Abstract

Spectral in-water measurements of downward irradiance (E d), upward irradiance (E u), and nadir radiance ( L u) are sufficient to calculate the scalar irradiances E 0, E 0d, and E 0u, the average cosines μ, μd, and μu, the light absorption coefficient a, the backscattering coefficient b b, and the so-called f factor that relates to R, a, and b b. The solar elevation of 42° is a special case in which μd is independent of all variables except solar elevation. The algorithms are valid for solar elevations between 12° and 81° for horizontally stratified clear and turbid deep waters.

© 2001 Optical Society of America

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References

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  1. H. R. Gordon, O. B. Brown, M. M. Jacobs, “Computed relationships between the inherent and apparent optical properties of a flat homogeneous ocean,” Appl. Opt. 14, 417–427 (1975).
    [CrossRef] [PubMed]
  2. A. Morel, L. Prieur, “Analyse spectrale des coefficients d’atténuation diffuse, de réflexion diffuse, d’absorption et de retrodiffusion pour diverses régions marines,” Cent. Rech. Oceanogr. Villefranche sur Mer 17, 1–157 (1975).
  3. A. Morel, B. Gentili, “Diffuse reflectance of oceanic waters: its dependence on Sun angle as influenced by the molecular scattering contribution,” Appl. Opt. 30, 4427–4438 (1991).
    [CrossRef] [PubMed]
  4. T. Oishi, “Significant relationship between the backward scattering coefficient of sea water and the scatterance at 120°,” Appl. Opt. 29, 4658–4665 (1990).
    [CrossRef] [PubMed]
  5. R. A. Maffione, D. R. Dana, “Instruments and methods for measuring the backward-scattering coefficient of ocean waters,” Appl. Opt. 36, 6057–6067 (1997).
    [CrossRef] [PubMed]
  6. N. K. Højerslev, “Inherent and apparent optical properties of the Western Mediterranean and the Hardangerfjord,” Rep. Inst. Phys. Oceanogr. U. Copenhagen 21, 1–72 (1973).
  7. N. K. Højerslev, “A spectral light absorption meter for measurements in the sea,” Limnol. Oceanogr. 20, 1024–1034 (1975).
    [CrossRef]
  8. E. Aas, N. K. Højerslev, “Analysis of underwater radiance observations: apparent optical properties and analytic functions describing the angular radiance distribution,” J. Geophys. Res. 104, 8015–8024 (1999).
    [CrossRef]
  9. E. Aas, J. Høkedal, “Reflection of spectral sky irradiance on the surface of the sea and related properties,” Remote Sens. Environ. 70, 181–190 (1999).
    [CrossRef]
  10. J. Tyler, “Radiance distribution as a function of depth in an underwater environment,” (Visibility Laboratory, Scripps Institution of Oceanography, La Jolla, Calif., 1960), pp. 363–412.
  11. E. Aas, “The absorption coefficient of clear ocean water,” Rep. Dept. Geophys. U. Oslo 67, 1–17 (1987).
  12. R. W. Austin, G. Halikas, “The index of refraction of sea water,” (Visibility Laboratory, Scripps Institution of Oceanography, La Jolla, Calif., 1976), pp. 1–171.
  13. R. C. Smith, K. S. Baker, “Irradiance transmittance through the air-water interface,” in Ocean Optics X, R. W. Spinrad, ed., Proc. SPIE1302, 556–565 (1990).
    [CrossRef]
  14. J. R. V. Zaneveld, “A theoretical derivation of the dependence of the remotely sensed reflectance of the ocean on the inherent optical properties,” J. Geophys. Res. 100, 13135–13142 (1995).
    [CrossRef]
  15. N. K. Højerslev, P. V. Jørgensen, “Modelling of key bio-optical parameters including spectral light backscattering and absorption coefficients by using in situ measurements of spectral upwelling and downwelling irradiances and light scattering at 140 degrees at 488 nm,” Remote Sens. Environ. (to be published).
  16. H. Buiteveld, J. H. Hakvoort, M. Donze, “Optical properties of pure water,” in Ocean Optics XII, J. S. Jaffe, ed., Proc. SPIE2258, 174–183 (1994).
    [CrossRef]

