Abstract

Based on the fact that the part of downward radiance that depends on the optical properties of the aerosol in the atmosphere can be extracted from the measured sky radiance, a new scheme for retrieval of the aerosol phase function and the single-scattering albedo over the ocean is developed. This retrieval algorithm is tested with simulations for several cases. It is found that the retrieved aerosol phase function and the single-scattering albedo are virtually error free if the vertical structure of the atmosphere is known and if the sky radiance and the aerosol optical thickness can be measured accurately. The robustness of the algorithm in realistic situations, in which the measurements are contaminated by calibration errors or noise, is examined. It is found that the retrieved value of ω0 is usually in error by ≲ 10%, and the phase function is accurately retrieved for ϴ ≲ 90°. However, as the aerosol optical thickness becomes small, e.g., ≲ 0.1, errors in the sky radiance measurement can lead to serious problems with the retrieval algorithm, especially in the blue. The use of the retrieval scheme should be limited to the red and near IR when the aerosol optical thickness is small.

© 1993 Optical Society of America

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  1. R. J. Charlson, S. E. Schwartz, J. M. Hales, R. D. Cess, J. A. Coakley, J. E. Hansen, D. J. Hofmann, “Climate forcing by anthropogenic aerosols,” Science 225, 423–430 (1992).
    [CrossRef]
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    [CrossRef]
  3. T. Nakajima, M. Tanaka, M. Yamano, M. Shiobara, K. Arao, Y. Nakanishi, “Aerosol optical characteristics in the yellow sand events observed in May 1982 at Nagasaki—Part II Models,” J. Meteorol. Soc. Jpn. 67, 279–291 (1989).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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  13. S. B. Hooker, W. E. Esaias, G. C. Feldman, W. W. Gregg, C. R. McClain, An Overview of SeaWiFS and Ocean Color, Volume 1 of SeaWiFS Tech. Rep. Series, NASA Tech. Memo. 104566 (NASA, Greenbelt, Md., 1992).
  14. V. V. Salomonson, W. L. Barnes, P. W. Maymon, H. E. Montgomery, H. Ostrow, “MODIS: advanced facility instrument for studies of the Earth as a system,” IEEE Trans. Geosci. Remote Sensing 27, 145–152 (1989).
    [CrossRef]
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    [CrossRef] [PubMed]
  17. 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]
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    [CrossRef]
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  21. H. R. Gordon, D. J. Castaño, “Coastal zone color scanner atmospheric correction algorithm: multiple scattering effects,” Appl. Opt. 26, 2111–2122 (1987).
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  24. H. Quenzel, M. Kastner, “Optical properties of the atmosphere: calculated variability and application to satellite remote sensing of phytoplankton,” Appl. Opt. 19, 1338–1344 (1980).
    [CrossRef] [PubMed]
  25. D. Deirmendjian, Electromagnetic Scattering on Spherical Polydispersions (Elsevier, New York, 1969).
  26. G. W. Kattawar, “A three-parameter analytic phase function for multiple scattering calculations,” J. Quant. Spectrosc. Radiat. Transfer 15, 839–849 (1975).
    [CrossRef]
  27. H. R. Gordon, M. Wang, “Surface roughness considerations for atmospheric correction of ocean color sensors. 1: The Raleigh scattering component,” Appl. Opt. 31, 4247– 4260 (1992).
    [CrossRef] [PubMed]
  28. H. R. Gordon, M. Wang, “Surface roughness considerations for atmospheric correction of ocean color sensors. 2: Error in the retrieved water-leaving radiance,” Appl. Opt. 31, 4261–4267 (1992).
    [CrossRef] [PubMed]
  29. M. D. King, “Number of terms required in the Fourier expansion of the reflection function for optically thick atmospheres,” J. Quant. Spectrosc. Radiat. Transfer 30, 143–161 (1983).
    [CrossRef]

1992 (3)

1991 (1)

M. Wendisch, W. von Hoyningen-Huene, “High speed version of the method of ‘successive order of scattering’ and its application to remote sensing,” Beitr. Phys. Atmosph. 64, 83–91 (1991).

1989 (3)

T. Nakajima, M. Tanaka, M. Yamano, M. Shiobara, K. Arao, Y. Nakanishi, “Aerosol optical characteristics in the yellow sand events observed in May 1982 at Nagasaki—Part II Models,” J. Meteorol. Soc. Jpn. 67, 279–291 (1989).

V. V. Salomonson, W. L. Barnes, P. W. Maymon, H. E. Montgomery, H. Ostrow, “MODIS: advanced facility instrument for studies of the Earth as a system,” IEEE Trans. Geosci. Remote Sensing 27, 145–152 (1989).
[CrossRef]

H. R. Gordon, D. J. Castaño, “Aerosol analysis with the Coastal Zone Color Scanner: a simple method for including multiple scattering effects,” Appl. Opt. 28, 1320–1326 (1989).
[CrossRef] [PubMed]

1987 (3)

H. R. Gordon, D. J. Castaño, “Coastal zone color scanner atmospheric correction algorithm: multiple scattering effects,” Appl. Opt. 26, 2111–2122 (1987).
[CrossRef] [PubMed]

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. J. Charlson, J. E. Lovelock, M. O. Andreae, S. G. Warren, “Oceanic phytoplankton, atmospheric sulphur, cloud albedo and climate,” Nature (London) 326, 655–661 (1987).
[CrossRef]

1986 (1)

1983 (5)

1982 (1)

1981 (1)

