Abstract

For improved analysis of Coastal Zone Color Scanner (CZCS) imagery, the radiance reflected from a plane-parallel atmosphere and flat sea surface in the absence of aerosols (Rayleigh radiance) has been computed with an exact multiple scattering code, i.e., including polarization. The results indicate that the single scattering approximation normally used to compute this radiance can cause errors of up to 5% for small and moderate solar zenith angles. At large solar zenith angles, such as encountered in the analysis of high-latitude imagery, the errors can become much larger, e.g., >10% in the blue band. The single scattering error also varies along individual scan lines. Comparison with multiple scattering computations using scalar transfer theory, i.e., ignoring polarization, show that scalar theory can yield errors of approximately the same magnitude as single scattering when compared with exact computations at small to moderate values of the solar zenith angle. The exact computations can be easily incorporated into CZCS processing algorithms, and, for application to future instruments with higher radiometric sensitivity, a scheme is developed with which the effect of variations in the surface pressure could be easily and accurately included in the exact computation of the Rayleigh radiance. Direct application of these computations to CZCS imagery indicates that accurate atmospheric corrections can be made with solar zenith angles at least as large as 65° and probably up to at least 70° with a more sensitive instrument. This suggests that the new Rayleigh radiance algorithm should produce more consistent pigment retrievals, particularly at high latitudes.