1999 (2)

E. Aas, N. K. Højerslev, “Analysis of underwater radiance observations: apparent optical properties and analytic functions describing the angular radiance distribution,” J. Geophys. Res. 104, 8015–8024 (1999).
[CrossRef]

E. Aas, J. Høkedal, “Reflection of spectral sky irradiance on the surface of the sea and related properties,” Remote Sens. Environ. 70, 181–190 (1999).
[CrossRef]

1997 (1)

1995 (1)

J. R. V. Zaneveld, “A theoretical derivation of the dependence of the remotely sensed reflectance of the ocean on the inherent optical properties,” J. Geophys. Res. 100, 13135–13142 (1995).
[CrossRef]

1991 (1)

1990 (1)

1987 (1)

E. Aas, “The absorption coefficient of clear ocean water,” Rep. Dept. Geophys. U. Oslo 67, 1–17 (1987).

1975 (3)

H. R. Gordon, O. B. Brown, M. M. Jacobs, “Computed relationships between the inherent and apparent optical properties of a flat homogeneous ocean,” Appl. Opt. 14, 417–427 (1975).
[CrossRef] [PubMed]

A. Morel, L. Prieur, “Analyse spectrale des coefficients d’atténuation diffuse, de réflexion diffuse, d’absorption et de retrodiffusion pour diverses régions marines,” Cent. Rech. Oceanogr. Villefranche sur Mer 17, 1–157 (1975).

N. K. Højerslev, “A spectral light absorption meter for measurements in the sea,” Limnol. Oceanogr. 20, 1024–1034 (1975).
[CrossRef]

1973 (1)

N. K. Højerslev, “Inherent and apparent optical properties of the Western Mediterranean and the Hardangerfjord,” Rep. Inst. Phys. Oceanogr. U. Copenhagen 21, 1–72 (1973).

Aas, E.

E. Aas, N. K. Højerslev, “Analysis of underwater radiance observations: apparent optical properties and analytic functions describing the angular radiance distribution,” J. Geophys. Res. 104, 8015–8024 (1999).
[CrossRef]

E. Aas, J. Høkedal, “Reflection of spectral sky irradiance on the surface of the sea and related properties,” Remote Sens. Environ. 70, 181–190 (1999).
[CrossRef]

E. Aas, “The absorption coefficient of clear ocean water,” Rep. Dept. Geophys. U. Oslo 67, 1–17 (1987).

Austin, R. W.

R. W. Austin, G. Halikas, “The index of refraction of sea water,” (Visibility Laboratory, Scripps Institution of Oceanography, La Jolla, Calif., 1976), pp. 1–171.

Baker, K. S.

R. C. Smith, K. S. Baker, “Irradiance transmittance through the air-water interface,” in Ocean Optics X, R. W. Spinrad, ed., Proc. SPIE1302, 556–565 (1990).
[CrossRef]

Brown, O. B.

Buiteveld, H.

H. Buiteveld, J. H. Hakvoort, M. Donze, “Optical properties of pure water,” in Ocean Optics XII, J. S. Jaffe, ed., Proc. SPIE2258, 174–183 (1994).
[CrossRef]

Dana, D. R.

Donze, M.

H. Buiteveld, J. H. Hakvoort, M. Donze, “Optical properties of pure water,” in Ocean Optics XII, J. S. Jaffe, ed., Proc. SPIE2258, 174–183 (1994).
[CrossRef]

Gentili, B.

Gordon, H. R.

Hakvoort, J. H.

H. Buiteveld, J. H. Hakvoort, M. Donze, “Optical properties of pure water,” in Ocean Optics XII, J. S. Jaffe, ed., Proc. SPIE2258, 174–183 (1994).
[CrossRef]

Halikas, G.

R. W. Austin, G. Halikas, “The index of refraction of sea water,” (Visibility Laboratory, Scripps Institution of Oceanography, La Jolla, Calif., 1976), pp. 1–171.

Højerslev, N. K.

