Abstract

We report a sensitivity analysis for the algorithm presented by Gordon and Zhang [Appl. Opt. 34, 5552 (1995)] for inverting the radiance exiting the top and bottom of the atmosphere to yield the aerosol-scattering phase function [P(Θ)] and single-scattering albedo (ω0). The study of the algorithm’s sensitivity to radiometric calibration errors, mean-zero instrument noise, sea-surface roughness, the curvature of the Earth’s atmosphere, the polarization of the light field, and incorrect assumptions regarding the vertical structure of the atmosphere, indicates that the retrieved ω0 has excellent stability even for very large values (∼2) of the aerosol optical thickness; however, the error in the retrieved P(Θ) strongly depends on the measurement error and on the assumptions made in the retrieval algorithm. The retrieved phase functions in the blue are usually poor compared with those in the near infrared.

© 1997 Optical Society of America

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References

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  1. 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]
  2. T. Zhang, “Remote sensing of aerosol properties over the ocean by combining surface and aircraft measurements,” Ph.D. dissertation (University of Miami, Coral Gables, Fla., 1995).
  3. 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]
  4. 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]
  5. G. W. Kattawar, “A three-parameter analytic phase function for multiple scattering calculations,” J. Quant. Spectrosc. Radiat. Transfer 15, 839–849 (1975).
    [CrossRef]
  6. 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., 1979).
  7. P. J. Reddy, F. W. Kreiner, J. J. Deluisi, Y. Kim, “Aerosol optical depths over the Atlantic derived from shipboard sunphotometer observations during the 1988 Global Change Expedition,” Global Biogeochem. Cycles 4, 225–240 (1990).
    [CrossRef]
  8. G. K. Korotaev, S. M. Sakerin, A. M. Ignatov, L. L. Stowe, E. P. McClain, “Sun-photometer observations of aerosol optical thickness over the North Atlantic from a Soviet research vessel for validation of satellite measurements,” J. Atmos. Oceanic Technol. 10, 725–735 (1993).
    [CrossRef]
  9. Y. V. Villevalde, A. V. Smirnov, N. T. O’Neill, S. P. Smyshlyaev, V. V. Yakovlev, “Measurement of aerosol optical depth in the Pacific Ocean and North Atlantic,” J. Geophys. Res. 99 D, 20983–20988 (1994).
    [CrossRef]
  10. C. Cox, W. Munk, “Measurements of the roughness of the sea surface from photographs of the Sun’s glitter,” J. Opt. Soc. Am. 44, 838–850 (1954).
    [CrossRef]
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  12. G. W. Kattawar, G. N. Plass, S. J. Hitzfelder, “Multiple scattered radiation emerging from Rayleigh and continental haze layers. 1: Radiance, polarization, and neutral points,” Appl. Opt. 15, 632–647 (1976).
    [CrossRef] [PubMed]
  13. H. R. Gordon, J. W. Brown, R. H. Evans, “Exact Rayleigh scattering calculations for use with the Nimbus-7 coastal zone color scanner,” Appl. Opt. 27, 862–871 (1988).
    [CrossRef] [PubMed]
  14. H. R. Gordon, M. Wang, “Surface roughness considerations for atmospheric correction of ocean color sensors. 1: The Rayleigh scattering component,” Appl. Opt. 31, 4247–4260 (1992).
    [CrossRef] [PubMed]
  15. 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]
  16. 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]
  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. D. J. Diner, C. J. Bruegge, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, P. J. Sellers, J. Clark, J. A. Daniels, E. D. Danielson, V. G. Duval, K. P. Klaasen, G. W. L. A. D. I. Nakamoto, R. Pagano, T. H. Reilly, “MISR: a Multi-Angle Imaging SpectroRadiometer for geophysical and climatological research from EOS,” IEEE Trans. Geosci. Remote Sensing 27, 200–214 (1989).
    [CrossRef]

1995 (1)

1994 (2)

Y. V. Villevalde, A. V. Smirnov, N. T. O’Neill, S. P. Smyshlyaev, V. V. Yakovlev, “Measurement of aerosol optical depth in the Pacific Ocean and North Atlantic,” J. Geophys. Res. 99 D, 20983–20988 (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)

G. K. Korotaev, S. M. Sakerin, A. M. Ignatov, L. L. Stowe, E. P. McClain, “Sun-photometer observations of aerosol optical thickness over the North Atlantic from a Soviet research vessel for validation of satellite measurements,” J. Atmos. Oceanic Technol. 10, 725–735 (1993).
[CrossRef]