© 1988 Optical Society of America

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References

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  1. W. A. Hovis et al., “Nimbus 7 Coastal Zone Color Scanner: System Description and Initial Imagery,” Science 210, 60 (1980).
    [CrossRef] [PubMed]
  2. 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 (1980).
    [CrossRef] [PubMed]
  3. H. R. Gordon, A. Y. Morel, Remote Assessment of Ocean Color for Interpretation of Satellite Visible Imagery: A Review (Springer-Verlag, New York, 1983).
  4. H. R. Gordon, “Removal of Atmospheric Effects from Satellite Imagery of the Oceans,” Appl. Opt. 17, 1631 (1978).
    [CrossRef] [PubMed]
  5. H. R. Gordon, D. K. Clark, “Atmospheric Effects in the Remote Sensing of Phytoplankton Pigments,” Boundary-Layer Meteorol. 18, 299 (1980).
    [CrossRef]
  6. M. Viollier, D. Tanre, P. Y. Deschamps, “An Algorithm for Remote Sensing of Water Color from Space,” Boundary-Layer Meterol. 18, 247 (1980).
    [CrossRef]
  7. 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 (1983).
    [CrossRef] [PubMed]
  8. H. R. Gordon, D. J. Castano, “The Coastal Zone Color Scanner Atmospheric Correction Algorithm: Multiple Scattering Effects,” Appl. Opt. 26, 2111 (1987).
    [CrossRef] [PubMed]
  9. H. R. Gordon, D. K. Clark, “Clear Water Radiances for Atmospheric Correction of Coastal Zone Color Scanner Imagery,” Appl. Opt. 20, 4175 (1981).
    [CrossRef] [PubMed]
  10. 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 (1976).
    [CrossRef] [PubMed]
  11. S. Chandrasekhar, Radiative Transfer (Oxford U.P., London, 1950).
  12. J. E. Hansen, L. D. Travis, “Light Scattering in Planetary Atmospheres,” Space Sci. Rev. 16, 527 (1974).
    [CrossRef]
  13. H. C. van de Hulst, Multiple Light Scattering (Academic, New York, 1980).
  14. W. A. Shurcliff, Polarized Light (Harvard U.P., Cambridge, MA, 1962).
  15. O. P. Bahethi, R. S. Fraser, “Effect of Molecular Anisotropy on the Intensity and Degree of Polarization of Light Scattered from Model Atmospheres,” Appl. Opt. 19, 1333 (1980).
    [CrossRef] [PubMed]
  16. A. T. Young, “Revised Depolarization Corrections for Atmospheric Extinction,” Appl. Opt. 19, 3427 (1980).
    [CrossRef] [PubMed]
  17. K. L. Coulson, J. V. Dave, Z. Sekera, Tables Relating to Radiation Emerging from a Planetary Atmosphere with Rayleigh Scattering (U. California Press, Berkeley, 1960).
  18. Z. Ahmad, R. S. Fraser, “An Iterative Radiative Transfer Code for Ocean Atmosphere Systems,” J. Atmos. Sci. 39, 656 (1982).
    [CrossRef]
  19. Z. Sekera, “The Effect of Sea Surface Reflection of the Sky Radiation,” Union Géodés. Géophys. Int. 10, 66 (1961).
  20. M. Abramowitz, I. A. Stegun, Eds., Handbook of Mathematical Functions (Dover, New York, 1970).
  21. The smallest value of ϑ in the set is 1.71°. For values of ϑ less than this, the principle of reciprocity11 was used to generate I0(0°,ϑ0) from I0(ϑ,0°). This requires one additional interpolation. Since I is a slowly varying function of ϑ near 0° this interpolation introduces little additional error; however, the error there may be somewhat >0.1%.
  22. D. G. Collins, W. G. Blattner, M. B. Wells, H. G. Horak, “Backward Monte Carlo Calculations of the Polarization Characteristics of the Radiation Emerging from Spherical-Shell Atmospheres,” Appl. Opt. 11, 2684 (1972).
    [CrossRef] [PubMed]
  23. C. N. Adams, G. W. Kattawar, “Radiative Transfer in Spherical Shell Atmospheres I. Rayleigh Scattering,” Icarus 35, 139 (1978).
    [CrossRef]
  24. Equation (2) is not the exact solution of the SRTE for single scattering. Rather, it is the limit of the exact solution as τr → 0.
  25. D. K. Clark, N. G. Maynard, “Coastal Zone Color Scanner Imagery of Phytoplankton Pigment Distribution in Icelandic Waters,” Proc. Soc. Photo-Opt. Instrum. Eng. 637, 350 (1986).
  26. 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 (1983).
    [CrossRef] [PubMed]
  27. H. Neckel, D. Labs, “The Solar Radiation Between 3300 and 12500 Å,” Sol. Phys. 90, 205 (1984).
    [CrossRef]
  28. H. Neckel, D. Labs, “Improved Data of Solar Spectral Irradiance from 0.33 to 1.25 μ,”Sol. Phys. 74, 231 (1981).
    [CrossRef]
  29. The normalized water-leaving radiance9 is defined according to Lw = [Lw]N cosϑ0t(ϑ0), where t(ϑ0) is the diffuse transmittance of the atmosphere. [Lw]N approximates the value of Lw that would be observed in the absence of the atmosphere with the sun at the zenith. Its use allows quantitative comparison of imagery acquired at different locations.
  30. The water-leaving radiance observed at the satellite is tLw, and since [Lw]N = Lw/cosϑ0t(ϑ0) the digitization interval for [Lw]N is much coarser than that for tLw, e.g., for ϑ0 = 65° at sensor gain 4 one dc corresponds to 0.0895, 0.0460, and 0.0367 mW/cm2μm sr in [Lw]N, respectively, at 443, 520, and 550 nm.
  31. When the CZCS saturates on scanning across a bright cloud from west to east, there is a residual effect due to electronic overshoot that can be observed for 50–100 pixels to the east of the cloud.
  32. Recall that the CZCS is in an ascending orbit with the node occurring near local noon. Therefore the values of ϑ0 associated with the imagery refer to times near local noon, i.e., the smallest values of ϑ0 for the entire day.
  33. D. K. Clark, “Phytoplankton Algorithms for the Nimbus-7 CZCS,” in Oceanography from Space, J. R. F. Gower, Ed. (Plenum, New York, 1981), pp. 227–238.
    [CrossRef]

1987

1986

D. K. Clark, N. G. Maynard, “Coastal Zone Color Scanner Imagery of Phytoplankton Pigment Distribution in Icelandic Waters,” Proc. Soc. Photo-Opt. Instrum. Eng. 637, 350 (1986).