E. Aas, N. K. Højerslev, “Analysis of underwater radiance observations: apparent optical properties and analytic functions describing the angular radiance distribution,” J. Geophys. Res. 104, 8015–8024 (1999).
[CrossRef]

N. K. Højerslev, “A spectral light absorption meter for measurements in the sea,” Limnol. Oceanogr. 20, 1024–1034 (1975).
[CrossRef]

N. K. Højerslev, “Inherent and apparent optical properties of the Western Mediterranean and the Hardangerfjord,” Rep. Inst. Phys. Oceanogr. U. Copenhagen 21, 1–72 (1973).

N. K. Højerslev, P. V. Jørgensen, “Modelling of key bio-optical parameters including spectral light backscattering and absorption coefficients by using in situ measurements of spectral upwelling and downwelling irradiances and light scattering at 140 degrees at 488 nm,” Remote Sens. Environ. (to be published).

Høkedal, J.

E. Aas, J. Høkedal, “Reflection of spectral sky irradiance on the surface of the sea and related properties,” Remote Sens. Environ. 70, 181–190 (1999).
[CrossRef]

Jacobs, M. M.

Jørgensen, P. V.

N. K. Højerslev, P. V. Jørgensen, “Modelling of key bio-optical parameters including spectral light backscattering and absorption coefficients by using in situ measurements of spectral upwelling and downwelling irradiances and light scattering at 140 degrees at 488 nm,” Remote Sens. Environ. (to be published).

Maffione, R. A.

Morel, A.

A. Morel, B. Gentili, “Diffuse reflectance of oceanic waters: its dependence on Sun angle as influenced by the molecular scattering contribution,” Appl. Opt. 30, 4427–4438 (1991).
[CrossRef] [PubMed]

A. Morel, L. Prieur, “Analyse spectrale des coefficients d’atténuation diffuse, de réflexion diffuse, d’absorption et de retrodiffusion pour diverses régions marines,” Cent. Rech. Oceanogr. Villefranche sur Mer 17, 1–157 (1975).

Oishi, T.

Prieur, L.

A. Morel, L. Prieur, “Analyse spectrale des coefficients d’atténuation diffuse, de réflexion diffuse, d’absorption et de retrodiffusion pour diverses régions marines,” Cent. Rech. Oceanogr. Villefranche sur Mer 17, 1–157 (1975).

Smith, R. C.

R. C. Smith, K. S. Baker, “Irradiance transmittance through the air-water interface,” in Ocean Optics X, R. W. Spinrad, ed., Proc. SPIE1302, 556–565 (1990).
[CrossRef]

Tyler, J.

J. Tyler, “Radiance distribution as a function of depth in an underwater environment,” (Visibility Laboratory, Scripps Institution of Oceanography, La Jolla, Calif., 1960), pp. 363–412.

Zaneveld, J. R. V.

J. R. V. Zaneveld, “A theoretical derivation of the dependence of the remotely sensed reflectance of the ocean on the inherent optical properties,” J. Geophys. Res. 100, 13135–13142 (1995).
[CrossRef]

Appl. Opt. (4)

Cent. Rech. Oceanogr. Villefranche sur Mer (1)

A. Morel, L. Prieur, “Analyse spectrale des coefficients d’atténuation diffuse, de réflexion diffuse, d’absorption et de retrodiffusion pour diverses régions marines,” Cent. Rech. Oceanogr. Villefranche sur Mer 17, 1–157 (1975).

J. Geophys. Res. (2)

E. Aas, N. K. Højerslev, “Analysis of underwater radiance observations: apparent optical properties and analytic functions describing the angular radiance distribution,” J. Geophys. Res. 104, 8015–8024 (1999).
[CrossRef]

J. R. V. Zaneveld, “A theoretical derivation of the dependence of the remotely sensed reflectance of the ocean on the inherent optical properties,” J. Geophys. Res. 100, 13135–13142 (1995).
[CrossRef]

Limnol. Oceanogr. (1)

N. K. Højerslev, “A spectral light absorption meter for measurements in the sea,” Limnol. Oceanogr. 20, 1024–1034 (1975).
[CrossRef]

Remote Sens. Environ. (1)

E. Aas, J. Høkedal, “Reflection of spectral sky irradiance on the surface of the sea and related properties,” Remote Sens. Environ. 70, 181–190 (1999).
[CrossRef]

Rep. Dept. Geophys. U. Oslo (1)

E. Aas, “The absorption coefficient of clear ocean water,” Rep. Dept. Geophys. U. Oslo 67, 1–17 (1987).

Rep. Inst. Phys. Oceanogr. U. Copenhagen (1)

N. K. Højerslev, “Inherent and apparent optical properties of the Western Mediterranean and the Hardangerfjord,” Rep. Inst. Phys. Oceanogr. U. Copenhagen 21, 1–72 (1973).