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]

1992 (2)

1990 (1)

P. J. Reddy, F. W. Kreiner, J. J. Deluisi, Y. Kim, “Aerosol optical depths over the Atlantic derived from shipboard sunphotometer observations during the 1988 Global Change Expedition,” Global Biogeochem. Cycles 4, 225–240 (1990).
[CrossRef]

1989 (2)

D. J. Diner, C. J. Bruegge, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, P. J. Sellers, J. Clark, J. A. Daniels, E. D. Danielson, V. G. Duval, K. P. Klaasen, G. W. L. A. D. I. Nakamoto, R. Pagano, T. H. Reilly, “MISR: a Multi-Angle Imaging SpectroRadiometer for geophysical and climatological research from EOS,” IEEE Trans. Geosci. Remote Sensing 27, 200–214 (1989).
[CrossRef]

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]

1988 (1)

1979 (1)

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]

1976 (1)

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]

1954 (1)

Ackerman, T. P.

D. J. Diner, C. J. Bruegge, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, P. J. Sellers, J. Clark, J. A. Daniels, E. D. Danielson, V. G. Duval, K. P. Klaasen, G. W. L. A. D. I. Nakamoto, R. Pagano, T. H. Reilly, “MISR: a Multi-Angle Imaging SpectroRadiometer for geophysical and climatological research from EOS,” IEEE Trans. Geosci. Remote Sensing 27, 200–214 (1989).
[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]

Browell, E. V.

Brown, J. W.

Bruegge, C. J.

D. J. Diner, C. J. Bruegge, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, P. J. Sellers, J. Clark, J. A. Daniels, E. D. Danielson, V. G. Duval, K. P. Klaasen, G. W. L. A. D. I. Nakamoto, R. Pagano, T. H. Reilly, “MISR: a Multi-Angle Imaging SpectroRadiometer for geophysical and climatological research from EOS,” IEEE Trans. Geosci. Remote Sensing 27, 200–214 (1989).
[CrossRef]

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, J.

D. J. Diner, C. J. Bruegge, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, P. J. Sellers, J. Clark, J. A. Daniels, E. D. Danielson, V. G. Duval, K. P. Klaasen, G. W. L. A. D. I. Nakamoto, R. Pagano, T. H. Reilly, “MISR: a Multi-Angle Imaging SpectroRadiometer for geophysical and climatological research from EOS,” IEEE Trans. Geosci. Remote Sensing 27, 200–214 (1989).
[CrossRef]

Cox, C.

Daniels, J. A.

D. J. Diner, C. J. Bruegge, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, P. J. Sellers, J. Clark, J. A. Daniels, E. D. Danielson, V. G. Duval, K. P. Klaasen, G. W. L. A. D. I. Nakamoto, R. Pagano, T. H. Reilly, “MISR: a Multi-Angle Imaging SpectroRadiometer for geophysical and climatological research from EOS,” IEEE Trans. Geosci. Remote Sensing 27, 200–214 (1989).
[CrossRef]

Danielson, E. D.

D. J. Diner, C. J. Bruegge, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, P. J. Sellers, J. Clark, J. A. Daniels, E. D. Danielson, V. G. Duval, K. P. Klaasen, G. W. L. A. D. I. Nakamoto, R. Pagano, T. H. Reilly, “MISR: a Multi-Angle Imaging SpectroRadiometer for geophysical and climatological research from EOS,” IEEE Trans. Geosci. Remote Sensing 27, 200–214 (1989).
[CrossRef]

Davies, R.

D. J. Diner, C. J. Bruegge, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, P. J. Sellers, J. Clark, J. A. Daniels, E. D. Danielson, V. G. Duval, K. P. Klaasen, G. W. L. A. D. I. Nakamoto, R. Pagano, T. H. Reilly, “MISR: a Multi-Angle Imaging SpectroRadiometer for geophysical and climatological research from EOS,” IEEE Trans. Geosci. Remote Sensing 27, 200–214 (1989).
[CrossRef]

Deluisi, J. J.

P. J. Reddy, F. W. Kreiner, J. J. Deluisi, Y. Kim, “Aerosol optical depths over the Atlantic derived from shipboard sunphotometer observations during the 1988 Global Change Expedition,” Global Biogeochem. Cycles 4, 225–240 (1990).
[CrossRef]

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]

Diner, D. J.