1984

H. Neckel, D. Labs, “The Solar Radiation Between 3300 and 12500 Å,” Sol. Phys. 90, 205 (1984).
[CrossRef]

1983

1982

Z. Ahmad, R. S. Fraser, “An Iterative Radiative Transfer Code for Ocean Atmosphere Systems,” J. Atmos. Sci. 39, 656 (1982).
[CrossRef]

1981

1980

H. R. Gordon, D. K. Clark, “Atmospheric Effects in the Remote Sensing of Phytoplankton Pigments,” Boundary-Layer Meteorol. 18, 299 (1980).
[CrossRef]

M. Viollier, D. Tanre, P. Y. Deschamps, “An Algorithm for Remote Sensing of Water Color from Space,” Boundary-Layer Meterol. 18, 247 (1980).
[CrossRef]

W. A. Hovis et al., “Nimbus 7 Coastal Zone Color Scanner: System Description and Initial Imagery,” Science 210, 60 (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 (1980).
[CrossRef] [PubMed]

O. P. Bahethi, R. S. Fraser, “Effect of Molecular Anisotropy on the Intensity and Degree of Polarization of Light Scattered from Model Atmospheres,” Appl. Opt. 19, 1333 (1980).
[CrossRef] [PubMed]

A. T. Young, “Revised Depolarization Corrections for Atmospheric Extinction,” Appl. Opt. 19, 3427 (1980).
[CrossRef] [PubMed]

1978

H. R. Gordon, “Removal of Atmospheric Effects from Satellite Imagery of the Oceans,” Appl. Opt. 17, 1631 (1978).
[CrossRef] [PubMed]

C. N. Adams, G. W. Kattawar, “Radiative Transfer in Spherical Shell Atmospheres I. Rayleigh Scattering,” Icarus 35, 139 (1978).
[CrossRef]

1976

1974

J. E. Hansen, L. D. Travis, “Light Scattering in Planetary Atmospheres,” Space Sci. Rev. 16, 527 (1974).
[CrossRef]

1972

1961

Z. Sekera, “The Effect of Sea Surface Reflection of the Sky Radiation,” Union Géodés. Géophys. Int. 10, 66 (1961).

Adams, C. N.

C. N. Adams, G. W. Kattawar, “Radiative Transfer in Spherical Shell Atmospheres I. Rayleigh Scattering,” Icarus 35, 139 (1978).
[CrossRef]

Ahmad, Z.

Z. Ahmad, R. S. Fraser, “An Iterative Radiative Transfer Code for Ocean Atmosphere Systems,” J. Atmos. Sci. 39, 656 (1982).
[CrossRef]

Bahethi, O. P.

Blattner, W. G.

Broenkow, W. W.

Brown, J. W.

Brown, O. B.

Castano, D. J.

Chandrasekhar, S.

S. Chandrasekhar, Radiative Transfer (Oxford U.P., London, 1950).

Clark, D. K.

D. K. Clark, N. G. Maynard, “Coastal Zone Color Scanner Imagery of Phytoplankton Pigment Distribution in Icelandic Waters,” Proc. Soc. Photo-Opt. Instrum. Eng. 637, 350 (1986).

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 (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 (1983).
[CrossRef] [PubMed]

H. R. Gordon, D. K. Clark, “Clear Water Radiances for Atmospheric Correction of Coastal Zone Color Scanner Imagery,” Appl. Opt. 20, 4175 (1981).
[CrossRef] [PubMed]

H. R. Gordon, D. K. Clark, “Atmospheric Effects in the Remote Sensing of Phytoplankton Pigments,” Boundary-Layer Meteorol. 18, 299 (1980).
[CrossRef]

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 (1980).
[CrossRef] [PubMed]

D. K. Clark, “Phytoplankton Algorithms for the Nimbus-7 CZCS,” in Oceanography from Space, J. R. F. Gower, Ed. (Plenum, New York, 1981), pp. 227–238.
[CrossRef]

Collins, D. G.