M. A. Box, A. Deepak, “An approximation to multiple scattering in the Earth's atmosphere: almucantar radiance formulation,” J. Atmos. Sci. 38, 1037–1048 (1981).
[CrossRef]

1980 (3)

W. A. Hovis, D. K. Clark, F. Anderson, R. W. Austin, W. H. Wilson, E. T. Baker, D. Ball, H. R. Gordon, J. L. Mueller, S. Y. E. Sayed, B. Strum, R. C. Wrigley, C. S. Yentsch, “Nimbus 7 coastal zone color scanner: system description and initial imagery,” Science 210, 60–63 (1980).
[CrossRef] [PubMed]

H. R. Gordon, D. K. Clark, J. L. Mueller, W. A. Hovis, “Phytoplankton pigments derived from the Nimbus-7 CZCS: initial comparisons with surface measurements,” Science 210, 63–66 (1980).
[CrossRef] [PubMed]

H. Quenzel, M. Kastner, “Optical properties of the atmosphere: calculated variability and application to satellite remote sensing of phytoplankton,” Appl. Opt. 19, 1338–1344 (1980).
[CrossRef] [PubMed]

1979 (2)

M. A. Box, A. Deepak, “Retrieval of aerosol size distributions by inversion of simulated aureole data in the presence of multiple scattering,” Appl. Opt. 18, 1376–1382 (1979).
[CrossRef] [PubMed]

M. D. King, B. M. Herman, “Determination of the ground albedo and the index of absorption of atmospheric particulates by remote sensing. Part I: Theory,” J. Atmos. Sci. 36, 163–173 (1979).
[CrossRef]

1975 (1)

G. W. Kattawar, “A three-parameter analytic phase function for multiple scattering calculations,” J. Quant. Spectrosc. Radiat. Transfer 15, 839–849 (1975).
[CrossRef]

1908 (1)

G. Mie, “Beiträge zur Optik trüber Medien, speziell kollidalen Metall-lösungen,” Ann. Phys. 25, 377–445 (1908).
[CrossRef]

Anderson, F.

W. A. Hovis, D. K. Clark, F. Anderson, R. W. Austin, W. H. Wilson, E. T. Baker, D. Ball, H. R. Gordon, J. L. Mueller, S. Y. E. Sayed, B. Strum, R. C. Wrigley, C. S. Yentsch, “Nimbus 7 coastal zone color scanner: system description and initial imagery,” Science 210, 60–63 (1980).
[CrossRef] [PubMed]

Andreae, M. O.

R. J. Charlson, J. E. Lovelock, M. O. Andreae, S. G. Warren, “Oceanic phytoplankton, atmospheric sulphur, cloud albedo and climate,” Nature (London) 326, 655–661 (1987).
[CrossRef]

Arao, K.

T. Nakajima, M. Tanaka, M. Yamano, M. Shiobara, K. Arao, Y. Nakanishi, “Aerosol optical characteristics in the yellow sand events observed in May 1982 at Nagasaki—Part II Models,” J. Meteorol. Soc. Jpn. 67, 279–291 (1989).

Austin, R. W.

W. A. Hovis, D. K. Clark, F. Anderson, R. W. Austin, W. H. Wilson, E. T. Baker, D. Ball, H. R. Gordon, J. L. Mueller, S. Y. E. Sayed, B. Strum, R. C. Wrigley, C. S. Yentsch, “Nimbus 7 coastal zone color scanner: system description and initial imagery,” Science 210, 60–63 (1980).
[CrossRef] [PubMed]

Baker, E. T.

W. A. Hovis, D. K. Clark, F. Anderson, R. W. Austin, W. H. Wilson, E. T. Baker, D. Ball, H. R. Gordon, J. L. Mueller, S. Y. E. Sayed, B. Strum, R. C. Wrigley, C. S. Yentsch, “Nimbus 7 coastal zone color scanner: system description and initial imagery,” Science 210, 60–63 (1980).
[CrossRef] [PubMed]

Ball, D.

W. A. Hovis, D. K. Clark, F. Anderson, R. W. Austin, W. H. Wilson, E. T. Baker, D. Ball, H. R. Gordon, J. L. Mueller, S. Y. E. Sayed, B. Strum, R. C. Wrigley, C. S. Yentsch, “Nimbus 7 coastal zone color scanner: system description and initial imagery,” Science 210, 60–63 (1980).
[CrossRef] [PubMed]

Barnes, W. L.

V. V. Salomonson, W. L. Barnes, P. W. Maymon, H. E. Montgomery, H. Ostrow, “MODIS: advanced facility instrument for studies of the Earth as a system,” IEEE Trans. Geosci. Remote Sensing 27, 145–152 (1989).
[CrossRef]

Biggar, S. F.

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]

Box, M. A.

M. A. Box, A. Deepak, “An approximation to multiple scattering in the Earth's atmosphere: almucantar radiance formulation,” J. Atmos. Sci. 38, 1037–1048 (1981).
[CrossRef]

M. A. Box, A. Deepak, “Retrieval of aerosol size distributions by inversion of simulated aureole data in the presence of multiple scattering,” Appl. Opt. 18, 1376–1382 (1979).
[CrossRef] [PubMed]

Broenkow, W. W.

Brown, J. W.

Brown, O. B.

Castaño, D. J.

Cess, R. D.

R. J. Charlson, S. E. Schwartz, J. M. Hales, R. D. Cess, J. A. Coakley, J. E. Hansen, D. J. Hofmann, “Climate forcing by anthropogenic aerosols,” Science 225, 423–430 (1992).
[CrossRef]

Charlson, R. J.

