for the aerosols of the lower atmosphere and the effects of humidity variations on their optical properties, (U.S. Air Force Geophysics Laboratory, Hanscomb Air Force Base, Mass. 01731, 1979).

Fraser, R. S.

Frouin, R.

R. Frouin, C. Gautier, “Calibration of NOAA-7 AVHRR, GOES-5, and GOES-6 VISSR/VAS solar channels,” Remote Sensing Environ. 22, 73–101 (1987).
[CrossRef]

Gautier, C.

R. Frouin, C. Gautier, “Calibration of NOAA-7 AVHRR, GOES-5, and GOES-6 VISSR/VAS solar channels,” Remote Sensing Environ. 22, 73–101 (1987).
[CrossRef]

Gellman, D. I.

S. F. Biggar, P. N. Slater, D. I. Gellman, “Uncertainties in the in-flight calibration of sensors with reference to measured ground sites in the 0.4 to 1.1 µm range,” Remote Sensing Environ. 48, 245–252 (1994).
[CrossRef]

Gordon, H. R.

T. Zhang, H. R. Gordon, “Columnar aerosol properties over oceans by combining surface and aircraft measurements: sensitivity analysis,” Appl. Opt. 36, 2650–2662 (1997).
[CrossRef] [PubMed]

H. R. Gordon, T. Zhang, “How well can radiance reflected from the ocean-atmosphere system be predicted from measurements at the sea surface?” Appl. Opt. 35, 6527–6543 (1996).
[CrossRef] [PubMed]

H. R. Gordon, T. Zhang, “Columnar aerosol properties over oceans by combining surface and aircraft measurements: simulations,” Appl. Opt. 34, 5552–5555 (1995).
[CrossRef] [PubMed]

M. Wang, H. R. Gordon, “Retrieval of the columnar aerosol phase function and single-scattering albedo from sky radiance over the ocean: simulations,” Appl. Opt. 32, 4598–4609 (1993).
[CrossRef] [PubMed]

H. R. Gordon, J. W. Brown, O. B. Brown, R. H. Evans, D. K. Clark, “Nimbus 7 CZCS: reduction of its radiometric sensitivity with time,” Appl. Opt. 22, 3929–3931 (1983).
[CrossRef] [PubMed]

H. R. Gordon, D. K. Clark, J. W. Brown, O. B. Brown, R. H. Evans, W. W. Broenkow, “Phytoplankton pigment concentrations in the Middle Atlantic Bight: comparison of ship determinations and CZCS estimates,” Appl. Opt. 22, 20–36 (1983).
[CrossRef] [PubMed]

H. R. Gordon, “Reduction of error introduced in the processing of coastal zone color scanner-type imagery resulting from sensor calibration and solar irradiance uncertainty,” Appl. Opt. 20, 207–210 (1981).
[CrossRef] [PubMed]

H. R. Gordon, “A preliminary assessment of the Nimbus-7 CZCS atmospheric correction algorithm in a horizontally inhomogeneous atmosphere,” in Oceanography from Space, J. R. F. Gower, ed. (Plenum, New York, 1981) pp. 257–266.
[CrossRef]

Holben, B. N.

Y. J. Kaufman, B. N. Holben, “Calibration of the AVHRR visible and near-IR bands by atmospheric scattering, ocean glint, and desert reflection,” Int. J. Remote Sensing 14, 21–52 (1993).
[CrossRef]

Holm, R. G.

P. N. Slater, S. F. Biggar, R. G. Holm, R. D. Jackson, Y. Mao, M. S. Moran, J. M. Palmer, B. Yuan, “Reflectance- and radiance-based methods for the in-flight absolute calibration of multispectral sensors,” Remote Sensing Environ. 22, 11–37 (1987).
[CrossRef]

Hovis, W. A.

Jackson, R. D.

P. N. Slater, S. F. Biggar, R. G. Holm, R. D. Jackson, Y. Mao, M. S. Moran, J. M. Palmer, B. Yuan, “Reflectance- and radiance-based methods for the in-flight absolute calibration of multispectral sensors,” Remote Sensing Environ. 22, 11–37 (1987).
[CrossRef]

Kaufman, Y. J.

Y. J. Kaufman, B. N. Holben, “Calibration of the AVHRR visible and near-IR bands by atmospheric scattering, ocean glint, and desert reflection,” Int. J. Remote Sensing 14, 21–52 (1993).
[CrossRef]

R. S. Fraser, Y. J. Kaufman, “Calibration of satellite sensors after launch,” Appl. Opt. 25, 1177–1185 (1986).
[CrossRef] [PubMed]

Knoll, J. S.

Koepke, P.

Leroy, M.

