Abstract

A full multiple-scattering algorithm for inverting upwelling radiance (L u) or irradiance (E u) and downwelling irradiance (E d) profiles in homogeneous natural waters to obtain the absorption (a) and backscattering (b b) coefficients is described and tested with simulated data. An attractive feature of the algorithm is that it does not require precise knowledge of the scattering phase function of the medium. For the E uE d algorithm, tests suggest that the error in the retrieved a should usually be ≲1%, and the error in b b ≲10–20%. The performance of the L uE d algorithm is not as good because it is more sensitive to the scattering phase function employed in the inversions; however, the error in a is usually still small, i.e., ≲3%. When the algorithm is extended to accommodate the presence of a Lambertian-reflecting bottom, the retrievals of a are still excellent, even when the presence of the bottom significantly influences the upwelling light field; however, the error in b b can be large.

© 1997 Optical Society of America

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References

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  1. C. D. Mobley, Light and Water; Radiative Transfer in Natural Waters (Academic, New York, 1994).
  2. H. R. Gordon, A. Y. Morel, Remote Assessment of Ocean Color for Interpretation of Satellite Visible Imagery: A Review (Springer-Verlag, New York, 1983).
    [CrossRef]
  3. J. T. O. Kirk, “Estimation of the scattering coefficient of natural waters using underwater irradiance measurements,” Aust. J. Mar. Freshwater Res. 32, 533–539 (1981).
    [CrossRef]
  4. J. T. O. Kirk, “Estimation of the absorption and scattering coefficients of natural waters by the use of underwater irradiance measurements,” Appl. Opt. 33, 3276–3278 (1994).
    [CrossRef] [PubMed]
  5. H. R. Gordon, “Absorption and scattering estimates from irradiance measurements: Monte Carlo simulations,” Limnol. Oceanogr. 36, 769–777 (1991).
    [CrossRef]
  6. H. R. Gordon, “Sensitivity of radiative transfer to small-angle scattering in the ocean: a quantitative assessment,” Appl. Opt. 32, 7505–7511 (1993).
    [CrossRef] [PubMed]
  7. 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]
  8. A. Morel, L. Prieur, “Analysis of variations in ocean color,” Limnol. Oceanogr. 22, 709–722 (1977).
    [CrossRef]
  9. G. W. Kattawar, “A three-parameter analytic phase function for multiple scattering calculations,” J. Quant. Spectrosc. Radiat. Transfer 15, 839–849 (1975).
    [CrossRef]
  10. C. D. Mobley, B. Gentili, H. R. Gordon, Z. Jin, G. W. Kattawar, A. Morel, P. Reinersman, K. Stamnes, R. H. Stavn, “Comparison of numerical models for computing underwater light fields,” Appl. Opt. 32, 7484–7504 (1993).
    [CrossRef] [PubMed]
  11. J. E. Tyler, “Radiance distribution as a function of depth in an underwater environment,” Bull. Scripps Inst. Oceanogr. 7, 363–411 (1960).
  12. J. E. Tyler, R. W. Preisendorfer, “Transmission of energy within the sea: light,” in The Sea, M. N. Hill, ed. (Interscience, New York, 1962) pp. 397–451.
  13. R. W. Preisendorfer, “Application of radiative transfer theory to light measurements in the sea,” Union Geodes. Geophys. Int. 10, 11–30 (1961).
  14. R. W. Austin, “The remote sensing of spectral radiance from below the ocean surface,” in Optical Aspects of Oceanography, N. G. Jerlov, E. S. Nielsen, eds. (Academic, London, 1974) pp. 317–344.
  15. H. R. Gordon, “Simple calculation of the diffuse reflectance of the ocean,” Appl. Opt. 12, 2803–2804 (1973).
    [CrossRef] [PubMed]
  16. H. R. Gordon, “Modeling and simulating radiative transfer in the ocean,” in Ocean Optics, R. W. Spinrad, K. L. Carder, M. J. Perry, eds. (Oxford U. Press, Oxford, 1994), pp. 3–39.
  17. T. J. Petzold, “Volume scattering functions for selected natural waters,” (Scripps Institution of Oceanography, Visibility Laboratory, San Diego, Calif., 1972).
  18. R. H. Stavn, A. D. Weidemann, “Optical modeling of clear ocean light fields: Raman scattering effects,” Appl. Opt. 27, 4002–4011 (1988).
    [CrossRef] [PubMed]
  19. B. R. Marshall, R. C. Smith, “Raman scattering and in-water ocean optical properties,” Appl. Opt. 29, 71–84 (1990).
    [CrossRef] [PubMed]
  20. T. G. Peacock, K. L. Carder, C. O. Davis, R. G. Steward, “Effects of fluorescence and water Raman scattering on models of remote sensing reflectance,” in Ocean Optics X, R. W. Spinrad, ed., Proc. SPIE1302, 303–319 (1990).
    [CrossRef]
  21. Y. Ge, K. J. Voss, H. R. Gordon, “In situ measurements of inelastic scattering in Monterey Bay using solar Fraunhofer lines,” J. Geophys. Res. 100, 13,227–13,236 (1995).
    [CrossRef]