Coulson, K. L.

K. L. Coulson, J. V. Dave, Z. Sekera, Tables Relating to Radiation Emerging from a Planetary Atmosphere with Rayleigh Scattering (U. California Press, Berkeley, 1960).

Dave, J. V.

K. L. Coulson, J. V. Dave, Z. Sekera, Tables Relating to Radiation Emerging from a Planetary Atmosphere with Rayleigh Scattering (U. California Press, Berkeley, 1960).

Deschamps, P. Y.

M. Viollier, D. Tanre, P. Y. Deschamps, “An Algorithm for Remote Sensing of Water Color from Space,” Boundary-Layer Meterol. 18, 247 (1980).
[CrossRef]

Evans, R. H.

Fraser, R. S.

Gordon, H. R.

Hansen, J. E.

J. E. Hansen, L. D. Travis, “Light Scattering in Planetary Atmospheres,” Space Sci. Rev. 16, 527 (1974).
[CrossRef]

Hitzfelder, S. J.

Horak, H. G.

Hovis, W. A.

W. A. Hovis et al., “Nimbus 7 Coastal Zone Color Scanner: System Description and Initial Imagery,” Science 210, 60 (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 (1980).
[CrossRef] [PubMed]

Kattawar, G. W.

Labs, D.

H. Neckel, D. Labs, “The Solar Radiation Between 3300 and 12500 Å,” Sol. Phys. 90, 205 (1984).
[CrossRef]

H. Neckel, D. Labs, “Improved Data of Solar Spectral Irradiance from 0.33 to 1.25 μ,”Sol. Phys. 74, 231 (1981).
[CrossRef]

Maynard, N. G.

D. K. Clark, N. G. Maynard, “Coastal Zone Color Scanner Imagery of Phytoplankton Pigment Distribution in Icelandic Waters,” Proc. Soc. Photo-Opt. Instrum. Eng. 637, 350 (1986).

Morel, A. Y.

H. R. Gordon, A. Y. Morel, Remote Assessment of Ocean Color for Interpretation of Satellite Visible Imagery: A Review (Springer-Verlag, New York, 1983).

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 (1980).
[CrossRef] [PubMed]

Neckel, H.

H. Neckel, D. Labs, “The Solar Radiation Between 3300 and 12500 Å,” Sol. Phys. 90, 205 (1984).
[CrossRef]

H. Neckel, D. Labs, “Improved Data of Solar Spectral Irradiance from 0.33 to 1.25 μ,”Sol. Phys. 74, 231 (1981).
[CrossRef]

Plass, G. N.

Sekera, Z.

Z. Sekera, “The Effect of Sea Surface Reflection of the Sky Radiation,” Union Géodés. Géophys. Int. 10, 66 (1961).

K. L. Coulson, J. V. Dave, Z. Sekera, Tables Relating to Radiation Emerging from a Planetary Atmosphere with Rayleigh Scattering (U. California Press, Berkeley, 1960).

Shurcliff, W. A.

W. A. Shurcliff, Polarized Light (Harvard U.P., Cambridge, MA, 1962).

Tanre, D.

M. Viollier, D. Tanre, P. Y. Deschamps, “An Algorithm for Remote Sensing of Water Color from Space,” Boundary-Layer Meterol. 18, 247 (1980).
[CrossRef]

Travis, L. D.

J. E. Hansen, L. D. Travis, “Light Scattering in Planetary Atmospheres,” Space Sci. Rev. 16, 527 (1974).
[CrossRef]

van de Hulst, H. C.

H. C. van de Hulst, Multiple Light Scattering (Academic, New York, 1980).

Viollier, M.

M. Viollier, D. Tanre, P. Y. Deschamps, “An Algorithm for Remote Sensing of Water Color from Space,” Boundary-Layer Meterol. 18, 247 (1980).
[CrossRef]

Wells, M. B.

