Abstract

A methodology for determination of the effects of radiometric noise on the performance of ocean color sensors is developed and applied to the Coastal Zone Color Scanner on Nimbus 7 and the Moderate Resolution Imaging Spectrometer planned for the Earth Observing System.

© 1990 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, 60–63 (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, 63–66 (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), 114 pp.
  4. J. J. Walsh, “The Marine Resources Experiment (MAREX),” NASA Goddard Space Flight Center, Report of the Ocean Color Science Working Group, 1982 (U.S. Government Printing Office: 1983-397-034).
  5. NASA, “Earth Observing System: Science and Mission Requirements Working Group Report,” (Technical Memorandum 86129, August1984).
  6. NASA and the Earth Observations Satellite Company, “System Concept for Wide-Field-of-View Observations of Ocean Phenomena from Space,” (August1987).
  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 between Ship Determinations and Coastal Zone Color Scanner Estimates,” Appl. Opt. 22, 20–36 (1983).
    [CrossRef] [PubMed]
  8. D. Tanre, M. Herman, P. Y. Deschamps, A. de Leffe, “Atmospheric Modeling for Space Measurements of Ground Reflectances, Including Bidirectional Properties,” Appl. Opt. 18, 3587–3594 (1979).
    [CrossRef] [PubMed]
  9. H. R. Gordon, D. K. Clark, “Clear Water Radiances for Atmospheric Correction of Coastal Zone Color Scanner Imagery,” Appl. Opt. 20, 4175–4180 (1981).
    [CrossRef] [PubMed]
  10. 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]
  11. H. R. Gordon, D. J. Castano, “The Coastal Zone Color Scanner Atmospheric Correction Algorithm: Multiple Scattering Effects,” Appl. Opt. 26, 2111–2122 (1987).
    [CrossRef] [PubMed]
  12. D. K. Clark, “Phytoplankton Algorithms for the Nimbus-7 CZCS,” in Oceanography from Space, J. R. F. Gower, Ed. (Plenum, New York, 1981) p. 227–238.
    [CrossRef]
  13. H. R. Gordon et al., “A Semi-Analytic Radiance Model of Ocean Color,” J. Geophys. Res. 93, 10909–10924 (1988).
    [CrossRef]
  14. A Morel, L. Prieur, “Analysis of Variations in Ocean Color,” Limnol. and Oceanog. 22, 709–722 (1977).
    [CrossRef]
  15. 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]
  16. NASA, “Earth Observing System (EOS) Background Information Package, Announcement of Opportunity No. OSSA-1-88,” (Announcement of Opportunity No. OSSA-1-88,” January1988).
  17. Ball Aerospace Division, Boulder CO, Development of the Coastal Zone Color Scanner for Nimbus-7: Volume 2—Test and Performance Data (Final Report F78–11, Rev. A NASA Contract NAS5-20900, May1979).

1988 (2)

1987 (1)

1983 (2)

1981 (1)

1980 (2)

W. A. Hovis et al., “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]

1979 (1)

1977 (1)

A Morel, L. Prieur, “Analysis of Variations in Ocean Color,” Limnol. and Oceanog. 22, 709–722 (1977).
[CrossRef]

Broenkow, W. W.

Brown, J. W.

Brown, O. B.

Castano, D. J.

Clark, D. K.

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 between Ship Determinations and Coastal Zone Color Scanner Estimates,” Appl. Opt. 22, 20–36 (1983).
[CrossRef] [PubMed]

H. R. Gordon, D. K. Clark, “Clear Water Radiances for Atmospheric Correction of Coastal Zone Color Scanner Imagery,” Appl. Opt. 20, 4175–4180 (1981).
[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]

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

de Leffe, A.

Deschamps, P. Y.

Evans, R. H.

Gordon, H. R.

Herman, M.

Hovis, W. A.

W. A. Hovis et al., “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]

Morel, A

A Morel, L. Prieur, “Analysis of Variations in Ocean Color,” Limnol. and Oceanog. 22, 709–722 (1977).
[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.

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]

Prieur, L.

A Morel, L. Prieur, “Analysis of Variations in Ocean Color,” Limnol. and Oceanog. 22, 709–722 (1977).
[CrossRef]

Tanre, D.

Walsh, J. J.

J. J. Walsh, “The Marine Resources Experiment (MAREX),” NASA Goddard Space Flight Center, Report of the Ocean Color Science Working Group, 1982 (U.S. Government Printing Office: 1983-397-034).

Appl. Opt. (6)

J. Geophys. Res. (1)

H. R. Gordon et al., “A Semi-Analytic Radiance Model of Ocean Color,” J. Geophys. Res. 93, 10909–10924 (1988).
[CrossRef]

Limnol. and Oceanog. (1)

A Morel, L. Prieur, “Analysis of Variations in Ocean Color,” Limnol. and Oceanog. 22, 709–722 (1977).
[CrossRef]

Science (2)

W. A. Hovis et al., “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 (7)

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.

J. J. Walsh, “The Marine Resources Experiment (MAREX),” NASA Goddard Space Flight Center, Report of the Ocean Color Science Working Group, 1982 (U.S. Government Printing Office: 1983-397-034).

