Abstract

Effects of the ocean surface reflection for solar irradiance on the normalized water-leaving radiance in the visible wavelengths are evaluated and discussed for various conditions of the atmosphere, solar-zenith angles, and wind speeds. The surface reflection effects on water-leaving radiance are simply due to the fact that the radiance that is backscattered out of the water is directly proportional to the downward solar irradiance just beneath the ocean surface. The larger the solar-zenith angle, the less the downward solar irradiance just beneath the ocean surface (i.e., more photons are reflected by the ocean surface), leading to a reduced value of the radiance that is backscattered out of the ocean. For cases of large solar-zenith angles, the effects of surface irradiance reflection need to be accounted for in both the satellite-derived and in situ measured water-leaving radiances.

© 2006 Optical Society of America

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References

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    [CrossRef] [PubMed]
  2. H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, and D. K. Clark, 'A semianalytic radiance model of ocean color,' J. Geophys. Res. 93, 10909-10924 (1988).
    [CrossRef]
  3. H. R. Gordon and D. K. Clark, 'Clear water radiances for atmospheric correction of coastal zone color scanner imagery,' Appl. Opt. 20, 4175-4180 (1981).
    [CrossRef] [PubMed]
  4. A. Morel, D. Antoine, and B. Gentili, 'Bidirectional reflectance of oceanic waters: accounting for Raman emission and varying particle scattering phase function,' Appl. Opt. 41, 6289-6306 (2002).
    [CrossRef] [PubMed]
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    [CrossRef]
  9. K. J. Voss and A. Morel, 'Bidirectional reflectance function for oceanic waters with varying chlorophyll concentrations: measurements versus predictions,' Limnol. Oceanogr. 50, 698-705 (2005).
    [CrossRef]
  10. C. K. Gatebe, M. D. King, A. I. Lyapustin, G. T. Arnold, and J. Redemann, 'Airborne spectral measurements of ocean directional reflectance,' J. Atmos. Sci. 62, 1072-1092 (2005).
    [CrossRef]
  11. J. T. O. Kirk, 'Dependence of the relationship between inherent and apparent optical properties of water on solar altitude,' Limnol. Oceanogr. 29, 350-356 (1984).
    [CrossRef]
  12. R. W. Austin, 'The remote sensing of spectral radiance from below the ocean surface,' in Optical Aspects of Oceanography, N. G. Jerlov and E. S. Nielsen, eds. (Academic, 1974), pp. 317-344.
  13. H. R. Gordon and M. Wang, 'Surface roughness considerations for atmospheric correction of ocean color sensors. 1: The Rayleigh scattering component,' Appl. Opt. 31, 4247-4260 (1992).
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  14. H. R. Gordon and M. Wang, 'Retrieval of water-leaving radiance and aerosol optical thickness over the oceans with SeaWiFS: a preliminary algorithm,' Appl. Opt. 33, 443-452 (1994).
    [CrossRef] [PubMed]
  15. E. P. Shettle and 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 Report AFGL-TR-79-0214 (U.S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1979).
  16. C. Cox and 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]

2005 (3)

H. R. Gordon, 'Normalized water-leaving radiance: revisiting the influence of surface roughness,' Appl. Opt. 44, 241-248 (2005).
[CrossRef] [PubMed]

K. J. Voss and A. Morel, 'Bidirectional reflectance function for oceanic waters with varying chlorophyll concentrations: measurements versus predictions,' Limnol. Oceanogr. 50, 698-705 (2005).
[CrossRef]

C. K. Gatebe, M. D. King, A. I. Lyapustin, G. T. Arnold, and J. Redemann, 'Airborne spectral measurements of ocean directional reflectance,' J. Atmos. Sci. 62, 1072-1092 (2005).
[CrossRef]

2002 (1)

1996 (1)

1995 (1)

A. Morel, K. J. Voss, and B. Gentili, 'Bidirectional reflectance of oceanic waters--a comparison of modeled and measured upward radiance fields,' J. Geophys. Res. [Oceans] 100, 13143-13150 (1995).
[CrossRef]

1994 (1)

1993 (1)

1992 (1)

1991 (1)

1988 (1)

H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, and D. K. Clark, 'A semianalytic radiance model of ocean color,' J. Geophys. Res. 93, 10909-10924 (1988).
[CrossRef]

1984 (1)

J. T. O. Kirk, 'Dependence of the relationship between inherent and apparent optical properties of water on solar altitude,' Limnol. Oceanogr. 29, 350-356 (1984).
[CrossRef]

1981 (1)

1954 (1)

Antoine, D.