Young, A. T.

Appl. Opt.

D. G. Collins, W. G. Blattner, M. B. Wells, H. G. Horak, “Backward Monte Carlo Calculations of the Polarization Characteristics of the Radiation Emerging from Spherical-Shell Atmospheres,” Appl. Opt. 11, 2684 (1972).
[CrossRef] [PubMed]

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 (1976).
[CrossRef] [PubMed]

H. R. Gordon, “Removal of Atmospheric Effects from Satellite Imagery of the Oceans,” Appl. Opt. 17, 1631 (1978).
[CrossRef] [PubMed]

O. P. Bahethi, R. S. Fraser, “Effect of Molecular Anisotropy on the Intensity and Degree of Polarization of Light Scattered from Model Atmospheres,” Appl. Opt. 19, 1333 (1980).
[CrossRef] [PubMed]

H. R. Gordon, D. K. Clark, “Clear Water Radiances for Atmospheric Correction of Coastal Zone Color Scanner Imagery,” Appl. Opt. 20, 4175 (1981).
[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 (1983).
[CrossRef] [PubMed]

H. R. Gordon, D. J. Castano, “The Coastal Zone Color Scanner Atmospheric Correction Algorithm: Multiple Scattering Effects,” Appl. Opt. 26, 2111 (1987).
[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 (1983).
[CrossRef] [PubMed]

A. T. Young, “Revised Depolarization Corrections for Atmospheric Extinction,” Appl. Opt. 19, 3427 (1980).
[CrossRef] [PubMed]

Boundary-Layer Meteorol.

H. R. Gordon, D. K. Clark, “Atmospheric Effects in the Remote Sensing of Phytoplankton Pigments,” Boundary-Layer Meteorol. 18, 299 (1980).
[CrossRef]

Boundary-Layer Meterol.

M. Viollier, D. Tanre, P. Y. Deschamps, “An Algorithm for Remote Sensing of Water Color from Space,” Boundary-Layer Meterol. 18, 247 (1980).
[CrossRef]

Icarus

C. N. Adams, G. W. Kattawar, “Radiative Transfer in Spherical Shell Atmospheres I. Rayleigh Scattering,” Icarus 35, 139 (1978).
[CrossRef]

J. Atmos. Sci.

Z. Ahmad, R. S. Fraser, “An Iterative Radiative Transfer Code for Ocean Atmosphere Systems,” J. Atmos. Sci. 39, 656 (1982).
[CrossRef]

Proc. Soc. Photo-Opt. Instrum. Eng.

D. K. Clark, N. G. Maynard, “Coastal Zone Color Scanner Imagery of Phytoplankton Pigment Distribution in Icelandic Waters,” Proc. Soc. Photo-Opt. Instrum. Eng. 637, 350 (1986).

Science

W. A. Hovis et al., “Nimbus 7 Coastal Zone Color Scanner: System Description and Initial Imagery,” Science 210, 60 (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 (1980).
[CrossRef] [PubMed]

Sol. Phys.

H. Neckel, D. Labs, “The Solar Radiation Between 3300 and 12500 Å,” Sol. Phys. 90, 205 (1984).
[CrossRef]

H. Neckel, D. Labs, “Improved Data of Solar Spectral Irradiance from 0.33 to 1.25 μ,”Sol. Phys. 74, 231 (1981).
[CrossRef]

Space Sci. Rev.

J. E. Hansen, L. D. Travis, “Light Scattering in Planetary Atmospheres,” Space Sci. Rev. 16, 527 (1974).
[CrossRef]

Union Géodés. Géophys. Int.