R. J. Charlson, S. E. Schwartz, J. M. Hales, R. D. Cess, J. A. Coakley, J. E. Hansen, D. J. Hofmann, “Climate forcing by anthropogenic aerosols,” Science 225, 423–430 (1992).
[CrossRef]

R. J. Charlson, J. E. Lovelock, M. O. Andreae, S. G. Warren, “Oceanic phytoplankton, atmospheric sulphur, cloud albedo and climate,” Nature (London) 326, 655–661 (1987).
[CrossRef]

Clark, D. K.

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, D. K. Clark, J. L. Mueller, W. A. Hovis, “Phytoplankton pigments derived from the Nimbus-7 CZCS: initial comparisons with surface measurements,” Science 210, 63–66 (1980).
[CrossRef] [PubMed]

W. A. Hovis, D. K. Clark, F. Anderson, R. W. Austin, W. H. Wilson, E. T. Baker, D. Ball, H. R. Gordon, J. L. Mueller, S. Y. E. Sayed, B. Strum, R. C. Wrigley, C. S. Yentsch, “Nimbus 7 coastal zone color scanner: system description and initial imagery,” Science 210, 60–63 (1980).
[CrossRef] [PubMed]

Coakley, J. A.

R. J. Charlson, S. E. Schwartz, J. M. Hales, R. D. Cess, J. A. Coakley, J. E. Hansen, D. J. Hofmann, “Climate forcing by anthropogenic aerosols,” Science 225, 423–430 (1992).
[CrossRef]

Deepak, A.

M. A. Box, A. Deepak, “An approximation to multiple scattering in the Earth's atmosphere: almucantar radiance formulation,” J. Atmos. Sci. 38, 1037–1048 (1981).
[CrossRef]

M. A. Box, A. Deepak, “Retrieval of aerosol size distributions by inversion of simulated aureole data in the presence of multiple scattering,” Appl. Opt. 18, 1376–1382 (1979).
[CrossRef] [PubMed]

Deirmendjian, D.

D. Deirmendjian, Electromagnetic Scattering on Spherical Polydispersions (Elsevier, New York, 1969).

Deschamps, P. Y.

Esaias, W. E.

S. B. Hooker, W. E. Esaias, G. C. Feldman, W. W. Gregg, C. R. McClain, An Overview of SeaWiFS and Ocean Color, Volume 1 of SeaWiFS Tech. Rep. Series, NASA Tech. Memo. 104566 (NASA, Greenbelt, Md., 1992).

Evans, R. H.

Feldman, G. C.

S. B. Hooker, W. E. Esaias, G. C. Feldman, W. W. Gregg, C. R. McClain, An Overview of SeaWiFS and Ocean Color, Volume 1 of SeaWiFS Tech. Rep. Series, NASA Tech. Memo. 104566 (NASA, Greenbelt, Md., 1992).

Fraser, R. S.

Gordon, H. R.

H. R. Gordon, M. Wang, “Surface roughness considerations for atmospheric correction of ocean color sensors. 1: The Raleigh scattering component,” Appl. Opt. 31, 4247– 4260 (1992).
[CrossRef] [PubMed]

H. R. Gordon, M. Wang, “Surface roughness considerations for atmospheric correction of ocean color sensors. 2: Error in the retrieved water-leaving radiance,” Appl. Opt. 31, 4261–4267 (1992).
[CrossRef] [PubMed]

H. R. Gordon, D. J. Castaño, “Aerosol analysis with the Coastal Zone Color Scanner: a simple method for including multiple scattering effects,” Appl. Opt. 28, 1320–1326 (1989).
[CrossRef] [PubMed]

H. R. Gordon, D. J. Castaño, “Coastal zone color scanner atmospheric correction algorithm: multiple scattering effects,” Appl. Opt. 26, 2111–2122 (1987).
[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]

H. R. Gordon, D. K. Clark, J. L. Mueller, W. A. Hovis, “Phytoplankton pigments derived from the Nimbus-7 CZCS: initial comparisons with surface measurements,” Science 210, 63–66 (1980).
[CrossRef] [PubMed]

W. A. Hovis, D. K. Clark, F. Anderson, R. W. Austin, W. H. Wilson, E. T. Baker, D. Ball, H. R. Gordon, J. L. Mueller, S. Y. E. Sayed, B. Strum, R. C. Wrigley, C. S. Yentsch, “Nimbus 7 coastal zone color scanner: system description and initial imagery,” Science 210, 60–63 (1980).
[CrossRef] [PubMed]

Gregg, W. W.

S. B. Hooker, W. E. Esaias, G. C. Feldman, W. W. Gregg, C. R. McClain, An Overview of SeaWiFS and Ocean Color, Volume 1 of SeaWiFS Tech. Rep. Series, NASA Tech. Memo. 104566 (NASA, Greenbelt, Md., 1992).

Hales, J. M.

R. J. Charlson, S. E. Schwartz, J. M. Hales, R. D. Cess, J. A. Coakley, J. E. Hansen, D. J. Hofmann, “Climate forcing by anthropogenic aerosols,” Science 225, 423–430 (1992).
[CrossRef]

Hansen, J. E.

R. J. Charlson, S. E. Schwartz, J. M. Hales, R. D. Cess, J. A. Coakley, J. E. Hansen, D. J. Hofmann, “Climate forcing by anthropogenic aerosols,” Science 225, 423–430 (1992).
[CrossRef]

Herman, B. M.