1995

Y. Ge, K. J. Voss, H. R. Gordon, “In situ measurements of inelastic scattering in Monterey Bay using solar Fraunhofer lines,” J. Geophys. Res. 100, 13,227–13,236 (1995).
[CrossRef]

1994

1993

1991

H. R. Gordon, “Absorption and scattering estimates from irradiance measurements: Monte Carlo simulations,” Limnol. Oceanogr. 36, 769–777 (1991).
[CrossRef]

1990

1988

1981

J. T. O. Kirk, “Estimation of the scattering coefficient of natural waters using underwater irradiance measurements,” Aust. J. Mar. Freshwater Res. 32, 533–539 (1981).
[CrossRef]

1977

A. Morel, L. Prieur, “Analysis of variations in ocean color,” Limnol. Oceanogr. 22, 709–722 (1977).
[CrossRef]

1975

G. W. Kattawar, “A three-parameter analytic phase function for multiple scattering calculations,” J. Quant. Spectrosc. Radiat. Transfer 15, 839–849 (1975).
[CrossRef]

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]

1973

1961

R. W. Preisendorfer, “Application of radiative transfer theory to light measurements in the sea,” Union Geodes. Geophys. Int. 10, 11–30 (1961).

1960

J. E. Tyler, “Radiance distribution as a function of depth in an underwater environment,” Bull. Scripps Inst. Oceanogr. 7, 363–411 (1960).

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, E. S. Nielsen, eds. (Academic, London, 1974) pp. 317–344.

Brown, O. B.

Carder, K. L.

T. G. Peacock, K. L. Carder, C. O. Davis, R. G. Steward, “Effects of fluorescence and water Raman scattering on models of remote sensing reflectance,” in Ocean Optics X, R. W. Spinrad, ed., Proc. SPIE1302, 303–319 (1990).
[CrossRef]

Davis, C. O.

T. G. Peacock, K. L. Carder, C. O. Davis, R. G. Steward, “Effects of fluorescence and water Raman scattering on models of remote sensing reflectance,” in Ocean Optics X, R. W. Spinrad, ed., Proc. SPIE1302, 303–319 (1990).
[CrossRef]

Ge, Y.

Y. Ge, K. J. Voss, H. R. Gordon, “In situ measurements of inelastic scattering in Monterey Bay using solar Fraunhofer lines,” J. Geophys. Res. 100, 13,227–13,236 (1995).
[CrossRef]

Gentili, B.

Gordon, H. R.