Z. Sekera, “The Effect of Sea Surface Reflection of the Sky Radiation,” Union Géodés. Géophys. Int. 10, 66 (1961).

Other

M. Abramowitz, I. A. Stegun, Eds., Handbook of Mathematical Functions (Dover, New York, 1970).

The smallest value of ϑ in the set is 1.71°. For values of ϑ less than this, the principle of reciprocity11 was used to generate I0(0°,ϑ0) from I0(ϑ,0°). This requires one additional interpolation. Since I is a slowly varying function of ϑ near 0° this interpolation introduces little additional error; however, the error there may be somewhat >0.1%.

Equation (2) is not the exact solution of the SRTE for single scattering. Rather, it is the limit of the exact solution as τr → 0.

H. C. van de Hulst, Multiple Light Scattering (Academic, New York, 1980).

W. A. Shurcliff, Polarized Light (Harvard U.P., Cambridge, MA, 1962).

K. L. Coulson, J. V. Dave, Z. Sekera, Tables Relating to Radiation Emerging from a Planetary Atmosphere with Rayleigh Scattering (U. California Press, Berkeley, 1960).

H. R. Gordon, A. Y. Morel, Remote Assessment of Ocean Color for Interpretation of Satellite Visible Imagery: A Review (Springer-Verlag, New York, 1983).

S. Chandrasekhar, Radiative Transfer (Oxford U.P., London, 1950).

The normalized water-leaving radiance9 is defined according to Lw = [Lw]N cosϑ0t(ϑ0), where t(ϑ0) is the diffuse transmittance of the atmosphere. [Lw]N approximates the value of Lw that would be observed in the absence of the atmosphere with the sun at the zenith. Its use allows quantitative comparison of imagery acquired at different locations.

The water-leaving radiance observed at the satellite is tLw, and since [Lw]N = Lw/cosϑ0t(ϑ0) the digitization interval for [Lw]N is much coarser than that for tLw, e.g., for ϑ0 = 65° at sensor gain 4 one dc corresponds to 0.0895, 0.0460, and 0.0367 mW/cm2μm sr in [Lw]N, respectively, at 443, 520, and 550 nm.

When the CZCS saturates on scanning across a bright cloud from west to east, there is a residual effect due to electronic overshoot that can be observed for 50–100 pixels to the east of the cloud.

Recall that the CZCS is in an ascending orbit with the node occurring near local noon. Therefore the values of ϑ0 associated with the imagery refer to times near local noon, i.e., the smallest values of ϑ0 for the entire day.

D. K. Clark, “Phytoplankton Algorithms for the Nimbus-7 CZCS,” in Oceanography from Space, J. R. F. Gower, Ed. (Plenum, New York, 1981), pp. 227–238.
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

Relative error Δ(single) (%) in the single scattering computation of Lr compared to the exact result across a CZCS scan line for Orbit 130. Pixel 0 is at the western edge of the scan and pixel 1968 is at the eastern edge. The sensor is operating in the untilted mode and ϑ0 ≈ 42°. The curves labeled 1, 3, and 4 correspond, respectively, to CZCS Bands 1, 3, and 4. The result for Band 2 (not shown) is similar to Band 3.

Fig. 2
Fig. 2

Relative error Δ(single) (%) in the single scattering computation of Lr compared to the exact result across a CZCS scan line for Orbit 3226. Pixel 0 is at the western edge of the scan and pixel 1968 is at the eastern edge. The sensor is operating with a tilt of 20° and ϑ0 ≈ 22°. The curves labeled 1, 3, and 4 correspond, respectively, to CZCS Bands 1, 3, and 4. The result for Band 2 (not shown) is similar to Band 3.

Fig. 3
Fig. 3

Relative error Δ(single) (%) in the single scattering computation of Lr compared to the exact result at the center of the scan as a function of latitude for Orbit 2381. The sensor is operating in the untilted mode. The numbers written just above the shorter latitude tick marks provide ϑ0 at the given location. The curves labeled 1, 3, and 4 correspond, respectively, to CZCS Bands 1, 3, and 4. The result for Band 2 (not shown) is similar to Band 3.