M. D. King, B. M. Herman, “Determination of the ground albedo and the index of absorption of atmospheric particulates by remote sensing. Part I: Theory,” J. Atmos. Sci. 36, 163–173 (1979).
[CrossRef]

Herman, M.

Hofmann, D. J.

R. J. Charlson, S. E. Schwartz, J. M. Hales, R. D. Cess, J. A. Coakley, J. E. Hansen, D. J. Hofmann, “Climate forcing by anthropogenic aerosols,” Science 225, 423–430 (1992).
[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]

Hooker, S. B.

S. B. Hooker, W. E. Esaias, G. C. Feldman, W. W. Gregg, C. R. McClain, An Overview of SeaWiFS and Ocean Color, Volume 1 of SeaWiFS Tech. Rep. Series, NASA Tech. Memo. 104566 (NASA, Greenbelt, Md., 1992).

Hovis, W. A.

H. R. Gordon, D. K. Clark, J. L. Mueller, W. A. Hovis, “Phytoplankton pigments derived from the Nimbus-7 CZCS: initial comparisons with surface measurements,” Science 210, 63–66 (1980).
[CrossRef] [PubMed]

W. A. Hovis, D. K. Clark, F. Anderson, R. W. Austin, W. H. Wilson, E. T. Baker, D. Ball, H. R. Gordon, J. L. Mueller, S. Y. E. Sayed, B. Strum, R. C. Wrigley, C. S. Yentsch, “Nimbus 7 coastal zone color scanner: system description and initial imagery,” Science 210, 60–63 (1980).
[CrossRef] [PubMed]

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]

Kastner, M.

Kattawar, G. W.

G. W. Kattawar, “A three-parameter analytic phase function for multiple scattering calculations,” J. Quant. Spectrosc. Radiat. Transfer 15, 839–849 (1975).
[CrossRef]

Kaufman, Y. J.

King, M. D.

M. D. King, “Number of terms required in the Fourier expansion of the reflection function for optically thick atmospheres,” J. Quant. Spectrosc. Radiat. Transfer 30, 143–161 (1983).
[CrossRef]

M. D. King, B. M. Herman, “Determination of the ground albedo and the index of absorption of atmospheric particulates by remote sensing. Part I: Theory,” J. Atmos. Sci. 36, 163–173 (1979).
[CrossRef]

Koepke, P.

Lovelock, J. E.

R. J. Charlson, J. E. Lovelock, M. O. Andreae, S. G. Warren, “Oceanic phytoplankton, atmospheric sulphur, cloud albedo and climate,” Nature (London) 326, 655–661 (1987).
[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]

Maymon, P. W.

V. V. Salomonson, W. L. Barnes, P. W. Maymon, H. E. Montgomery, H. Ostrow, “MODIS: advanced facility instrument for studies of the Earth as a system,” IEEE Trans. Geosci. Remote Sensing 27, 145–152 (1989).
[CrossRef]

McClain, C. R.

S. B. Hooker, W. E. Esaias, G. C. Feldman, W. W. Gregg, C. R. McClain, An Overview of SeaWiFS and Ocean Color, Volume 1 of SeaWiFS Tech. Rep. Series, NASA Tech. Memo. 104566 (NASA, Greenbelt, Md., 1992).

Mie, G.

G. Mie, “Beiträge zur Optik trüber Medien, speziell kollidalen Metall-lösungen,” Ann. Phys. 25, 377–445 (1908).
[CrossRef]

Montgomery, H. E.

V. V. Salomonson, W. L. Barnes, P. W. Maymon, H. E. Montgomery, H. Ostrow, “MODIS: advanced facility instrument for studies of the Earth as a system,” IEEE Trans. Geosci. Remote Sensing 27, 145–152 (1989).
[CrossRef]

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]

Mueller, J. L.

H. R. Gordon, D. K. Clark, J. L. Mueller, W. A. Hovis, “Phytoplankton pigments derived from the Nimbus-7 CZCS: initial comparisons with surface measurements,” Science 210, 63–66 (1980).
[CrossRef] [PubMed]

W. A. Hovis, D. K. Clark, F. Anderson, R. W. Austin, W. H. Wilson, E. T. Baker, D. Ball, H. R. Gordon, J. L. Mueller, S. Y. E. Sayed, B. Strum, R. C. Wrigley, C. S. Yentsch, “Nimbus 7 coastal zone color scanner: system description and initial imagery,” Science 210, 60–63 (1980).
[CrossRef] [PubMed]

Nakajima, T.

T. Nakajima, M. Tanaka, M. Yamano, M. Shiobara, K. Arao, Y. Nakanishi, “Aerosol optical characteristics in the yellow sand events observed in May 1982 at Nagasaki—Part II Models,” J. Meteorol. Soc. Jpn. 67, 279–291 (1989).

T. Nakajima, M. Tanaka, T. Yamauchi, “Retrieval of the optical properties of aerosols from aureole and extinction data,” Appl. Opt. 22, 2951–2959 (1983).
[CrossRef] [PubMed]

Nakanishi, Y.

T. Nakajima, M. Tanaka, M. Yamano, M. Shiobara, K. Arao, Y. Nakanishi, “Aerosol optical characteristics in the yellow sand events observed in May 1982 at Nagasaki—Part II Models,” J. Meteorol. Soc. Jpn. 67, 279–291 (1989).

Ostrow, H.

V. V. Salomonson, W. L. Barnes, P. W. Maymon, H. E. Montgomery, H. Ostrow, “MODIS: advanced facility instrument for studies of the Earth as a system,” IEEE Trans. Geosci. Remote Sensing 27, 145–152 (1989).
[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]

Quenzel, H.