P. Y. Deschamps, F. M. Bréon, M. Leroy, A. Podaire, A. Bricaud, J. C. Buriez, G. Sèze, “The POLDER mission: instrument characteristics and scientific objectives,” IEEE Trans. Geosci. Remote Sensing 32, 598–615 (1994).
[CrossRef]

Liu, Y.

K. J. Voss, Y. Liu, “Polarized radiance distribution measurements of skylight. 1: system description and characterization,” Appl. Opt. 36, 0000–0000 (1997).
[CrossRef]

Mao, Y.

P. N. Slater, S. F. Biggar, R. G. Holm, R. D. Jackson, Y. Mao, M. S. Moran, J. M. Palmer, B. Yuan, “Reflectance- and radiance-based methods for the in-flight absolute calibration of multispectral sensors,” Remote Sensing Environ. 22, 11–37 (1987).
[CrossRef]

Mishchenko, M. I.

Moran, M. S.

P. N. Slater, S. F. Biggar, R. G. Holm, R. D. Jackson, Y. Mao, M. S. Moran, J. M. Palmer, B. Yuan, “Reflectance- and radiance-based methods for the in-flight absolute calibration of multispectral sensors,” Remote Sensing Environ. 22, 11–37 (1987).
[CrossRef]

Palmer, J. M.

P. N. Slater, S. F. Biggar, R. G. Holm, R. D. Jackson, Y. Mao, M. S. Moran, J. M. Palmer, B. Yuan, “Reflectance- and radiance-based methods for the in-flight absolute calibration of multispectral sensors,” Remote Sensing Environ. 22, 11–37 (1987).
[CrossRef]

Podaire, A.

P. Y. Deschamps, F. M. Bréon, M. Leroy, A. Podaire, A. Bricaud, J. C. Buriez, G. Sèze, “The POLDER mission: instrument characteristics and scientific objectives,” IEEE Trans. Geosci. Remote Sensing 32, 598–615 (1994).
[CrossRef]

Sasano, Y.

Sèze, G.

P. Y. Deschamps, F. M. Bréon, M. Leroy, A. Podaire, A. Bricaud, J. C. Buriez, G. Sèze, “The POLDER mission: instrument characteristics and scientific objectives,” IEEE Trans. Geosci. Remote Sensing 32, 598–615 (1994).
[CrossRef]

Shettle, E. P.

E. P. Shettle, R. W. Fenn, “Models for the aerosols of the lower atmosphere and the effects of humidity variations on their optical properties, (U.S. Air Force Geophysics Laboratory, Hanscomb Air Force Base, Mass. 01731, 1979).

Slater, P. N.

S. F. Biggar, P. N. Slater, D. I. Gellman, “Uncertainties in the in-flight calibration of sensors with reference to measured ground sites in the 0.4 to 1.1 µm range,” Remote Sensing Environ. 48, 245–252 (1994).
[CrossRef]

P. N. Slater, S. F. Biggar, R. G. Holm, R. D. Jackson, Y. Mao, M. S. Moran, J. M. Palmer, B. Yuan, “Reflectance- and radiance-based methods for the in-flight absolute calibration of multispectral sensors,” Remote Sensing Environ. 22, 11–37 (1987).
[CrossRef]

Smith, G. R.

Travis, L. D.

Viollier, M.

Voss, K. J.

K. J. Voss, Y. Liu, “Polarized radiance distribution measurements of skylight. 1: system description and characterization,” Appl. Opt. 36, 0000–0000 (1997).
[CrossRef]

Wang, M.

Yuan, B.

P. N. Slater, S. F. Biggar, R. G. Holm, R. D. Jackson, Y. Mao, M. S. Moran, J. M. Palmer, B. Yuan, “Reflectance- and radiance-based methods for the in-flight absolute calibration of multispectral sensors,” Remote Sensing Environ. 22, 11–37 (1987).
[CrossRef]

Zhang, T.

Appl. Opt. (14)

H. R. Gordon, “Reduction of error introduced in the processing of coastal zone color scanner-type imagery resulting from sensor calibration and solar irradiance uncertainty,” Appl. Opt. 20, 207–210 (1981).
[CrossRef] [PubMed]

P. Koepke, “Vicarious satellite calibration in the solar spectral range by means of calculated radiances and its application to Meteosat,” Appl. Opt. 21, 2845–2854 (1982).
[CrossRef] [PubMed]

M. Viollier, “Radiance calibration of the Coastal Zone Color Scanner on Nimbus 7: a proposed adjustment,” Appl. Opt. 21, 1142–1145 (1982).
[CrossRef] [PubMed]