Other (5)

J. Tyler, “Radiance distribution as a function of depth in an underwater environment,” (Visibility Laboratory, Scripps Institution of Oceanography, La Jolla, Calif., 1960), pp. 363–412.

R. W. Austin, G. Halikas, “The index of refraction of sea water,” (Visibility Laboratory, Scripps Institution of Oceanography, La Jolla, Calif., 1976), pp. 1–171.

R. C. Smith, K. S. Baker, “Irradiance transmittance through the air-water interface,” in Ocean Optics X, R. W. Spinrad, ed., Proc. SPIE1302, 556–565 (1990).
[CrossRef]

N. K. Højerslev, P. V. Jørgensen, “Modelling of key bio-optical parameters including spectral light backscattering and absorption coefficients by using in situ measurements of spectral upwelling and downwelling irradiances and light scattering at 140 degrees at 488 nm,” Remote Sens. Environ. (to be published).

H. Buiteveld, J. H. Hakvoort, M. Donze, “Optical properties of pure water,” in Ocean Optics XII, J. S. Jaffe, ed., Proc. SPIE2258, 174–183 (1994).
[CrossRef]

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Equations (36)

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R=f bba=f bba+bb,
dE/dz=-aE0,
a=Kd1-R+1/KddRdzEdE0=Kd-RKuEdE0,
a=Kd-RKu/1/μd+R/μu.
μ=a/KE,
μ=Kd-RKuKE1/μd+R/μu.
μd*=sec θs+1/μddiff, w-sec θs1.03N1.03-1.
EuLu=2π 1+αzαz2αz-ln1+αz,
μd=μd*1-1.2±0.1R.
μd=1-1.2Rsec θs+1/μddiff, w-sec θs1.03N1.03,
μd=0.831-1.2R
n=1.33518+20.93×10-5 S-6.67×10-5 T.
μddiff, w=0.886±0.010-0.121±0.0015×90-hs×10-2
Nλ, 90-hs=1.1×10-650-hs3+1.095×10-450-hs2+4.15×10-3×50-hs+2.0×10-6λ-5002-8.0×10-4λ-500×1+3.0×10-350-hs+0.3735.
Nλ, 90-hs=1.1×10-650-hs3+1.097×10-450-hs2+4.15×10-3×50-hs+1.86×10-6λ-5002-1.12×10-3λ-500×1+6.9×10-350-hs+0.359.
μ=μd1-R1+2.5Rμd,
fbb=Ra,
Lu=E0dβ180-θsa+k,
Lu=Edμdβ180-θsa+Ku.
1Q=β180-θsRμda+Ku.
fQ=β180-θsbbaμda+Ku,
Xθ=1.14-0.0620θ-120,
f=Q2πX180-θsa/μda+Ku,
LuEd=β180-θsμda+Ku
LuEd=β180-θsa1+μd.
Eu=EdbbμdX180-θs1+αα2α-ln1+αa+Ku
R=bbμdX180-θs1+αα2α-ln1+αa+Ku.
f=1+KuaX180-θsμd-11+αα2×α-ln1+α.
R=bb*Kd+Ku.
dEuz=Ed0-exp-Kdzbb*dz.
dEu0-=Ed0-exp-Kdzbb*dz exp-Kuz.
0dEu0-=Eu0-=Ed0-bb*/Kd+Ku,
f=0.5μbb*/bb.
bb*bb=Kd+Kua+KuX180-θsμd-11+αα2×α-ln1+α.
bb=Ra+KuX180-θsμdα21+αα-ln1+α.
E0, E0d, E0uWm-2 nm-1,  RSR=Lu/E0dsr-1, μd=Ed/E0d,  μu=Eu/E0u,  μ=E/E0, am-1,  bbm-1,  f=Ra/bb.

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