Salomonson, V. V.

V. V. Salomonson, W. L. Barnes, P. W. Maymon, H. E. Montgomery, H. Ostrow, “MODIS: advanced facility instrument for studies of the Earth as a system,” IEEE Trans. Geosci. Remote Sensing 27, 145–152 (1989).
[CrossRef]

Sayed, S. Y. E.

W. A. Hovis, D. K. Clark, F. Anderson, R. W. Austin, W. H. Wilson, E. T. Baker, D. Ball, H. R. Gordon, J. L. Mueller, S. Y. E. Sayed, B. Strum, R. C. Wrigley, C. S. Yentsch, “Nimbus 7 coastal zone color scanner: system description and initial imagery,” Science 210, 60–63 (1980).
[CrossRef] [PubMed]

Schwartz, S. E.

R. J. Charlson, S. E. Schwartz, J. M. Hales, R. D. Cess, J. A. Coakley, J. E. Hansen, D. J. Hofmann, “Climate forcing by anthropogenic aerosols,” Science 225, 423–430 (1992).
[CrossRef]

Shiobara, M.

T. Nakajima, M. Tanaka, M. Yamano, M. Shiobara, K. Arao, Y. Nakanishi, “Aerosol optical characteristics in the yellow sand events observed in May 1982 at Nagasaki—Part II Models,” J. Meteorol. Soc. Jpn. 67, 279–291 (1989).

Slater, P. N.

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]

Strum, B.

W. A. Hovis, D. K. Clark, F. Anderson, R. W. Austin, W. H. Wilson, E. T. Baker, D. Ball, H. R. Gordon, J. L. Mueller, S. Y. E. Sayed, B. Strum, R. C. Wrigley, C. S. Yentsch, “Nimbus 7 coastal zone color scanner: system description and initial imagery,” Science 210, 60–63 (1980).
[CrossRef] [PubMed]

Tanaka, M.

T. Nakajima, M. Tanaka, M. Yamano, M. Shiobara, K. Arao, Y. Nakanishi, “Aerosol optical characteristics in the yellow sand events observed in May 1982 at Nagasaki—Part II Models,” J. Meteorol. Soc. Jpn. 67, 279–291 (1989).

T. Nakajima, M. Tanaka, T. Yamauchi, “Retrieval of the optical properties of aerosols from aureole and extinction data,” Appl. Opt. 22, 2951–2959 (1983).
[CrossRef] [PubMed]

Tanre, D.

von Hoyningen-Huene, W.

M. Wendisch, W. von Hoyningen-Huene, “High speed version of the method of ‘successive order of scattering’ and its application to remote sensing,” Beitr. Phys. Atmosph. 64, 83–91 (1991).

Wang, M.

Warren, S. G.

R. J. Charlson, J. E. Lovelock, M. O. Andreae, S. G. Warren, “Oceanic phytoplankton, atmospheric sulphur, cloud albedo and climate,” Nature (London) 326, 655–661 (1987).
[CrossRef]

Wendisch, M.

M. Wendisch, W. von Hoyningen-Huene, “High speed version of the method of ‘successive order of scattering’ and its application to remote sensing,” Beitr. Phys. Atmosph. 64, 83–91 (1991).

Wilson, W. H.

W. A. Hovis, D. K. Clark, F. Anderson, R. W. Austin, W. H. Wilson, E. T. Baker, D. Ball, H. R. Gordon, J. L. Mueller, S. Y. E. Sayed, B. Strum, R. C. Wrigley, C. S. Yentsch, “Nimbus 7 coastal zone color scanner: system description and initial imagery,” Science 210, 60–63 (1980).
[CrossRef] [PubMed]

Wrigley, R. C.

W. A. Hovis, D. K. Clark, F. Anderson, R. W. Austin, W. H. Wilson, E. T. Baker, D. Ball, H. R. Gordon, J. L. Mueller, S. Y. E. Sayed, B. Strum, R. C. Wrigley, C. S. Yentsch, “Nimbus 7 coastal zone color scanner: system description and initial imagery,” Science 210, 60–63 (1980).
[CrossRef] [PubMed]

Yamano, M.

T. Nakajima, M. Tanaka, M. Yamano, M. Shiobara, K. Arao, Y. Nakanishi, “Aerosol optical characteristics in the yellow sand events observed in May 1982 at Nagasaki—Part II Models,” J. Meteorol. Soc. Jpn. 67, 279–291 (1989).

Yamauchi, T.

Yentsch, C. S.

W. A. Hovis, D. K. Clark, F. Anderson, R. W. Austin, W. H. Wilson, E. T. Baker, D. Ball, H. R. Gordon, J. L. Mueller, S. Y. E. Sayed, B. Strum, R. C. Wrigley, C. S. Yentsch, “Nimbus 7 coastal zone color scanner: system description and initial imagery,” Science 210, 60–63 (1980).
[CrossRef] [PubMed]

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]

Ann. Phys. (1)

G. Mie, “Beiträge zur Optik trüber Medien, speziell kollidalen Metall-lösungen,” Ann. Phys. 25, 377–445 (1908).
[CrossRef]

Appl. Opt. (1)

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]

Appl. Opt. (11)

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

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]

M. A. Box, A. Deepak, “Retrieval of aerosol size distributions by inversion of simulated aureole data in the presence of multiple scattering,” Appl. Opt. 18, 1376–1382 (1979).
[CrossRef] [PubMed]