Arnold, G. T.

C. K. Gatebe, M. D. King, A. I. Lyapustin, G. T. Arnold, and J. Redemann, 'Airborne spectral measurements of ocean directional reflectance,' J. Atmos. Sci. 62, 1072-1092 (2005).
[CrossRef]

Austin, R. W.

R. W. Austin, 'The remote sensing of spectral radiance from below the ocean surface,' in Optical Aspects of Oceanography, N. G. Jerlov and E. S. Nielsen, eds. (Academic, 1974), pp. 317-344.

Baker, K. S.

H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, and D. K. Clark, 'A semianalytic radiance model of ocean color,' J. Geophys. Res. 93, 10909-10924 (1988).
[CrossRef]

Brown, J. W.

H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, and D. K. Clark, 'A semianalytic radiance model of ocean color,' J. Geophys. Res. 93, 10909-10924 (1988).
[CrossRef]

Brown, O. B.

H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, and D. K. Clark, 'A semianalytic radiance model of ocean color,' J. Geophys. Res. 93, 10909-10924 (1988).
[CrossRef]

Clark, D. K.

H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, and D. K. Clark, 'A semianalytic radiance model of ocean color,' J. Geophys. Res. 93, 10909-10924 (1988).
[CrossRef]

H. R. Gordon and D. K. Clark, 'Clear water radiances for atmospheric correction of coastal zone color scanner imagery,' Appl. Opt. 20, 4175-4180 (1981).
[CrossRef] [PubMed]

Cox, C.

Evans, R. H.

H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, and D. K. Clark, 'A semianalytic radiance model of ocean color,' J. Geophys. Res. 93, 10909-10924 (1988).
[CrossRef]

Fenn, R. W.

E. P. Shettle and 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 Report AFGL-TR-79-0214 (U.S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1979).

Gatebe, C. K.

C. K. Gatebe, M. D. King, A. I. Lyapustin, G. T. Arnold, and J. Redemann, 'Airborne spectral measurements of ocean directional reflectance,' J. Atmos. Sci. 62, 1072-1092 (2005).
[CrossRef]

Gentili, B.

A. Morel, D. Antoine, and B. Gentili, 'Bidirectional reflectance of oceanic waters: accounting for Raman emission and varying particle scattering phase function,' Appl. Opt. 41, 6289-6306 (2002).
[CrossRef] [PubMed]

A. Morel, K. J. Voss, and B. Gentili, 'Bidirectional reflectance of oceanic waters--a comparison of modeled and measured upward radiance fields,' J. Geophys. Res. [Oceans] 100, 13143-13150 (1995).
[CrossRef]

Gentili, G.

Gordon, H. R.

King, M. D.

C. K. Gatebe, M. D. King, A. I. Lyapustin, G. T. Arnold, and J. Redemann, 'Airborne spectral measurements of ocean directional reflectance,' J. Atmos. Sci. 62, 1072-1092 (2005).
[CrossRef]

Kirk, J. T. O.

J. T. O. Kirk, 'Dependence of the relationship between inherent and apparent optical properties of water on solar altitude,' Limnol. Oceanogr. 29, 350-356 (1984).
[CrossRef]

Lyapustin, A. I.

C. K. Gatebe, M. D. King, A. I. Lyapustin, G. T. Arnold, and J. Redemann, 'Airborne spectral measurements of ocean directional reflectance,' J. Atmos. Sci. 62, 1072-1092 (2005).
[CrossRef]

Morel, A.

Munk, W.

Redemann, J.