D. J. Diner, C. J. Bruegge, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, P. J. Sellers, J. Clark, J. A. Daniels, E. D. Danielson, V. G. Duval, K. P. Klaasen, G. W. L. A. D. I. Nakamoto, R. Pagano, T. H. Reilly, “MISR: a Multi-Angle Imaging SpectroRadiometer for geophysical and climatological research from EOS,” IEEE Trans. Geosci. Remote Sensing 27, 200–214 (1989).
[CrossRef]

Ding, K.

K. Ding, “Radiative transfer in spherical shell atmospheres for correction of ocean color remote sensing,” Ph.D. dissertation (University of Miami, Coral Gables, Fla., 1993), 89 pp.

Duval, V. G.

D. J. Diner, C. J. Bruegge, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, P. J. Sellers, J. Clark, J. A. Daniels, E. D. Danielson, V. G. Duval, K. P. Klaasen, G. W. L. A. D. I. Nakamoto, R. Pagano, T. H. Reilly, “MISR: a Multi-Angle Imaging SpectroRadiometer for geophysical and climatological research from EOS,” IEEE Trans. Geosci. Remote Sensing 27, 200–214 (1989).
[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., 1979).

Gerstl, S. A. W.

D. J. Diner, C. J. Bruegge, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, P. J. Sellers, J. Clark, J. A. Daniels, E. D. Danielson, V. G. Duval, K. P. Klaasen, G. W. L. A. D. I. Nakamoto, R. Pagano, T. H. Reilly, “MISR: a Multi-Angle Imaging SpectroRadiometer for geophysical and climatological research from EOS,” IEEE Trans. Geosci. Remote Sensing 27, 200–214 (1989).
[CrossRef]

Gordon, H. R.

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]

Hitzfelder, S. J.

Ignatov, A. M.

G. K. Korotaev, S. M. Sakerin, A. M. Ignatov, L. L. Stowe, E. P. McClain, “Sun-photometer observations of aerosol optical thickness over the North Atlantic from a Soviet research vessel for validation of satellite measurements,” J. Atmos. Oceanic Technol. 10, 725–735 (1993).
[CrossRef]

Kattawar, G. W.

G. W. Kattawar, G. N. Plass, S. J. Hitzfelder, “Multiple scattered radiation emerging from Rayleigh and continental haze layers. 1: Radiance, polarization, and neutral points,” Appl. Opt. 15, 632–647 (1976).
[CrossRef] [PubMed]

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

Kim, Y.

P. J. Reddy, F. W. Kreiner, J. J. Deluisi, Y. Kim, “Aerosol optical depths over the Atlantic derived from shipboard sunphotometer observations during the 1988 Global Change Expedition,” Global Biogeochem. Cycles 4, 225–240 (1990).
[CrossRef]

King, M. D.

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]

Klaasen, K. P.

D. J. Diner, C. J. Bruegge, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, P. J. Sellers, J. Clark, J. A. Daniels, E. D. Danielson, V. G. Duval, K. P. Klaasen, G. W. L. A. D. I. Nakamoto, R. Pagano, T. H. Reilly, “MISR: a Multi-Angle Imaging SpectroRadiometer for geophysical and climatological research from EOS,” IEEE Trans. Geosci. Remote Sensing 27, 200–214 (1989).
[CrossRef]

Korotaev, G. K.

G. K. Korotaev, S. M. Sakerin, A. M. Ignatov, L. L. Stowe, E. P. McClain, “Sun-photometer observations of aerosol optical thickness over the North Atlantic from a Soviet research vessel for validation of satellite measurements,” J. Atmos. Oceanic Technol. 10, 725–735 (1993).
[CrossRef]

Kreiner, F. W.

P. J. Reddy, F. W. Kreiner, J. J. Deluisi, Y. Kim, “Aerosol optical depths over the Atlantic derived from shipboard sunphotometer observations during the 1988 Global Change Expedition,” Global Biogeochem. Cycles 4, 225–240 (1990).
[CrossRef]

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]

Martonchik, J. V.