T. Nakajima, M. Tanaka, T. Yamauchi, “Retrieval of the optical properties of aerosols from aureole and extinction data,” Appl. Opt. 22, 2951–2959 (1983).
[CrossRef] [PubMed]

P. Y. Deschamps, M. Herman, D. Tanre, “Modeling of the atmospheric effects and its application to the remote sensing of ocean color,” Appl. Opt. 22, 3751–3758 (1983).
[CrossRef] [PubMed]

H. R. Gordon, D. J. Castaño, “Coastal zone color scanner atmospheric correction algorithm: multiple scattering effects,” Appl. Opt. 26, 2111–2122 (1987).
[CrossRef] [PubMed]

H. R. Gordon, D. J. Castaño, “Aerosol analysis with the Coastal Zone Color Scanner: a simple method for including multiple scattering effects,” Appl. Opt. 28, 1320–1326 (1989).
[CrossRef] [PubMed]

H. Quenzel, M. Kastner, “Optical properties of the atmosphere: calculated variability and application to satellite remote sensing of phytoplankton,” Appl. Opt. 19, 1338–1344 (1980).
[CrossRef] [PubMed]

H. R. Gordon, M. Wang, “Surface roughness considerations for atmospheric correction of ocean color sensors. 1: The Raleigh scattering component,” Appl. Opt. 31, 4247– 4260 (1992).
[CrossRef] [PubMed]

H. R. Gordon, M. Wang, “Surface roughness considerations for atmospheric correction of ocean color sensors. 2: Error in the retrieved water-leaving radiance,” Appl. Opt. 31, 4261–4267 (1992).
[CrossRef] [PubMed]

Beitr. Phys. Atmosph. (1)

M. Wendisch, W. von Hoyningen-Huene, “High speed version of the method of ‘successive order of scattering’ and its application to remote sensing,” Beitr. Phys. Atmosph. 64, 83–91 (1991).

IEEE Trans. Geosci. Remote Sensing (1)

V. V. Salomonson, W. L. Barnes, P. W. Maymon, H. E. Montgomery, H. Ostrow, “MODIS: advanced facility instrument for studies of the Earth as a system,” IEEE Trans. Geosci. Remote Sensing 27, 145–152 (1989).
[CrossRef]

J. Atmos. Sci. (2)

M. D. King, B. M. Herman, “Determination of the ground albedo and the index of absorption of atmospheric particulates by remote sensing. Part I: Theory,” J. Atmos. Sci. 36, 163–173 (1979).
[CrossRef]

M. A. Box, A. Deepak, “An approximation to multiple scattering in the Earth's atmosphere: almucantar radiance formulation,” J. Atmos. Sci. 38, 1037–1048 (1981).
[CrossRef]

J. Meteorol. Soc. Jpn. (1)

T. Nakajima, M. Tanaka, M. Yamano, M. Shiobara, K. Arao, Y. Nakanishi, “Aerosol optical characteristics in the yellow sand events observed in May 1982 at Nagasaki—Part II Models,” J. Meteorol. Soc. Jpn. 67, 279–291 (1989).

J. Quant. Spectrosc. Radiat. Transfer (1)

M. D. King, “Number of terms required in the Fourier expansion of the reflection function for optically thick atmospheres,” J. Quant. Spectrosc. Radiat. Transfer 30, 143–161 (1983).
[CrossRef]

J. Quant. Spectrosc. Radiat. Transfer (1)

G. W. Kattawar, “A three-parameter analytic phase function for multiple scattering calculations,” J. Quant. Spectrosc. Radiat. Transfer 15, 839–849 (1975).
[CrossRef]

Nature (London) (1)

R. J. Charlson, J. E. Lovelock, M. O. Andreae, S. G. Warren, “Oceanic phytoplankton, atmospheric sulphur, cloud albedo and climate,” Nature (London) 326, 655–661 (1987).
[CrossRef]

Remote Sensing Environ. (1)

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]

Science (3)

R. J. Charlson, S. E. Schwartz, J. M. Hales, R. D. Cess, J. A. Coakley, J. E. Hansen, D. J. Hofmann, “Climate forcing by anthropogenic aerosols,” Science 225, 423–430 (1992).
[CrossRef]

W. A. Hovis, D. K. Clark, F. Anderson, R. W. Austin, W. H. Wilson, E. T. Baker, D. Ball, H. R. Gordon, J. L. Mueller, S. Y. E. Sayed, B. Strum, R. C. Wrigley, C. S. Yentsch, “Nimbus 7 coastal zone color scanner: system description and initial imagery,” Science 210, 60–63 (1980).
[CrossRef] [PubMed]

H. R. Gordon, D. K. Clark, J. L. Mueller, W. A. Hovis, “Phytoplankton pigments derived from the Nimbus-7 CZCS: initial comparisons with surface measurements,” Science 210, 63–66 (1980).
[CrossRef] [PubMed]

Other (4)

S. B. Hooker, W. E. Esaias, G. C. Feldman, W. W. Gregg, C. R. McClain, An Overview of SeaWiFS and Ocean Color, Volume 1 of SeaWiFS Tech. Rep. Series, NASA Tech. Memo. 104566 (NASA, Greenbelt, Md., 1992).

H. E. Gerber, E. E. Hindman, eds., Light Absorption by Aerosol Particles (Spectrum, Hampton, Va., 1982).

D. Deirmendjian, Electromagnetic Scattering on Spherical Polydispersions (Elsevier, New York, 1969).

M. Wang, “Atmospheric correction of the second generation ocean color sensors,” Ph.D. dissertation (University of Miami, Coral Gables, Fla., 1991).