C. K. Gatebe, M. D. King, A. I. Lyapustin, G. T. Arnold, and J. Redemann, 'Airborne spectral measurements of ocean directional reflectance,' J. Atmos. Sci. 62, 1072-1092 (2005).
[CrossRef]

Shettle, E. P.

E. P. Shettle and 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 Report AFGL-TR-79-0214 (U.S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1979).

Smith, R. C.

H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, and D. K. Clark, 'A semianalytic radiance model of ocean color,' J. Geophys. Res. 93, 10909-10924 (1988).
[CrossRef]

Voss, K. J.

K. J. Voss and A. Morel, 'Bidirectional reflectance function for oceanic waters with varying chlorophyll concentrations: measurements versus predictions,' Limnol. Oceanogr. 50, 698-705 (2005).
[CrossRef]

A. Morel, K. J. Voss, and B. Gentili, 'Bidirectional reflectance of oceanic waters--a comparison of modeled and measured upward radiance fields,' J. Geophys. Res. [Oceans] 100, 13143-13150 (1995).
[CrossRef]

Wang, M.

Appl. Opt. (8)

J. Atmos. Sci. (1)

C. K. Gatebe, M. D. King, A. I. Lyapustin, G. T. Arnold, and J. Redemann, 'Airborne spectral measurements of ocean directional reflectance,' J. Atmos. Sci. 62, 1072-1092 (2005).
[CrossRef]

J. Geophys. Res. (2)

H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, and D. K. Clark, 'A semianalytic radiance model of ocean color,' J. Geophys. Res. 93, 10909-10924 (1988).
[CrossRef]

A. Morel, K. J. Voss, and B. Gentili, 'Bidirectional reflectance of oceanic waters--a comparison of modeled and measured upward radiance fields,' J. Geophys. Res. [Oceans] 100, 13143-13150 (1995).
[CrossRef]

J. Opt. Soc. Am. (1)

Limnol. Oceanogr. (2)

K. J. Voss and A. Morel, 'Bidirectional reflectance function for oceanic waters with varying chlorophyll concentrations: measurements versus predictions,' Limnol. Oceanogr. 50, 698-705 (2005).
[CrossRef]

J. T. O. Kirk, 'Dependence of the relationship between inherent and apparent optical properties of water on solar altitude,' Limnol. Oceanogr. 29, 350-356 (1984).
[CrossRef]

Other (2)

R. W. Austin, 'The remote sensing of spectral radiance from below the ocean surface,' in Optical Aspects of Oceanography, N. G. Jerlov and E. S. Nielsen, eds. (Academic, 1974), pp. 317-344.

E. P. Shettle and 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 Report AFGL-TR-79-0214 (U.S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1979).

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Figures (3)

Fig. 1
Fig. 1

Results of (a) Ed (+) (λ, θ0, τ a , W), (b) Ed (−) (λ, θ0, τ a , W), (c) f (λ, θ0, τ a , W), and (d) Corf(Sun) (λ, θ0, τ a , W) as functions of the solar-zenith angle for cases of a flat ocean surface with the M80 aerosols and an aerosol optical thickness of 0.1 at various visible wavelengths.

Fig. 2
Fig. 2

Correction function Corf(Sun) (λ, θ0, τ a , W) at 443 nm as a function of the solar-zenith angle for a case of (a) the M80 model with various aerosol optical thicknesses and a flat surface; (b) various aerosol models with an aerosol optical thickness of 0.1 and a flat surface, and (c) the M80 model with an aerosol optical thickness of 0.1 for various wind speeds. (d) Ratio of Corf(Sun) (λ, θ0, τ a , W) computed for cases of no atmosphere and with atmosphere.

Fig. 3
Fig. 3

Differences (%) of the SeaWiFS-derived normalized water-leaving radiance at five visible bands with and without including the correction function Corf(Sun) (λ, θ0, τ a , W) as a function of (a) the northern latitudes from 10° to 50° in the Pacific Ocean and (b) time from 2002 July to 2004 September at 50°N of the Pacific Ocean.