D. J. Diner, C. J. Bruegge, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, P. J. Sellers, J. Clark, J. A. Daniels, E. D. Danielson, V. G. Duval, K. P. Klaasen, G. W. L. A. D. I. Nakamoto, R. Pagano, T. H. Reilly, “MISR: a Multi-Angle Imaging SpectroRadiometer for geophysical and climatological research from EOS,” IEEE Trans. Geosci. Remote Sensing 27, 200–214 (1989).
[CrossRef]

McClain, E. P.

G. K. Korotaev, S. M. Sakerin, A. M. Ignatov, L. L. Stowe, E. P. McClain, “Sun-photometer observations of aerosol optical thickness over the North Atlantic from a Soviet research vessel for validation of satellite measurements,” J. Atmos. Oceanic Technol. 10, 725–735 (1993).
[CrossRef]

Munk, W.

Nakamoto, G. W. L. A. D. I.

D. J. Diner, C. J. Bruegge, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, P. J. Sellers, J. Clark, J. A. Daniels, E. D. Danielson, V. G. Duval, K. P. Klaasen, G. W. L. A. D. I. Nakamoto, R. Pagano, T. H. Reilly, “MISR: a Multi-Angle Imaging SpectroRadiometer for geophysical and climatological research from EOS,” IEEE Trans. Geosci. Remote Sensing 27, 200–214 (1989).
[CrossRef]

O’Neill, N. T.

Y. V. Villevalde, A. V. Smirnov, N. T. O’Neill, S. P. Smyshlyaev, V. V. Yakovlev, “Measurement of aerosol optical depth in the Pacific Ocean and North Atlantic,” J. Geophys. Res. 99 D, 20983–20988 (1994).
[CrossRef]

Pagano, R.

D. J. Diner, C. J. Bruegge, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, P. J. Sellers, J. Clark, J. A. Daniels, E. D. Danielson, V. G. Duval, K. P. Klaasen, G. W. L. A. D. I. Nakamoto, R. Pagano, T. H. Reilly, “MISR: a Multi-Angle Imaging SpectroRadiometer for geophysical and climatological research from EOS,” IEEE Trans. Geosci. Remote Sensing 27, 200–214 (1989).
[CrossRef]

Plass, G. N.

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]

Reddy, P. J.

P. J. Reddy, F. W. Kreiner, J. J. Deluisi, Y. Kim, “Aerosol optical depths over the Atlantic derived from shipboard sunphotometer observations during the 1988 Global Change Expedition,” Global Biogeochem. Cycles 4, 225–240 (1990).
[CrossRef]

Reilly, T. H.

D. J. Diner, C. J. Bruegge, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, P. J. Sellers, J. Clark, J. A. Daniels, E. D. Danielson, V. G. Duval, K. P. Klaasen, G. W. L. A. D. I. Nakamoto, R. Pagano, T. H. Reilly, “MISR: a Multi-Angle Imaging SpectroRadiometer for geophysical and climatological research from EOS,” IEEE Trans. Geosci. Remote Sensing 27, 200–214 (1989).
[CrossRef]

Sakerin, S. M.

G. K. Korotaev, S. M. Sakerin, A. M. Ignatov, L. L. Stowe, E. P. McClain, “Sun-photometer observations of aerosol optical thickness over the North Atlantic from a Soviet research vessel for validation of satellite measurements,” J. Atmos. Oceanic Technol. 10, 725–735 (1993).
[CrossRef]

Sasano, Y.

Sellers, P. J.

D. J. Diner, C. J. Bruegge, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, P. J. Sellers, J. Clark, J. A. Daniels, E. D. Danielson, V. G. Duval, K. P. Klaasen, G. W. L. A. D. I. Nakamoto, R. Pagano, T. H. Reilly, “MISR: a Multi-Angle Imaging SpectroRadiometer for geophysical and climatological research from EOS,” IEEE Trans. Geosci. Remote Sensing 27, 200–214 (1989).
[CrossRef]

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., 1979).

Smirnov, A. V.

Y. V. Villevalde, A. V. Smirnov, N. T. O’Neill, S. P. Smyshlyaev, V. V. Yakovlev, “Measurement of aerosol optical depth in the Pacific Ocean and North Atlantic,” J. Geophys. Res. 99 D, 20983–20988 (1994).
[CrossRef]

Smyshlyaev, S. P.

Y. V. Villevalde, A. V. Smirnov, N. T. O’Neill, S. P. Smyshlyaev, V. V. Yakovlev, “Measurement of aerosol optical depth in the Pacific Ocean and North Atlantic,” J. Geophys. Res. 99 D, 20983–20988 (1994).
[CrossRef]

Stowe, L. L.