H. R. Gordon, D. K. Clark, J. W. Brown, O. B. Brown, R. H. Evans, W. W. Broenkow, “Phytoplankton pigment concentrations in the Middle Atlantic Bight: comparison of ship determinations and CZCS estimates,” Appl. Opt. 22, 20–36 (1983).
[CrossRef] [PubMed]

H. R. Gordon, J. W. Brown, O. B. Brown, R. H. Evans, D. K. Clark, “Nimbus 7 CZCS: reduction of its radiometric sensitivity with time,” Appl. Opt. 22, 3929–3931 (1983).
[CrossRef] [PubMed]

W. A. Hovis, J. S. Knoll, G. R. Smith, “Aircraft measurements for calibration of an orbiting spacecraft sensor,” Appl. Opt. 24, 407–410 (1985).
[CrossRef] [PubMed]

R. S. Fraser, Y. J. Kaufman, “Calibration of satellite sensors after launch,” Appl. Opt. 25, 1177–1185 (1986).
[CrossRef] [PubMed]

M. Wang, H. R. Gordon, “Retrieval of the columnar aerosol phase function and single-scattering albedo from sky radiance over the ocean: simulations,” Appl. Opt. 32, 4598–4609 (1993).
[CrossRef] [PubMed]

H. R. Gordon, T. Zhang, “Columnar aerosol properties over oceans by combining surface and aircraft measurements: simulations,” Appl. Opt. 34, 5552–5555 (1995).
[CrossRef] [PubMed]

T. Zhang, H. R. Gordon, “Columnar aerosol properties over oceans by combining surface and aircraft measurements: sensitivity analysis,” Appl. Opt. 36, 2650–2662 (1997).
[CrossRef] [PubMed]

H. R. Gordon, T. Zhang, “How well can radiance reflected from the ocean-atmosphere system be predicted from measurements at the sea surface?” Appl. Opt. 35, 6527–6543 (1996).
[CrossRef] [PubMed]

Y. Sasano, E. V. Browell, “Light scattering characteristics of various aerosol types derived from multiple wavelength lidar observations,” Appl. Opt. 28, 1670–1679 (1989).
[CrossRef] [PubMed]

K. J. Voss, Y. Liu, “Polarized radiance distribution measurements of skylight. 1: system description and characterization,” Appl. Opt. 36, 0000–0000 (1997).
[CrossRef]

M. I. Mishchenko, L. D. Travis, “Light scattering by polydispersions of randomly oriented spheroids with sizes comparable to wavelengths of observation,” Appl. Opt. 33, 7206–7225 (1994).
[CrossRef] [PubMed]

IEEE Trans. Geosci. Remote Sensing (1)

P. Y. Deschamps, F. M. Bréon, M. Leroy, A. Podaire, A. Bricaud, J. C. Buriez, G. Sèze, “The POLDER mission: instrument characteristics and scientific objectives,” IEEE Trans. Geosci. Remote Sensing 32, 598–615 (1994).
[CrossRef]

Int. J. Remote Sensing (1)

Y. J. Kaufman, B. N. Holben, “Calibration of the AVHRR visible and near-IR bands by atmospheric scattering, ocean glint, and desert reflection,” Int. J. Remote Sensing 14, 21–52 (1993).
[CrossRef]

Remote Sensing Environ. (3)

S. F. Biggar, P. N. Slater, D. I. Gellman, “Uncertainties in the in-flight calibration of sensors with reference to measured ground sites in the 0.4 to 1.1 µm range,” Remote Sensing Environ. 48, 245–252 (1994).
[CrossRef]

P. N. Slater, S. F. Biggar, R. G. Holm, R. D. Jackson, Y. Mao, M. S. Moran, J. M. Palmer, B. Yuan, “Reflectance- and radiance-based methods for the in-flight absolute calibration of multispectral sensors,” Remote Sensing Environ. 22, 11–37 (1987).
[CrossRef]

R. Frouin, C. Gautier, “Calibration of NOAA-7 AVHRR, GOES-5, and GOES-6 VISSR/VAS solar channels,” Remote Sensing Environ. 22, 73–101 (1987).
[CrossRef]

Other (2)

E. P. Shettle, R. W. Fenn, “Models for the aerosols of the lower atmosphere and the effects of humidity variations on their optical properties, (U.S. Air Force Geophysics Laboratory, Hanscomb Air Force Base, Mass. 01731, 1979).

H. R. Gordon, “A preliminary assessment of the Nimbus-7 CZCS atmospheric correction algorithm in a horizontally inhomogeneous atmosphere,” in Oceanography from Space, J. R. F. Gower, ed. (Plenum, New York, 1981) pp. 257–266.
[CrossRef]

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Figures (11)

Fig. 1
Fig. 1

Simplified ocean-atmosphere system used in the algorithm, and measurements needed to carry out the retrieval.

