Abstract

An analysis of the errors due to multiple scattering which are expected to be encountered in application of the current Coastal Zone Color Scanner (CZCS) atmospheric correction algorithm is presented in detail. This was prompted by the observations of others that significant errors would be encountered if the present algorithm were applied to a hypothetical instrument possessing higher radiometric sensitivity than the present CZCS. This study provides CZCS users sufficient information with which to judge the efficacy of the current algorithm with the current sensor and enables them to estimate the impact of the algorithm-induced errors on their applications in a variety of situations. The greatest source of error is the assumption that the molecular and aerosol contributions to the total radiance observed at the sensor can be computed separately. This leads to the requirement that a value ′(λ,λ0) for the atmospheric correction parameter, which bears little resemblance to its theoretically meaningful counterpart, must usually be employed in the algorithm to obtain an accurate atmospheric correction. The behavior of ′(λ,λ0) with the aerosol optical thickness and aerosol phase function is thoroughly investigated through realistic modeling of radiative transfer in a stratified atmosphere over a Fresnel reflecting ocean. A unique feature of the analysis is that it is carried out in scan coordinates rather than typical earth–sun coordinates allowing elucidation of the errors along typical CZCS scan lines; this is important since, in the normal application of the algorithm, it is assumed that the same value of ′ can be used for an entire CZCS scene or at least for a reasonably large subscene. Two types of variation of ′ are found in models for which it would be constant in the single scattering approximation: (1) variation with scan angle in scenes in which a relatively large portion of the aerosol scattering phase function would be examined by the sensor in the single scattering approximation and (2) variation with aerosol optical thickness in a manner that increases with increasing solar zenith angle. In the worst case examined, the error associated with the variation of ′ with scan angle was found to be 2.7–5.4 counts in Band 1 (depending on the turbidity of the atmosphere) for a marine aerosol, while the error associated with the variation of ′ with aerosol optical thickness was at most 3 counts but would be reduced to negligible values when ′ could be determined in regions of high aerosol optical thickness. Since the water-leaving radiance must be determined with an accuracy of ≈1–2 digital counts for maximum usefulness, these worst-case errors indicate that typically the algorithm will perform with the required accuracy in the case of CZCS, if limited to subscenes which are not too large. However, since for a variety of reasons it is highly desirable to be able to estimate the value of ′ at each pixel, computations were performed to determine how accurately the algorithm would perform in retrieving the water-leaving radiance in the blue, assuming that it was known in the green and red. It is found that the simple expediency of decreasing the derived value of ′ in the blue by 5% was sufficent to decrease the error in the retrieved water-leaving radiance to <2 counts for a variety of aerosol phase functions and aerosol optical thicknesses (including mildly absorbing aerosols) and for several orbit geometries. Thus we conclude that in situations where ′ can be estimated at each pixel, this modification will result in water-leaving radiances with the desired accuracy in most cases.

© 1987 Optical Society of America

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References

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  1. H. R. Gordon, A. Y. Morel, Remote Assessment of Ocean Color for Interpretation of Satellite Visible Imagery: A Review (Springer-Verlag, New York, 1983), 114 pp.
  2. H. R. Gordon, “Removal of Atmospheric Effects from Satellite Imagery of the Oceans,” Appl. Opt. 17, 1631 (1978).
    [CrossRef] [PubMed]
  3. 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 Coastal Zone Color Scanner Measurements,” Appl. Opt. 22, 20 (1983).
    [CrossRef] [PubMed]
  4. R. C. Smith, W. H. Wilson, “Ship and Satellite Bio-optical Research in the California Bight,” in Oceanography from Space, J. F. R. Gower, Ed. (Plenum, New York, 1981), pp. 281–294.
    [CrossRef]
  5. 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]
  6. 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 (1983).
    [CrossRef] [PubMed]
  7. L. Elterman, “Vertical Attenuation Model with Eight Surface Meteorological Ranges 2 to 13 Kilometers,” Report AFCRL-70-0200 (AFCRL, Bedford, MA, 1970).
  8. K. L. Davidson, C. W. Fairall, “Optical Properties of the Maine Atmospheric Boundary Layer: Aerosol Profiles,” Proc. Soc. Photo-Opt. Instrum. Eng. 637, 18 (1986).
  9. K. Bullrich, “Scattered Radiation in the Atmosphere and the Natural Aerosol,” in Advances in Geophysics, H. E. Landsberg, J. V. Mieghem, Eds. (Academic, New York, 1964), pp. 99–260.
    [CrossRef]
  10. H. Quenzel, M. Kastner, “Optical Properties of the Atmosphere: Calculated Variability and Application to Satellite Remote Sensing of Phytoplankton,” Appl. Opt. 19, 1338 (1980).
    [CrossRef] [PubMed]
  11. B. Sturm, “Ocean Color Remote Sensing and the Retrieval of Surface Chlorophyll in Coastal Waters using the Nimbus-7 CZCS,” in Oceanography from Space, J. F. R. Gower, Ed. (Plenum, New York, 1981), pp. 267–280.
    [CrossRef]
  12. H. C. van de Hulst, Multiple Light Scattering (Academic, New York, 1985), pp. 739.
  13. 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. 24, 3929 (1983).
    [CrossRef]
  14. J. L. Mueller, “Nimbus-7 CZCS: Confirmation of its Radiometric Sensitivity Decay Rate Through 1982,” Appl. Opt. 24, 1043 (1985).
    [CrossRef] [PubMed]
  15. G. W. Kattawar, “A Three-Parameter Analytic Phase Function for Multiple Scattering Calculations,” J. Quant. Spectrosc. Radiat. Transfer 15, 839 (1975).
    [CrossRef]
  16. D. Deirmendjian, Electromagnetic Scattering on Spherical Polydispersions (Elsevier, New York, 1969), pp. 290.
  17. H. R. Gordon, “Coastal Zone Color Scanner Processing Algorithms: Recent Developments,” J. Opt. Soc. Am. A 1, 1283 (1984).