NASA, “Earth Observing System: Science and Mission Requirements Working Group Report,” (Technical Memorandum 86129, August1984).

NASA and the Earth Observations Satellite Company, “System Concept for Wide-Field-of-View Observations of Ocean Phenomena from Space,” (August1987).

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

NASA, “Earth Observing System (EOS) Background Information Package, Announcement of Opportunity No. OSSA-1-88,” (Announcement of Opportunity No. OSSA-1-88,” January1988).

Ball Aerospace Division, Boulder CO, Development of the Coastal Zone Color Scanner for Nimbus-7: Volume 2—Test and Performance Data (Final Report F78–11, Rev. A NASA Contract NAS5-20900, May1979).

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Figures (18)

Fig. 1
Fig. 1

rSystem as a function of rBio and f.

Fig. 2
Fig. 2

Ea(443,560) as a function of [σt(765)] and [σt(865)]. The σt’s are in mW/cm2 μm sr. Contoured values of Ea(443,560) are 0.025, 0.050, 0.075, 0.100, and 0.125.

Fig. 3
Fig. 3

Ea(443,560) as a function of [σt(665)] and [σt(865)]. The σt’s are in mW/cm2, μm sr. Contoured values of Ea(443,560) are 0.025, 0.050, 0.075, 0.100, and 0.125.

Fig. 4
Fig. 4

Ea(443,560) as a function of [σt(765)] and [σt(865)]. The σt’s are in mW/cm2 μm sr. Contoured values of Ea(443,560) are 0.025, 0.050, 0.075, 0.100, and 0.125.

Fig. 5
Fig. 5

Ea(443,560) as a function of [σt(665)] and [σt(865)]. The σt’s are in mW/cm2 μm sr. Contoured values of Ea(443,560) are 0.025, 0.050, 0.075, 0.100, and 0.125.

Fig. 6
Fig. 6

Ea(443,560) as a function of [σt(765)] and [σt(865)]. The σt’s are in mW/cm2 μm sr. Contoured values of Ea(443,560) are 0.025, 0.050, 0.075, 0.100, and 0.125.

Fig. 7
Fig. 7

Ea(443,560) as a function of [σt(665)] and [σt(865)]. The σt’s are in mW/cm2 μm sr. Contoured values of Ea(443,560) are 0.025, 0.050, 0.075, 0.100, and 0.125.

Fig. 8
Fig. 8

Values of [σt(λ)] for MODIS–N and CZCS.

Fig. 9
Fig. 9

MODIS–N values of f as a function of C and n for the C13 bio-optical algorithm.

Fig. 10
Fig. 10

System error as a function of pigment concentration for two sensors. The dotted line represents the (δC/C)Bio limit.

Fig. 11
Fig. 11

Distribution of retrieved C for a sensor with the noise characteristics of MODIS–N, as a function of the Ångstrom exponent n, with θ0 = 70° and θv = 0.

Fig. 12
Fig. 12

Distribution of retrieved C for a sensor with the noise characteristics equivalent to, half as good, and twice as good as MODIS–N. n = 1, θ0 = 70° and θv = 0.

Fig. 13
Fig. 13

Effect of averaging to determine the Ångstrom exponent n on the distribution of retrieved C for a sensor with noise characteristics equivalent to ODIS–N. n = 1, θ0 = 70° and θv = 0.

Fig. 14
Fig. 14

Distribution of retrieved C for a sensor with the noise characteristics of CZCS, as a function of the Ångstrom exponent n, with θ0 = 70° and θv = 0.

Fig. 15
Fig. 15

SNR required as a function of Lt at 443 nm. Points connected by lines are along a scan line with θ0 = 60° at the center.

Fig. 16
Fig. 16

SNR required as a function of Lt at 560 nm. Points connected by lines are along a scan line with θ0 = 60° at the center.

Fig. 17
Fig. 17

SNR required as a function of Lt at 765 nm. Points connected by lines are along a scan line with θ0 = 60° at the center.

Fig. 18
Fig. 18

SNR required as a function of Lt at 865 nm. Points connected by lines are along a scan line with θ0 = 60° at the center.

Tables (2)

Tables Icon

Table I X2(λ,λ0, λ 0 )

Tables Icon

Table II [σ(λ)] Required to Make f = 1 for Two Values of Ea with θv = 0°, θ0 = 70°, and n = 0.5.