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Figures (22)

Fig. 1
Fig. 1

Scattering processes for downward radiance in the two-layer atmosphere. Note that the surface reflection effects and multiple interaction between the two layers are not shown.

Fig. 2
Fig. 2

Aerosol phase functions used in the study: dotted curve, Haze L; dashed curve, Haze C; solid curve, Marine aerosol model.

Fig. 3
Fig. 3

ρt − ρr exp(− τa/μ) as a function of ρas for θ0 = 60°, θ = 60°, and ϕ = 90° at λ = 665 nm.

Fig. 4
Fig. 4

ρt − ρr exp(−τa/μ) as a function of ρas for θ0 = 60°, θ = 60°, and ϕ = 90° at λ = 443 nm.

Fig. 5
Fig. 5

Retrieved ω0(λ) and phase function Pa(ϴ, λ) as a function of scattering angle for a Marine aerosol with θ0 = 60° and τa = 0.3 at λ = 665 nm. The true ω0(λ) = 0.8.

Fig. 6
Fig. 6

Retrieved ω0(λ) and phase function Pa(ϴ, λ) as a function of scattering angle for a Marino aorosol with θ0 = 60° and τa = 0.3 at λ = 443 nm. The true ω0(λ) = 0.8.

Fig. 7
Fig. 7

Retrieved ω0(λ) and phase function Pa(ϴ, λ) as a function of scattering angle for a Haze L aerosol with θ0 = 60° and τa = 0.3 at λ = 665 nm. The true ω0(λ) = 0.8.

Fig. 8
Fig. 8

Retrieved ω0(λ) and phase function Pa(ϴ, λ) as a function of scattering angle for a Haze L aerosol with θ0 = 60° and τa = 0.3 at λ = 443 nm. The true ω0(λ) = 0.8.

Fig. 9
Fig. 9

Retrieved ω0(λ) and phase function Pa(ϴ, λ) as a function of scattering angle for a Haze C aerosol with θ0 = 60° and τa = 0.3 at λ = 665 nm. The true ω0(λ) = 0.8.

Fig. 10
Fig. 10

Retrieved ω0(λ) and phase function Pa(ϴ, λ) as a function of scattering angle for a Haze C aerosol with θ0 = 60° and τa = 0.3 at λ = 443 nm. The true ω0(λ) = 0.8.

Fig. 11
Fig. 11

Retrieved ω0(λ) as a function of the number of iterations for Marine, Haze L, and Haze C aerosols with θ0 = 60°, τa = 0.3, and λ = 665 nm. The true ω0(λ) = 0.8.

Fig. 12
Fig. 12

Error (percentage) in almucantar radiances ρt for different numbers of iterations for a Marine aerosol with θ0= 60°, θ = 60°, τa = 0.3, and λ = 665 nm. The true ω0(λ) = 0.8.

Fig. 13
Fig. 13

Error (percentage) in almucantar radiances ρt for different numbers of iterations for a Haze L aerosol with θ0= 60°, θ = 60°, τa = 0.3, and λ = 665 nm. The true ω0(λ) = 0.8.

Fig. 14
Fig. 14

Error (percentage) in almucantar radiances ρt for different numbers of iterations for a Haze C aerosol with θ0 = 60°, θ = 60°, τa = 0.3, and λ = 665 nm. The true ω0(λ) = 0.8.

Fig. 15
Fig. 15

Retrieved ω0(λ) and phase function Pa(ω, λ) as a function of scattering angle for a Marine aerosol with θ0 = 60° and τ0 = 0.3 at λ = 665 nm. The true ω0(λ) = 0.8, and ρ t ( m ) has a +10% bias error.

Fig. 16
Fig. 16

Retrieved ω0(λ) and phase function Pa(ϴ, λ) as a function of scattering angle for a Marine aerosol with θ0 = 60° and τa = 0.3 at λ = 665 nm. The true ω0(λ) = 0.8, and ρ t ( m ) has a −10% bias error.

Fig. 17
Fig. 17

Retrieved ω0(λ) and phase function Pa(ϴ, λ) as a function of scattering angle for a Marine aerosol with θ0 = 60° and τa = 0.3 at λ = 665 nm. The true ω0(λ) = 0.8, and τa has a +10% error.

Fig. 18
Fig. 18

Retrieved ω0(λ) and phase function Pa(ϴ, λ) as a function of scattering angle for a Marino aorosol with θ0 = 60° and τa = 0.3 at λ = 665 nm. The true ω0(λ) = 0.8, and τa has a −10% error.

Fig. 19
Fig. 19

Retrieved ω0(λ) and phase function Pa(ϴ, λ) as a function of scattering angle for a Marine aerosol with θ0 = 60° and τa = 0.3 at λ = 665 nm. The true ω0(λ) = 0.8, and ρ t ( m ) has a ±2% noise.

Fig. 20
Fig. 20

Retrieved ω0(λ) and phase function Pa(ϴ, λ) as a function of scattering angle for a Marine aerosol with θ0 = 60° and τa = 0.3 at λ = 665 nm. The true ω0(λ) = 0.8, and vertical structure of atmosphere is unknown.

Fig. 21
Fig. 21

Retrieved ω0(λ) and phase function Pa(ϴ, λ) as a function of scattering angle for a Marine aerosol with θ0 = 60° and τa = 0.1 at λ = 665 nm. The true ω0(λ) = 0.8, and ρ t ( m ) has a +5% bias error.