1986 (1)

K. L. Davidson, C. W. Fairall, “Optical Properties of the Maine Atmospheric Boundary Layer: Aerosol Profiles,” Proc. Soc. Photo-Opt. Instrum. Eng. 637, 18 (1986).

1985 (1)

1984 (1)

H. R. Gordon, “Coastal Zone Color Scanner Processing Algorithms: Recent Developments,” J. Opt. Soc. Am. A 1, 1283 (1984).

1983 (3)

1981 (1)

1980 (1)

1978 (1)

1975 (1)

G. W. Kattawar, “A Three-Parameter Analytic Phase Function for Multiple Scattering Calculations,” J. Quant. Spectrosc. Radiat. Transfer 15, 839 (1975).
[CrossRef]

Broenkow, W. W.

Brown, J. W.

Brown, O. B.

Bullrich, K.

K. Bullrich, “Scattered Radiation in the Atmosphere and the Natural Aerosol,” in Advances in Geophysics, H. E. Landsberg, J. V. Mieghem, Eds. (Academic, New York, 1964), pp. 99–260.
[CrossRef]

Clark, D. K.

Davidson, K. L.

K. L. Davidson, C. W. Fairall, “Optical Properties of the Maine Atmospheric Boundary Layer: Aerosol Profiles,” Proc. Soc. Photo-Opt. Instrum. Eng. 637, 18 (1986).

Deirmendjian, D.

D. Deirmendjian, Electromagnetic Scattering on Spherical Polydispersions (Elsevier, New York, 1969), pp. 290.

Deschamps, P. Y.

Elterman, L.

L. Elterman, “Vertical Attenuation Model with Eight Surface Meteorological Ranges 2 to 13 Kilometers,” Report AFCRL-70-0200 (AFCRL, Bedford, MA, 1970).

Evans, R. H.

Fairall, C. W.

K. L. Davidson, C. W. Fairall, “Optical Properties of the Maine Atmospheric Boundary Layer: Aerosol Profiles,” Proc. Soc. Photo-Opt. Instrum. Eng. 637, 18 (1986).

Gordon, H. R.

Herman, M.

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 (1975).
[CrossRef]

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), 114 pp.

Mueller, J. L.

Quenzel, H.

Smith, R. C.

R. C. Smith, W. H. Wilson, “Ship and Satellite Bio-optical Research in the California Bight,” in Oceanography from Space, J. F. R. Gower, Ed. (Plenum, New York, 1981), pp. 281–294.
[CrossRef]

Sturm, B.

B. Sturm, “Ocean Color Remote Sensing and the Retrieval of Surface Chlorophyll in Coastal Waters using the Nimbus-7 CZCS,” in Oceanography from Space, J. F. R. Gower, Ed. (Plenum, New York, 1981), pp. 267–280.
[CrossRef]

Tanre, D.

van de Hulst, H. C.

H. C. van de Hulst, Multiple Light Scattering (Academic, New York, 1985), pp. 739.

Wilson, W. H.

R. C. Smith, W. H. Wilson, “Ship and Satellite Bio-optical Research in the California Bight,” in Oceanography from Space, J. F. R. Gower, Ed. (Plenum, New York, 1981), pp. 281–294.
[CrossRef]

Appl. Opt. (7)

J. Opt. Soc. Am. A (1)

H. R. Gordon, “Coastal Zone Color Scanner Processing Algorithms: Recent Developments,” J. Opt. Soc. Am. A 1, 1283 (1984).

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 (1975).
[CrossRef]

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

K. L. Davidson, C. W. Fairall, “Optical Properties of the Maine Atmospheric Boundary Layer: Aerosol Profiles,” Proc. Soc. Photo-Opt. Instrum. Eng. 637, 18 (1986).