G. K. Korotaev, S. M. Sakerin, A. M. Ignatov, L. L. Stowe, E. P. McClain, “Sun-photometer observations of aerosol optical thickness over the North Atlantic from a Soviet research vessel for validation of satellite measurements,” J. Atmos. Oceanic Technol. 10, 725–735 (1993).
[CrossRef]

Villevalde, Y. V.

Y. V. Villevalde, A. V. Smirnov, N. T. O’Neill, S. P. Smyshlyaev, V. V. Yakovlev, “Measurement of aerosol optical depth in the Pacific Ocean and North Atlantic,” J. Geophys. Res. 99 D, 20983–20988 (1994).
[CrossRef]

Wang, M.

Yakovlev, V. V.

Y. V. Villevalde, A. V. Smirnov, N. T. O’Neill, S. P. Smyshlyaev, V. V. Yakovlev, “Measurement of aerosol optical depth in the Pacific Ocean and North Atlantic,” J. Geophys. Res. 99 D, 20983–20988 (1994).
[CrossRef]

Zhang, T.

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, “Remote sensing of aerosol properties over the ocean by combining surface and aircraft measurements,” Ph.D. dissertation (University of Miami, Coral Gables, Fla., 1995).

Appl. Opt. (7)

Global Biogeochem. Cycles (1)

P. J. Reddy, F. W. Kreiner, J. J. Deluisi, Y. Kim, “Aerosol optical depths over the Atlantic derived from shipboard sunphotometer observations during the 1988 Global Change Expedition,” Global Biogeochem. Cycles 4, 225–240 (1990).
[CrossRef]

IEEE Trans. Geosci. Remote Sensing (2)

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]

D. J. Diner, C. J. Bruegge, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, P. J. Sellers, J. Clark, J. A. Daniels, E. D. Danielson, V. G. Duval, K. P. Klaasen, G. W. L. A. D. I. Nakamoto, R. Pagano, T. H. Reilly, “MISR: a Multi-Angle Imaging SpectroRadiometer for geophysical and climatological research from EOS,” IEEE Trans. Geosci. Remote Sensing 27, 200–214 (1989).
[CrossRef]

J. Atmos. Oceanic Technol. (1)

G. K. Korotaev, S. M. Sakerin, A. M. Ignatov, L. L. Stowe, E. P. McClain, “Sun-photometer observations of aerosol optical thickness over the North Atlantic from a Soviet research vessel for validation of satellite measurements,” J. Atmos. Oceanic Technol. 10, 725–735 (1993).
[CrossRef]

J. Atmos. Sci. (1)

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).
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J. Geophys. Res. (1)

Y. V. Villevalde, A. V. Smirnov, N. T. O’Neill, S. P. Smyshlyaev, V. V. Yakovlev, “Measurement of aerosol optical depth in the Pacific Ocean and North Atlantic,” J. Geophys. Res. 99 D, 20983–20988 (1994).
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J. Opt. Soc. Am. (1)

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).
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Other (3)

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., 1979).

T. Zhang, “Remote sensing of aerosol properties over the ocean by combining surface and aircraft measurements,” Ph.D. dissertation (University of Miami, Coral Gables, Fla., 1995).

K. Ding, “Radiative transfer in spherical shell atmospheres for correction of ocean color remote sensing,” Ph.D. dissertation (University of Miami, Coral Gables, Fla., 1993), 89 pp.

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Figures (12)

Fig. 1
Fig. 1

Scattering phase functions for the Shettle and Fenn models M99 and T50.

Fig. 2
Fig. 2

Comparison between the true ω0P a(Θ) (solid curves) and the retrieved ω0P a(Θ) (circles) for λ = 865 nm and θ0 = 60°: (a) M99, (b) T50. Lower curves, τ a = 0.2; upper curves, τ a = 2.0 (values for τ a = 2.0 are ×10).

Fig. 3
Fig. 3

Percent error in ω0P a(Θ) for τ a = 0.2 (dashed curves) and τ a = 2.0 (solid curves) for λ = 865 nm and θ0 = 60°: (a) M99, (b) T50.

Fig. 4
Fig. 4

Percent error in the retrieved ω0P(Θ) when the measured τ a has a +5% error (solid curves) and a -5% error (dashed curves) with θ0 = 60° and λ = 865 nm: (a) T50, true τ a = 0.2; (b) M99, true τ a = 0.2; (c) T50, true τ a = 2.0; (d) M99, true τ a = 2.0.