Fig. 22
Fig. 22

Retrieved ω0(λ) and phase function Pa(ϴ, λ) as a function of scattering angle for a Marine aerosol with θ0 = 60° and τa = 0.1 at λ = 443 nm. The true ω0(λ) = 0.8, and ρ t ( m ) has a +5% bias error.

Tables (4)

Tables Icon

Table 1 Error in Retrieved ω0(λ) and δave for Different Values of τa with θ0 = 60° and ω0 = 0.8

Tables Icon

Table 2 Error in Retrieved ω0(λ) and δave for Different Values of ω0 with θ0 = 60° and τa = 0.3

Tables Icon

Table 3 Error in Retrieved ω0(λ) and δave for Different Error Situations with τa = 0.3 and θ0 = 60°

Tables Icon

Table 4 Error in Retrieved ω0(λ) and δave for ±5% Bias Error in ρ t ( m ) with θ0 = 60° and τa = 0.1

Equations (25)

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

ρ = π L / F 0 cos θ 0 ,
ρ t ( λ ) = ρ r ( λ ) exp ( τ a / μ ) + ρ a ( λ ) exp ( τ r / μ 0 ) + ρ r a ( λ ) + ρ d ( λ ) exp [ ( τ r + τ a ) / μ 0 ] × δ ( μ μ 0 ) δ ( ϕ ϕ 0 ) ,
ρ t ( λ ) = ρ r ( λ ) exp ( τ a / μ ) + ρ a ( λ ) exp ( τ r / μ 0 ) + ρ r a ( λ ) .
ρ t ( λ ) ρ r ( λ ) exp ( τ a / μ ) = ρ a ( λ ) exp ( τ r / μ 0 ) + ρ r a ( λ ) .
ρ t ( λ ) ρ r ( λ ) exp ( τ a / μ ) ρ a s ( λ )
ρ a s ( λ ) = ω 0 ( λ ) τ a ( λ ) P a ( ϴ , λ ) / 4 cos θ cos θ 0 ,
cos ϴ = cos θ 0 cos θ + sin θ 0 sin θ cos ( ϕ ϕ 0 ) .
ρ t ( m ) ( λ ) ρ r ( c ) ( λ ) exp ( τ a / μ ) ρ a s ( m ) ( λ ) ,
ρ t ( c ) ( λ ) ρ r ( c ) ( λ ) exp ( τ a / μ ) ρ a s ( c ) ( λ ) ,
ρ a s ( m ) ( λ ) = τ a ( λ ) [ ω 0 ( λ ) P a ( ϴ , λ ) ] ( m ) / 4 cos θ cos θ 0 ,
ρ a s ( c ) = τ a ( λ ) [ ω 0 ( λ ) P a ( ϴ , λ ) ] ( c ) / 4 cos θ cos θ 0 .
ρ t ( c ) ( λ ) ρ t ( m ) ( λ ) ρ t ( m ) ( λ ) ρ r ( c ) ( λ ) exp ( τ a / μ ) = Δ [ ω 0 ( λ ) P a ( ϴ , λ ) ] [ ω 0 ( λ ) P a ( ϴ , λ ) ] ( m ) ,
Δ [ ω 0 ( λ ) P a ( ϴ , λ ) ] = [ ω 0 ( λ ) P a ( ϴ , λ ) ] ( c ) [ ω 0 ( λ ) P a ( ϴ , λ ) ] ( m ) .
Δ [ ω 0 ( λ ) P a ( ϴ , λ ) ] = ρ t ( c ) ( λ ) ρ t ( m ) ( λ ) ρ t ( m ) ( λ ) ρ r ( c ) ( λ ) exp ( τ a / μ ) [ ω 0 ( λ ) P a ( ϴ , λ ) ] ( m ) .
[ ω 0 ( λ ) P a ( ϴ , λ ) ] new = [ ω 0 ( λ ) P a ( ϴ , λ ) ] old C Δ [ ω 0 ( λ ) P a ( ϴ , λ ) ] ,
ω 0 ( λ ) = 1 2 0 π [ ω 0 ( λ ) P a ( ϴ , λ ) ] sin ϴ d ϴ ,
P a ( ϴ , λ ) = 1 ω 0 ( λ ) [ ω 0 ( λ ) P a ( ϴ , λ ) ] .
ρ t ( λ ) ρ r ( λ ) exp ( τ a / μ ) = a ( λ ) + b ( λ ) ρ a s ( λ ) + c ( λ ) ρ a s 2 ( λ ) .
ϴ max = θ 0 + ( π / 2 ) .
ω 0 ( λ ) P a ( ϴ , λ ) = ω 0 ( λ ) P a ( ϴ max , λ ) if ϴ > ϴ max ;
log [ ω 0 ( λ ) P a ( ϴ , λ ) ] ϴ if ϴ > ϴ max .
Δ [ ω 0 ( λ ) P a ( ϴ , λ ) ] = ρ t ( c ) ( λ ) ρ t ( m ) ( λ ) ρ t ( m ) ( λ ) ρ r ( c ) ( λ ) exp ( τ a / μ ) × [ ω 0 ( λ ) P a ( ϴ , λ ) ] old ,
[ ω 0 ( λ ) P a ( ϴ , λ ) ] new = [ ω 0 ( λ ) P a ( ϴ , λ ) ] old ½ Δ [ ω 0 ( λ ) P a ( ϴ , λ ) ] ,
δ i = [ ρ t ( c ) ] i [ ρ t ( m ) ] i [ ρ t ( m ) ] i 100 ,
δ ave = 1 N i = 1 N | δ i | ,

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