Other (7)

K. Bullrich, “Scattered Radiation in the Atmosphere and the Natural Aerosol,” in Advances in Geophysics, H. E. Landsberg, J. V. Mieghem, Eds. (Academic, New York, 1964), pp. 99–260.
[CrossRef]

B. Sturm, “Ocean Color Remote Sensing and the Retrieval of Surface Chlorophyll in Coastal Waters using the Nimbus-7 CZCS,” in Oceanography from Space, J. F. R. Gower, Ed. (Plenum, New York, 1981), pp. 267–280.
[CrossRef]

H. C. van de Hulst, Multiple Light Scattering (Academic, New York, 1985), pp. 739.

L. Elterman, “Vertical Attenuation Model with Eight Surface Meteorological Ranges 2 to 13 Kilometers,” Report AFCRL-70-0200 (AFCRL, Bedford, MA, 1970).

R. C. Smith, W. H. Wilson, “Ship and Satellite Bio-optical Research in the California Bight,” in Oceanography from Space, J. F. R. Gower, Ed. (Plenum, New York, 1981), pp. 281–294.
[CrossRef]

D. Deirmendjian, Electromagnetic Scattering on Spherical Polydispersions (Elsevier, New York, 1969), pp. 290.

H. R. Gordon, A. Y. Morel, Remote Assessment of Ocean Color for Interpretation of Satellite Visible Imagery: A Review (Springer-Verlag, New York, 1983), 114 pp.

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Figures (12)

Fig. 1
Fig. 1

Comparison between the model phase functions computed by Quenzel and Kastner10 (points) to represent marine aerosols at relative humidities of 70% (HMF7) and 90% (HMF9) and the two-term Henyey-Greenstein approximation (continuous curve) used in this study.

Fig. 2
Fig. 2

Sample computation of the total radiance across a CZCS scan line in Band 1 for Orbit 3226. The lower curve is the contribution due to Rayleigh scattering alone.

Fig. 3
Fig. 3

Variation of ′(λ14) across a CZCS scan line as a function τa(670) with n = 1 for Orbit 3226. The horizontal dashed line is the single-scattering value of 14) determined from Eq. (5).

Fig. 4
Fig. 4

Variation of 14) from Eq. (4) across a CZCS scan line as a function τa(670) with n = 1 for Orbit 3226, computed for an atmosphere with no Rayleigh scattering. The horizontal dashed line is the single scattering value of 14) determined from Eq. (5).

Fig. 5
Fig. 5

Variation of ′(λ14) across a CZCS scan line as a function τa(670) with n = 0 (lower curves) and 1 (upper curves) for Orbits 3226 (a), 2217 (b), 130 (c), and 2381 (d). Horizontal dashed lines are the single scattering values of 14) determined from Eq. (5).

Fig. 6
Fig. 6

Phase functions used in this study. The curve with the largest backscattering (scattering at Θ = 180°) is the two-term Henyey-Greenstein approximation to Haze L, the curve with intermediate backscattering the approximation to Haze C, and the lower curve the approximation to the marine aerosol model from Fig. 1.

Fig. 7
Fig. 7

Rayleigh–aerosol coupling term CR,P at 443 nm across a CZCS scan line for Orbit 2217 as a function of the aerosol phase function for τa(670) = 0.05 (a) and 0.20 (b) and n = 0. Curve L corresponds to Haze L, C to Haze C, and M to the marine aerosol model. Units for CR,P are CZCS gain 1 digital counts.

Fig. 8
Fig. 8

Variation of ′(λ14) across a CZCS scan line as a function of the aerosol phase function τa(670) with n = 0 (lower curves) and 1 (upper curves) for Orbit 2217: (a), for Haze C; and (b), for Haze L. The horizontal dashed lines are the single scattering values determined from Eq. (5).

Fig. 9
Fig. 9

Aerosol radiance at 670 nm (for the marine aerosol) as a function of τa(670) determined at the center of the scan for the four orbits considered in this study.

Fig. 10
Fig. 10

Variation of ′(λ,670) with wavelength (points) at the center of scan for Orbit 3226 with n = 0 (a) and n = 1 (b). The points correspond to τa(670) = 0.05, 0.10, 0.20, and 0.40; the solid lines are the fits to Eq. (13), and the dashed lines are the single scattering approximation to (λ,670) from Eq. (5).

Fig. 11
Fig. 11

Error in the recovered aerosol radiance (in digital counts) across the scan using the method described in the text for the four orbits studied with τa(670) = 0.2 and n = 0 (a), τa(670) = 0.2 and n = 1 (b), τa(670) = 0.4 and n = 1 (c), and τa(670) = 0.4 and n = 0 (d).