Fig. 5
Fig. 5

Percent error in the retrieved ω0P(Θ) when ρ B (m) and ρ T (m) contain a +5% or -5% error for θ0 = 60° and λ = 865 nm: (a), (b) true τ a = 0.2; (c), (d) true τ a = 2.0. Note the change of scale between (a) and (b) and (c) and (d).

Fig. 6
Fig. 6

Percent error in the retrieved ω0P(Θ) for M99 aerosol when ρ B (m) and ρ T (m) contain a ±0.5% mean-zero Gaussian noise when θ0 = 60°: (a) λ = 865 nm, τ a = 0.2; (b) λ = 865 nm, τ a = 2.0; (c) λ = 412 nm, τ a = 0.2; (d) λ = 412 nm, τ a = 2.0. Note the change of scale between λ = 412 and 865 nm.

Fig. 7
Fig. 7

Percent error in the retrieved ω0P(Θ) for M99 aerosol when ρ B (m) and ρ T (m) are computed for a rough sea surface with W = 7.5 m/s and θ0 = 60°: (a) λ = 865 nm, τ a = 0.2; (b) λ = 865 nm, τ a = 2.0; (c) λ = 412 nm, τ a = 2.0; (d) λ = 412 nm, τ a = 2.0, but the downwelling principal plane data were replaced by upwelling data. Note the change of scale between (a) and (b) and (c) and (d).

Fig. 8
Fig. 8

Percent error in the retrieved ω0P(Θ) for M99 aerosol when ρ B (m) and ρ T (m) are computed by assuming a spherical shell atmosphere, with θ0 = 60° and λ = 865 nm: (a) τ a = 0.2; (b) τ a = 2.0.

Fig. 9
Fig. 9

Percent error in the retrieved ω0P(Θ) for T50 aerosol when ρ B (m) and ρ T (m) are computed by using the vector radiative transfer theory, with θ0 = 60° and λ = 865 nm: (a) τ a = 0.2; (b) τ a = 2.0; (c) τ a = 2.0, but the downwelling principal plane data were replaced by upwelling data.

Fig. 10
Fig. 10

Comparison between the true ω0P(Θ) (solid curve) and the retrieved ω0P(Θ) for M99 aerosol when Rayleigh scattering and aerosol scattering are mixed in both layers, with θ0 = 60° and λ = 865 nm: (a) retrieval code uses the correct vertical structure in τ a ; (b) retrieval code uses an incorrect vertical structure.

Fig. 11
Fig. 11

Same as Fig. 10, except λ = 412 nm.

Fig. 12
Fig. 12

Comparison between the true ω0P(Θ) (dashed curves), the retrieved ω0P(Θ) (circles), and the averaged ω0P(Θ) (solid curve) for the vertical structure described in the text, with θ0 = 60° and λ = 865 nm: (a) correct vertical structure; (b) incorrect vertical structure; (c) same as (a) except that the downwelling principal plane data were replaced by upwelling data.

Tables (1)

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Table 1 Error in retrieved ω0 at λ = 865 nm (M99)a

Equations (16)

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ρ=πL/F0 cos θ0,
ρT=ρr+ρa+ρra+tρw,
ρa+ρra=ρT-ρr-tρw.
ρT-ρr-tρw  ρas.
ρas=-ω0τaPΘ4 cos θ cos θ0, θ>90°,
cos Θ=cos θ0 cos θ+sin θ0 sin θ cosϕ-ϕ0.
ρTm-ρrc-tρwm-τaω0PΘt4 cos θ cos θ0,
ρTc-ρrc-tρwm-τaω0PΘc4 cos θ cos θ0,
ρTc-ρTmρTm-ρrc-tρwm=Δω0PΘω0PΘt,
Δω0PΘ=ω0PΘc-ω0PΘt.
Δω0PΘ=ρTc-ρTmρTm-ρrc-tρwmω0PΘt.
ω0PΘnew=ω0PΘold-CΔω0PΘ,
ω0=120πω0PΘsin ΘdΘ,
PΘ=1ω0ω0PΘ.
ω0PΘeffective=ω0PΘTτT+ω0PΘBτBτT+τB,
ω0effective=ω0TτT+ω0BτBτT+τB,

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