Equations (33)

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L t ( λ ) = L r ( λ ) + L a ( λ ) + t ( θ v , λ ) L w ( λ ) ,
t ( θ v , λ ) exp { - [ τ r ( λ ) / 2 + τ O z ( λ ) ] / cos θ v } ,
C = A [ L w ( λ i ) L w ( λ i ) ] B ,
L w ( λ ) = t ( θ 0 , λ ) [ 1 - ρ ( θ 0 ) ] cos θ 0 [ L w ( λ ) ] ,
C = A [ [ L w ( λ i ) ] [ L w ( λ i ) ] ] B .
C = C 13 = 1.15 ( [ L w ( 443 ) ] [ L w ( 560 ) ] ) - 1.42             r 2 = 0.972 ,
C = C 23 = 3.64 ( [ L w ( 500 ) ] [ L w ( 560 ) ] ) - 2.62             r 2 = 0.960 ,
L x ( λ ) = t ( θ 0 , λ ) ( 1 - ρ ( θ 0 ) ) cos θ 0 [ L x ( λ ) ] ,
C = A ( t ( θ v , λ j ) t ( θ v , λ i ) ) B ( [ L t ( λ i ) ] - [ L r ( λ i ) ] - [ L a ( λ i ) ] [ L t ( λ j ) ] - [ L r ( λ j ) ] - [ L a ( λ j ) ] ) B .
L a ( λ ) = ( λ , λ 0 ) F 0 ( λ ) F 0 ( λ 0 ) L a ( λ 0 ) ,
L a ( λ ) = S ( λ , λ 0 ) L a ( λ 0 )
S ( λ , λ 0 ) = ( λ 0 λ ) n F 0 ( λ ) F 0 ( λ 0 ) .
[ L a ( λ ) ] = S ( λ , λ 0 ) t ( θ 0 , λ 0 ) t ( θ 0 , λ ) [ L a ( λ 0 ) ] S ( λ , λ 0 ) [ L a ( λ 0 ) ] .
S ( λ , λ 0 ) = S ( λ , λ 0 ) ( t ( 0 , λ 0 ) t ( 0 , λ ) ) 1 / cos θ 0 ,
[ L a ( λ 0 ) ] = [ L t ( λ 0 ) ] - [ L r ( λ 0 ) ] ,
σ C C = B [ σ t ( λ i ) ] 2 t ( θ v , λ i ) 2 [ L w ( λ i ) ] 2 + [ σ t ( λ j ) ] 2 t ( θ v , λ j ) 2 [ L w ( λ j ) ] 2 + ( [ σ a ( λ i ) ] t ( θ v , λ i ) [ L w ( λ i ) ] - [ σ a ( λ j ) ] t ( θ v , λ j ) [ L w ( λ j ) ] ) 2 B E ( λ i ) 2 + E ( λ j ) 2 + E a ( λ i , λ j ) 2 ,
σ t ( λ ) = t ( θ 0 , λ ) [ 1 - ρ ( θ 0 ) ] cos θ 0 [ σ t ( λ ) ] ,
[ σ a ( λ ) ] 2 [ L a ( λ ) ] 2 = [ σ t ( λ 0 ) ] 2 [ L a ( λ 0 ) ] 2 + [ σ S ( λ , λ 0 ) ) ] 2 S ( λ , λ 0 ) 2 ,
[ σ S ( λ , λ 0 ) ] S ( λ , λ 0 ) = n ( λ 0 λ ) σ n ,
[ L a ( λ 0 ) ] [ L a ( λ 0 ) ] = t ( θ 0 , λ 0 ) t ( θ 0 λ 0 ) F 0 ( λ 0 ) F 0 ( λ 0 ) ( λ 0 λ 0 ) n ,
σ n 2 = ( 1 n ( λ 0 / λ 0 ) ) 2 ( [ σ t ( λ 0 ) ] 2 [ L a ( λ 0 ) ] 2 + [ σ t ( λ 0 ) ] 2 [ L a ( λ 0 ) ] 2 ) ,
[ σ a ( λ ) ] 2 [ L a ( λ ) ] 2 = [ σ t ( λ 0 ) ] 2 [ L a ( λ 0 ) ] 2 + ( n ( λ 0 / λ ) n ( λ 0 / λ 0 ) ) 2 ( [ σ t ( λ 0 ) ] 2 [ L a ( λ 0 ) ] 2 + [ σ t ( λ 2 ) ] 2 [ L a ( λ 0 ) ] 2 ) ,
[ σ a ( λ ) ] 2 = [ σ t ( λ 0 ) ] 2 S ( λ , λ 0 ) 2 + X 2 ( λ , λ 0 , λ 0 ) × { [ σ t ( λ 0 ) ] 2 S ( λ , λ 0 ) 2 + [ σ t ( λ 0 ) ] 2 S ( λ , λ 0 ) 2 } ,
X ( λ , λ 0 , λ 0 ) = n ( λ 0 / λ ) n ( λ 0 / λ 0 ) ,
( δ C C ) System = ( δ C C ) Bio 2 + ( σ C C ) 2 .
( δ C c ) Bio = f ( σ C C )
( δ C C ) System = ( δ C c ) Bio 1 + 1 f 2 .
r Bio = Original ( δ C ) Bio Improved ( δ C ) Bio and r System = Original ( δ C ) System Improved ( δ C ) System ,
r System = r Bio 1 + f 2 r Bio 2 + f 2 .
0.189 1.42 E ( 443 ) 2 + E ( 560 ) 2 + E a ( 443 , 560 ) 2 ,
0.273 2.62 E ( 500 ) 2 + E ( 560 ) 2 + E a ( 500 , 560 ) 2 .
SNR = L t ( λ ) σ t ( λ )
τ a ( λ ) = [ 670 λ ] n τ a ( 670 ) .

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