Fig. 12
Fig. 12

Error in the recovered aerosol radiance (in digital counts) across the scan using the method described in the text for Orbit 2217 with τa(670) = 0.4, n = 0 (a) and n = 1 (b). Curve 1 is the marine aerosol model with ωa = 1, curve 2 is the marine aerosol model with ωa = 0.9, curve 3 is the Haze L model with ωa = 1, and curve 4 is the Haze C model with ωa = 1.

Tables (3)

Tables Icon

Table I Scenes Examined in the Present Studya

Tables Icon

Table II Radiance for 1 CZCS Digital Count and F0

Tables Icon

Table III Angular Range ΔΘ of the Phase Function Examined During the Scan in the Single-Scattering Approximationa

Equations (30)

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L t ( λ ) = L r ( λ ) + L a ( λ ) + t ( λ ) L w ( λ ) .
L x = ω x ( λ ) τ x ( λ ) F 0 ( λ ) p x ( θ , θ 0 , λ ) / 4 π cos θ ,
p x ( θ , θ 0 , λ ) = P x ( θ - , λ ) + [ ρ ( θ ) + ρ ( θ 0 ) ] P x ( θ + , λ ) , cos θ ± = ± cos θ 0 cos θ - sin θ 0 sin θ cos ( ϕ - ϕ 0 ) ,
F 0 = F 0 exp [ - τ O z ( 1 / cos θ + 1 / cos θ 0 ) ] ,
t ( λ ) = exp [ - ( τ r / 2 + τ O z ) / cos θ ] t a ( λ ) ,
t a ( λ ) = exp { - [ 1 - ω a ( λ ) F a ( λ ) ] τ a ( λ ) / cos θ } ,
L a ( λ 2 ) L a ( λ 1 ) = ( λ 2 , λ 1 ) F 0 ( λ 2 ) F 0 ( λ 1 ) ,
( λ 2 , λ 1 ) = ω a ( λ 2 ) τ a ( λ 2 ) p a ( θ , θ 0 , λ 2 ) ω a ( λ 1 ) τ a ( λ 1 ) p a ( θ , θ 0 , λ 1 ) .
t ( λ i ) L w ( λ i ) = L t ( λ i ) - L r ( λ i ) - S ( λ i , λ 4 ) × [ L t ( λ 4 ) - L r ( λ 4 ) - t ( λ 4 ) L w ( λ 4 ) ]
S ( λ i , λ 4 ) = ( λ i , λ 4 ) F 0 ( λ i ) F 0 ( λ 4 ) .
f [ L w ( λ 1 ) , L w ( λ 3 ) , L w ( λ 4 ) ] = 0 ,
t ( λ 4 ) L w ( λ 4 ) = 0.
L w ( λ ) = [ L w ( λ ) ] N cos θ 0 exp [ - ( τ r / 2 + τ O z ) / cos θ 0 ] ,
b x = b x 0 exp ( - z / H x ) ,
τ x = b x 0 H x .
P a ( θ ) = α f ( θ , g 1 ) + ( 1 - α ) f ( θ , g 2 ) ,
f ( θ , g ) = 1 4 π ( 1 - g 2 ) ( 1 + g 2 - 2 g cos θ ) 3 / 2
α = 0.983 , g 1 = 0.82 , and g 2 = - 0.55.
τ a ( λ ) = [ λ 0 λ ] n τ a ( λ 0 ) ,
( λ , λ 0 ) = [ λ 0 λ ] n
C = 1.12 [ L w ( λ 3 ) L w ( λ 1 ) ] 1.7 .
δ C C = 1.7 δ L w ( λ 3 ) L w ( λ 3 ) 2 + δ L w ( λ 1 ) L w ( λ 1 ) 2 .
0.15 δ C C 0.18 ,
( λ i , λ 4 ) = [ λ 4 λ i ] n ( i )
Δ L a ( λ 1 ) = L t ( λ 1 ) - L r ( λ 1 ) - ( λ 1 , λ 4 ) F 0 ( λ 1 ) F 0 ( λ 4 ) [ L t ( λ 4 ) - L r ( λ 4 ) ]
( λ , λ 0 ) = F 0 ( λ 0 ) F 0 ( λ ) [ L t ( λ ) - L r ( λ ) L t ( λ 0 ) - L r ( λ 0 ) ] .
C R , P = L t ( λ ) - L r ( λ ) - L a ( λ ) ,
C R , P ( λ 4 ) L a ( λ 4 ) C R , P ( λ 1 ) L a ( λ 1 ) ,
( λ 1 , λ 4 ) ( λ 1 , λ 4 ) [ 1 + C R , P ( λ 1 ) L a ( λ 1 ) ] .
Δ L a ( λ 1 ) = Δ ( λ 1 , λ 4 ) L a ( λ 4 ) F 0 ( λ 1 ) F 0 ( λ 4 ) .

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