Y. Ge, K. J. Voss, H. R. Gordon, “In situ measurements of inelastic scattering in Monterey Bay using solar Fraunhofer lines,” J. Geophys. Res. 100, 13,227–13,236 (1995).
[CrossRef]

C. D. Mobley, B. Gentili, H. R. Gordon, Z. Jin, G. W. Kattawar, A. Morel, P. Reinersman, K. Stamnes, R. H. Stavn, “Comparison of numerical models for computing underwater light fields,” Appl. Opt. 32, 7484–7504 (1993).
[CrossRef] [PubMed]

H. R. Gordon, “Sensitivity of radiative transfer to small-angle scattering in the ocean: a quantitative assessment,” Appl. Opt. 32, 7505–7511 (1993).
[CrossRef] [PubMed]

H. R. Gordon, “Absorption and scattering estimates from irradiance measurements: Monte Carlo simulations,” Limnol. Oceanogr. 36, 769–777 (1991).
[CrossRef]

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]

H. R. Gordon, “Simple calculation of the diffuse reflectance of the ocean,” Appl. Opt. 12, 2803–2804 (1973).
[CrossRef] [PubMed]

H. R. Gordon, “Modeling and simulating radiative transfer in the ocean,” in Ocean Optics, R. W. Spinrad, K. L. Carder, M. J. Perry, eds. (Oxford U. Press, Oxford, 1994), pp. 3–39.

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

Jacobs, M. M.

Jin, Z.

Kattawar, G. W.

Kirk, J. T. O.

J. T. O. Kirk, “Estimation of the absorption and scattering coefficients of natural waters by the use of underwater irradiance measurements,” Appl. Opt. 33, 3276–3278 (1994).
[CrossRef] [PubMed]

J. T. O. Kirk, “Estimation of the scattering coefficient of natural waters using underwater irradiance measurements,” Aust. J. Mar. Freshwater Res. 32, 533–539 (1981).
[CrossRef]

Marshall, B. R.

Mobley, C. D.

Morel, A.

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).
[CrossRef]

Peacock, T. G.

T. G. Peacock, K. L. Carder, C. O. Davis, R. G. Steward, “Effects of fluorescence and water Raman scattering on models of remote sensing reflectance,” in Ocean Optics X, R. W. Spinrad, ed., Proc. SPIE1302, 303–319 (1990).
[CrossRef]

Petzold, T. J.

T. J. Petzold, “Volume scattering functions for selected natural waters,” (Scripps Institution of Oceanography, Visibility Laboratory, San Diego, Calif., 1972).

Preisendorfer, R. W.

R. W. Preisendorfer, “Application of radiative transfer theory to light measurements in the sea,” Union Geodes. Geophys. Int. 10, 11–30 (1961).

J. E. Tyler, R. W. Preisendorfer, “Transmission of energy within the sea: light,” in The Sea, M. N. Hill, ed. (Interscience, New York, 1962) pp. 397–451.

Prieur, L.

A. Morel, L. Prieur, “Analysis of variations in ocean color,” Limnol. Oceanogr. 22, 709–722 (1977).
[CrossRef]

Reinersman, P.

Smith, R. C.

Stamnes, K.

Stavn, R. H.

Steward, R. G.

T. G. Peacock, K. L. Carder, C. O. Davis, R. G. Steward, “Effects of fluorescence and water Raman scattering on models of remote sensing reflectance,” in Ocean Optics X, R. W. Spinrad, ed., Proc. SPIE1302, 303–319 (1990).
[CrossRef]

Tyler, J. E.

J. E. Tyler, “Radiance distribution as a function of depth in an underwater environment,” Bull. Scripps Inst. Oceanogr. 7, 363–411 (1960).

J. E. Tyler, R. W. Preisendorfer, “Transmission of energy within the sea: light,” in The Sea, M. N. Hill, ed. (Interscience, New York, 1962) pp. 397–451.

Voss, K. J.

Y. Ge, K. J. Voss, H. R. Gordon, “In situ measurements of inelastic scattering in Monterey Bay using solar Fraunhofer lines,” J. Geophys. Res. 100, 13,227–13,236 (1995).
[CrossRef]

Weidemann, A. D.

Appl. Opt.

Aust. J. Mar. Freshwater Res.

J. T. O. Kirk, “Estimation of the scattering coefficient of natural waters using underwater irradiance measurements,” Aust. J. Mar. Freshwater Res. 32, 533–539 (1981).
[CrossRef]

Bull. Scripps Inst. Oceanogr.

J. E. Tyler, “Radiance distribution as a function of depth in an underwater environment,” Bull. Scripps Inst. Oceanogr. 7, 363–411 (1960).