Fig. 4
Fig. 4

Relative error Δ(scalar) (%) in the single scattering computation of Lr compared to the exact result across a CZCS scan line for Orbit 130. Pixel 0 is at the western edge of the scan and pixel 1968 is at the eastern edge. The sensor is operating in the untilted mode and ϑ0 ≈ 42°. The curves labeled 1, 3, and 4 correspond, respectively, to CZCS Bands 1, 3, and 4. The result for Band 2 (not shown) is similar to Band 3.

Fig. 5
Fig. 5

Relative error Δ(scalar) (%) in the single scattering computation of Lr compared to the exact result across a CZCS scan line for Orbit 3226. Pixel 0 is at the western edge of the scan and pixel 1968 is at the eastern edge. The sensor is operating with a tilt of 20° and ϑ0 ≈ 22°. The curves labeled 1, 3, and 4 correspond, respectively, to CZCS Bands 1, 3, and 4. The result for Band 2 (not shown) is similar to Band 3.

Fig. 6
Fig. 6

Geographical setting of the CZCS imagery from Orbit 1020 near Japan. Over the light gray background, the white areas are open water, the dark gray areas are land, and the medium gray areas are clouds. The normalized water-leaving radiances presented in Figs. 7 and 8 were computed along the two lines drawn in the figure.

Fig. 7
Fig. 7

Recovered values of [Lw(443)]N along the western line drawn in Fig. 6. The exact computation of Lr is Used for the upper curve and the single scattering approximation to Lr has been used for the lower curve. The data have been edited to remove clouds and filtered to reduce noise.

Fig. 8
Fig. 8

Recovered values of (a) [Lw(443)]N, (b) [Lw(520)]N, and (c) [Lw(550)]N along the eastern line drawn in Fig. 6. The exact computation of Lr is used for the upper curves and the single scattering approximation to Lr has been used for the lower curves. (d) La(670) is the aerosol radiance deduced using the exact computation of Lr. The data have been edited to remove clouds and filtered to reduce noise.

Tables (2)

Tables Icon

Table I Variation of Lr Across the CZCS Scan

Tables Icon

Table II Values of C(λ) and F0(λ) (mW/cm2μm sr) to be Used with the Exact (New) and the Single Scattering (Old) Computations of Lr

Equations (14)

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

L t = L r + L a + t L w ,
L r = τ r ( λ ) F 0 ( λ ) p r ( ϑ , ϑ 0 , λ ) / 4 π ,
p r ( ϑ , ϑ 0 , λ ) = { P r ( ϑ , λ ) + [ ρ ( ϑ ) + ρ ( ϑ 0 ) ] P r ( ϑ + , λ ) } / cos ϑ , cos ϑ ± = ± cos ϑ 0 cos ϑ sin ϑ 0 sin ϑ cos ( φ φ 0 ) ,
P r ( α ) = 3 4 [ 1 + cos 2 α ] ,
F 0 = F 0 exp [ τ Oz ( 1 / cos ϑ + 1 / cos ϑ 0 ) ] ,
I ( ϑ , ϑ 0 , Δ φ ) = m = 0 2 I m ( ϑ , ϑ 0 ) cos m Δ φ ,
k s = 8 π 3 3 ( n 2 1 ) 2 λ 4 N [ 6 + 3 δ 6 7 δ ] ,
τ r = 0 k s ρ ( z ) d z ,
τ r 0 = 0 . 008569 λ 4 ( 1 + 0 . 0113 λ 2 + 0 . 00013 λ 4 ) ,
τ r = P P 0 τ r 0 .
Δ ( single ) L r ( single ) L r ( exact ) L r ( exact )
Δ ( scalar ) L r ( scalar ) L r ( exact ) L r ( exact ) .
I I = [ 1 exp ( τ r / cos ϑ ) ] [ 1 exp ( τ r / cos ϑ ) ] .
L t ( λ ) = C ( λ ) [ A ( λ ) N ( λ ) + B ( λ ) ] f 1 ( λ , t ) ,

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