Tables (1)

Tables Icon

Table 1 Coefficients [ c i (λ, W ), i = 1, 4] to Fit Eq. (16)

Equations (16)

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[ L w ( λ , θ 0 , θ , Δ ϕ ) ] N = L w ( λ , θ 0 , θ , Δ ϕ ) F ¯ 0 ( λ ) E d ( + ) ( λ , θ 0 ) ( d d 0 ) 2 L w ( λ , θ 0 , θ , Δ ϕ ) t ( λ , θ 0 ) cos θ 0 ,
[ L w ( λ ) ] N Exact = [ L w ( λ , θ 0 , θ , Δ ϕ ) ] N × { ( f / Q ) Eff } × [ 0 ( λ , τ a , W ) ( λ , θ 0 , θ , τ a , W ) ] ,
{ ( f / Q ) Eff } = { [ f 0 ( λ , IOP ) Q 0 ( λ , IOP ) ] / [ f ( λ , θ 0 ,  IOP ) Q ( λ , θ 0 ,   θ , Δ ϕ ,  IOP ) ] } ,
( λ , θ 0 , θ , τ a , W ) = [ 1 ρ ¯ f ( λ , θ 0 , τ a , W ) 1 r ¯ R ( λ , θ 0 ) ] × [ 1 ρ f ( λ , θ , W ) m 2 ] ,
( λ , θ 0 , θ , τ a , W ) = ( Sun ) ( λ , θ 0 , τ a , W ) × ( View ) ( λ , θ , W ) ,
( Sun ) ( λ , θ 0 , τ a , W ) = 1 ρ ¯ f ( λ , θ 0 , τ a , W ) 1 r ¯ R ( λ , θ 0 ) ,
( View ) ( λ , θ , W ) = 1 ρ f ( λ , θ , W ) m 2 .
[ L w ( λ ) ] N Exact = [ L w ( λ , θ 0 , θ ) ] N [ 0 ( Sun ) ( λ , τ a , W ) ( Sun ) ( λ , θ 0 , τ a , W ) ] × [ 0 ( View ) ( λ , W ) ( View ) ( λ , θ , W ) ] .
[ L w ( λ , θ 0 , θ = 0 ) ] N = [ L w ( λ , θ 0 , θ ) ] N × [ 0 ( View ) ( λ , W ) ( View ) ( λ , θ , W ) ] ,
[ L w ( λ ) ] N Exact = [ L w ( λ , θ 0 , θ = 0 ) ] N × [ 0 ( Sun ) ( λ , τ a , W ) ( Sun ) ( λ , θ 0 , τ a , W ) ] .
R ( λ , θ 0 ) = R ( λ , θ 0 = 0 ) [ 1.6 0.6 cos θ 0 ] .
1 r ¯ R ( λ , θ 0 ) 1 r ¯ R ( λ , θ 0 = 0 ) 1 r ¯ R ( λ , θ 0 ) + r ¯ R ( λ , θ 0 = 0 ) = 1 0.6 r ¯ R ( λ , θ 0 = 0 ) ( 1 cos θ 0 ) .
[ 0 ( Sun ) ( λ , τ a , W ) ( Sun ) ( λ , θ 0 , τ a , W ) ] 1 ρ ¯ f ( λ , θ 0 = 0 , τ a , W ) 1 ρ ¯ f ( λ , θ 0 , τ a , W ) t ¯ f ( λ , θ 0 = 0 , τ a , W ) t ¯ f ( λ , θ 0 , τ a , W ) ,
Corf ( Sun ) ( λ , θ 0 , τ a , W ) = t ¯ f ( λ , θ 0 = 0 , τ a , W ) t ¯ f ( λ , θ 0 , τ a , W ) .
t ¯ f ( λ , θ 0 , τ a , W ) = E d ( ) ( λ , θ 0 , τ a , W ) E d ( + ) ( λ , θ 0 , τ a , W ) ,
Corf ( Sun ) ( λ , θ 0 , W ) = 1 + i = 1 4 c i ( λ , W ) [ ln ( cos θ 0 ) ] i

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