Fig. 2
Fig. 2

Scattering phase matrix elements for the Shettle–Fenn19 aerosol models used in the study: (a) P11, (b) P12/P11, (c) P33/P11, and (d) P34/P11.

Fig. 3
Fig. 3

Comparison between the retrieved elements (circles) and the true values (solid curves) for T50 and τa = 0.20: (a) P11, with incorrect values for P33 and P34 used in the retrieval; (b) P11, with correct values for P33 and P34 used in the retrieval; (c) same as (a) but for P12/P11; and (d) same as (b) but for P12/P11.

Fig. 4
Fig. 4

Comparison between the retrieved elements (circles) and the true values (solid curves) for T50 and τa = 2.00: (a) P11, with incorrect values for P33 and P34 used in the retrieval; (b) P11, with correct values for P33 and P34 used in the retrieval; (c) same as (a) but for P12/P11 and (d) same as (b) but for P12/P11.

Fig. 5
Fig. 5

Same as Fig. 4 except that the downwelling principal-plane data are replaced by upwelling data for retrieval between 120° < Θ < 145°.

Fig. 6
Fig. 6

Comparison between the retrieved elements (circles) and the true values (solid curves) for M99 and τa = 0.20 (incorrect values for P33 and P34 are used in the retrieval): (a) P11, with 7 upwelling data used for retrieval for 145° < Θ < 180°; (b) P11, but with the number of upwelling data for 145° < Θ < 180° doubled; (c) same as (a) but for P12/P11; and (d) same as (b) but for P12/P11.

Fig. 7
Fig. 7

Comparison between the retrieved elements (circles) and the true values (solid curves) for τa = 0.20 when only surface measurements are used for retrieval (values for P33 and P34 are incorrect): (a) P11 for M99, (b)P11 for T50, (c) same as (a) but for P12/P11, and (d) same as (b) but for P12/P11.

Fig. 8
Fig. 8

Comparison between the errors in the estimation of ρT when retrieval/prediction uses the vector radiative transfer theory (solid curve) and the scalar radiative transfer theory (dashed curve) for T50: (a) θ0 = 60°, (b) θ0 = 50°, and (c) θ0 = 45°. The dotted line represents the zero point.

Fig. 9
Fig. 9

Errors in the estimation of (a) QT and (b) UT when retrieval/prediction uses the vector radiative transfer theory for T50 and τa = 0.20. The dotted line represents the zero point.

Fig. 10
Fig. 10

Comparison between the retrieved elements (circles) and the true values (solid curves) for the T50 aerosol model when the measured I, Q, and U all contain a 5% calibration error (incorrect values for P33 and P34 are used in the retrieval): (a) P11 for τa = 0.20; (b) P11 for τa = 2.00, but with the values for 120° < Θ < 180° retrieved from upwelling data; (c) same as (a) but for P12/P11; and (d) same as (b) but for P12/P11.

Fig. 11
Fig. 11

Comparison between the retrieved elements (circles) and the true values (solid curves) for the T50 aerosol model when the measured I, Q, and U contain 0.5% Gaussian noise (incorrect values for P33 and P34 are used in the retrieval): (a) P11 for τa = 0.20; (b) P11 for τa = 2.00, but with the values for 120° < Θ < 180° retrieved from upwelling data; (c) same as (a) but for P12/P11; and (d) same as (b) but for P12/P11.

Equations (12)

Equations on this page are rendered with MathJax. Learn more.

IQUV=ω0τa4πµ10000cos 2α-sin 2α00sin 2αcos 2α00001×P11ΘP12Θ00P12ΘP22Θ0000P33ΘP34Θ00-P34ΘP44ΘF0000=ω0τaF04πµP11ΘP12Θ cos 2αP12Θ sin 2α0,
ω0P11Θ=4πµτaF0I
ω0P12Θ=4πµτaF0 cos 2αQ
ω0P12Θ=4πµτaF0 sin 2αU.
ω0=1/20πω0P11Θ sin Θ dΘ,
ω0P11Θnew=ω0P11Θold-CIBc-IBm×ω0P11ΘoldIBm-IrBc exp -τa/µ,
ω0P12Θnew=ω0P12Θold-CQBc-QBm×4πµτaF0 cos 2α
ω0P12Θnew=ω0P12Θold-CUBc-UBm×4πµτaF0 sin 2α
ω0P12ΘQ=4πµτaF0 cos 2α
ω0P12ΘU=4πµτaF0 sin 2α.
P11Θ=1/ω0ω0P11Θ, P12Θ=1/ω0ω0P12Θ.
P11Θ=P11Θmax, P12Θ=180°-Θ180°-ΘmaxP12Θmax,

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