J. Geophys. Res.

Y. Ge, K. J. Voss, H. R. Gordon, “In situ measurements of inelastic scattering in Monterey Bay using solar Fraunhofer lines,” J. Geophys. Res. 100, 13,227–13,236 (1995).
[CrossRef]

J. Quant. Spectrosc. Radiat. Transfer

G. W. Kattawar, “A three-parameter analytic phase function for multiple scattering calculations,” J. Quant. Spectrosc. Radiat. Transfer 15, 839–849 (1975).
[CrossRef]

Limnol. Oceanogr.

H. R. Gordon, “Absorption and scattering estimates from irradiance measurements: Monte Carlo simulations,” Limnol. Oceanogr. 36, 769–777 (1991).
[CrossRef]

A. Morel, L. Prieur, “Analysis of variations in ocean color,” Limnol. Oceanogr. 22, 709–722 (1977).
[CrossRef]

Union Geodes. Geophys. Int.

R. W. Preisendorfer, “Application of radiative transfer theory to light measurements in the sea,” Union Geodes. Geophys. Int. 10, 11–30 (1961).

Other

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

H. R. Gordon, “Modeling and simulating radiative transfer in the ocean,” in Ocean Optics, R. W. Spinrad, K. L. Carder, M. J. Perry, eds. (Oxford U. Press, Oxford, 1994), pp. 3–39.

T. J. Petzold, “Volume scattering functions for selected natural waters,” (Scripps Institution of Oceanography, Visibility Laboratory, San Diego, Calif., 1972).

T. G. Peacock, K. L. Carder, C. O. Davis, R. G. Steward, “Effects of fluorescence and water Raman scattering on models of remote sensing reflectance,” in Ocean Optics X, R. W. Spinrad, ed., Proc. SPIE1302, 303–319 (1990).
[CrossRef]

C. D. Mobley, Light and Water; Radiative Transfer in Natural Waters (Academic, New York, 1994).

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

J. E. Tyler, R. W. Preisendorfer, “Transmission of energy within the sea: light,” in The Sea, M. N. Hill, ed. (Interscience, New York, 1962) pp. 397–451.

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Figures (3)

Fig. 1
Fig. 1

Scattering phase functions used in this study (normalized to unity).

Fig. 2
Fig. 2

Comparison between the true upwelling radiance (filled circles) and the values obtained by using the retrieved inherent optical properties (solid curves) in the presence of a reflecting bottom (z B = 4.75, A B = 1.0), using the correct P(Θ). Curves from left to right correspond to ω0 = 0.2, 0.6, and 0.8. The corresponding cases for an infinitely deep medium are provided by the open circles and the dotted curves.

Fig. 3
Fig. 3

Example of the fit of L u to the pseudodata when an incorrect value of A B is used in the retrievals. Here ω0 = 0.8, g = 0.85 (used to create the pseudodata and to operate the inversion algorithm), z B = 4.75 m, and the true A B was 0.5. The filled circles provide the L u(z) pseudodata using these parameters. The dotted, solid, and dashed curves are the L u profiles obtained by using the retrieved inherent optical properties with A B = 0.45, 0.50, and 0.55, respectively, used in the inversion algorithm.

Tables (5)

Tables Icon

Table 1 Test of the E u E d Algorithm with a Correct and Incorrect P(Θ) used in the Inversion

Tables Icon

Table 2 Test of the Algorithms with Tyler’s Radiance Data

Tables Icon

Table 3 Test of the L u E d Algorithm with a Correct and Incorrect P(Θ) used in the Inversion

Tables Icon

Table 4 Test of E u E d and E u E d Algorithmsa

Tables Icon

Table 5 Test of the L uE d Algorithm with a Correct and Incorrect P(Θ) used in the Inversiona

Equations (5)

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

az=μ¯zKEz,
a(0)=0zma0zfzdz0zmfzdz,
b˜bbbb=2π π/2π PΘsin Θ cos Θ dΘ.
δn=1Ni=1NlnEdnzi-lnEdzi+1Ni=1N×lnEunzi-lnEuzi,
Lu  Pπ-θ01+μ0,

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