Abstract

We examine the problem of uniqueness in the relationship between the remote-sensing reflectance (Rrs) and the inherent optical properties (IOPs) of ocean water. The results point to the fact that diffuse reflectance of plane irradiance from ocean water is inherently ambiguous. Furthermore, in the 400 < λ < 750 nm region of the spectrum, Rrs(λ) also suffers from ambiguity caused by the similarity in wavelength dependence of the coefficients of absorption by particulate matter and of absorption by colored dissolved organic matter. The absorption coefficients have overlapping exponential responses, which lead to the fact that more than one combination of IOPs can produce nearly the same Rrs spectrum. This ambiguity in absorption parameters demands that we identify the regions of the Rrs spectrum where we can isolate the effects that are due only to scattering by particulates and to absorption by pure water. The results indicate that the spectral shape of the absorption coefficient of phytoplankton, a ph(λ), cannot be derived from a multiparameter fit to Rrs(λ). However, the magnitude and the spectral dependence of the absorption coefficient can be estimated from the difference between the measured Rrs(λ) and the best fit to Rrs(λ) in terms of IOPs that exclude a ph(λ).

© 2004 Optical Society of America

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References

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  1. C. D. Mobley, “Inverse methods,” in Light and Water (Academic, San Diego, Calif., 1994), pp. 473–497.
  2. C. S. Roesler, E. Boss, “A novel reflectance inversion model: retrieval of beam attenuation coefficients and particle size distributions from ocean color” in Ocean Optics XVI (CD-ROM) (Office of Naval Research, Washington, D.C., 2002), PDF 099.
  3. H. R. Gordon, O. B. Brown, M. M. Jacobs, “Computed relationships between the inherent and apparent optical properties of a flat homogenous ocean,” Appl. Opt. 14, 417–427 (1975).
    [CrossRef] [PubMed]
  4. J. H. Jerome, R. P. Bukata, J. R. Miller, “Remote sensing and its relationship to optical properties on natural waters,” Int. J. Remote Sens. 17, 3135–3155 (1996).
    [CrossRef]
  5. A. Morel, L. Prieur, “Analysis of variations in ocean color,” Limn. Oceanogr. 22, 709–722 (1977).
    [CrossRef]
  6. A. Morel, J. V. Voss, B. Gentili, “Bidirectional reflectance of oceanic water: a comparison of modeled and measured upward radiance,” J. Geophys. Res. 100, 143–151 (1995).
    [CrossRef]
  7. S. D. Ladner, R. A. Arnone, R. W. Gould, A. D. Weidermann, V. I. Haltrin, Z. Lee, P. Martinolich, T. Bergmann, “Variability in the backscattering to scattering and f/Q ratios observed in natural waters,” in Ocean Optics XVI(CD-ROM) (Office of Naval Research, Washington, D.C., 2002), PDF 194.
  8. V. I. Haltrin, M. E. Lee, E. B. Shybanov, R. A. Arnone, A. D. Weidermann, V. I. Mankovsky, W. S. Pegau, S. D. Ladner, “Relation between backscattering and beam scattering coefficients derived from measurements of light scattering phase function,” in Ocean Optics XVI(CD-ROM) (Office of Naval Research, Washington, D.C., 2002), PDF 094.
  9. M. Sydor, “Treatment of reflectance from coastal waters in terms of the probability for multiple scattering,” in Ocean Optics XVI(CD-ROM) (Office of Naval Research, Washington, D.C., 2002), PDF 049.
  10. T. J. Petzold, “Volume scattering functions for selected ocean waters,” Report SIO Ref. 72–78 (Visibility Laboratory, Scripps Institution of Oceanography, San Diego, Calif., 1972), p. 79.
  11. M. Sydor, D. B. Wolz, A. M. Thralow, “Spectral analysis of bulk reflectance from coastal waters,” J. Coastal Res. 18, 352–361 (2002).
  12. C. H. Whitlock, L. R. Poole, J. W. Usry, W. M. Houghton, W. G. Witte, W. D. Morris, E. A. Gurganus, “Comparison of reflectance with backscatter and absorption parameters for turbid water,” Appl. Opt. 20, 517–522 (1981).
    [CrossRef] [PubMed]
  13. E. B. Shybavov , “Method for retrieval of the spectral properties of optically active substances from measurement of water’s reflectance,” Ph.D. dissertation (Marine Hydrophysical Institute, National Academy of Ukraine, Sevastopol, Ukraine, 2002).

2002 (1)

M. Sydor, D. B. Wolz, A. M. Thralow, “Spectral analysis of bulk reflectance from coastal waters,” J. Coastal Res. 18, 352–361 (2002).

1996 (1)

J. H. Jerome, R. P. Bukata, J. R. Miller, “Remote sensing and its relationship to optical properties on natural waters,” Int. J. Remote Sens. 17, 3135–3155 (1996).
[CrossRef]

1995 (1)

A. Morel, J. V. Voss, B. Gentili, “Bidirectional reflectance of oceanic water: a comparison of modeled and measured upward radiance,” J. Geophys. Res. 100, 143–151 (1995).
[CrossRef]

1981 (1)

1977 (1)

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

1975 (1)

Arnone, R. A.

V. I. Haltrin, M. E. Lee, E. B. Shybanov, R. A. Arnone, A. D. Weidermann, V. I. Mankovsky, W. S. Pegau, S. D. Ladner, “Relation between backscattering and beam scattering coefficients derived from measurements of light scattering phase function,” in Ocean Optics XVI(CD-ROM) (Office of Naval Research, Washington, D.C., 2002), PDF 094.

S. D. Ladner, R. A. Arnone, R. W. Gould, A. D. Weidermann, V. I. Haltrin, Z. Lee, P. Martinolich, T. Bergmann, “Variability in the backscattering to scattering and f/Q ratios observed in natural waters,” in Ocean Optics XVI(CD-ROM) (Office of Naval Research, Washington, D.C., 2002), PDF 194.

Bergmann, T.

S. D. Ladner, R. A. Arnone, R. W. Gould, A. D. Weidermann, V. I. Haltrin, Z. Lee, P. Martinolich, T. Bergmann, “Variability in the backscattering to scattering and f/Q ratios observed in natural waters,” in Ocean Optics XVI(CD-ROM) (Office of Naval Research, Washington, D.C., 2002), PDF 194.

Boss, E.

C. S. Roesler, E. Boss, “A novel reflectance inversion model: retrieval of beam attenuation coefficients and particle size distributions from ocean color” in Ocean Optics XVI (CD-ROM) (Office of Naval Research, Washington, D.C., 2002), PDF 099.

Brown, O. B.

Bukata, R. P.

J. H. Jerome, R. P. Bukata, J. R. Miller, “Remote sensing and its relationship to optical properties on natural waters,” Int. J. Remote Sens. 17, 3135–3155 (1996).
[CrossRef]

Gentili, B.

A. Morel, J. V. Voss, B. Gentili, “Bidirectional reflectance of oceanic water: a comparison of modeled and measured upward radiance,” J. Geophys. Res. 100, 143–151 (1995).
[CrossRef]

Gordon, H. R.

Gould, R. W.

S. D. Ladner, R. A. Arnone, R. W. Gould, A. D. Weidermann, V. I. Haltrin, Z. Lee, P. Martinolich, T. Bergmann, “Variability in the backscattering to scattering and f/Q ratios observed in natural waters,” in Ocean Optics XVI(CD-ROM) (Office of Naval Research, Washington, D.C., 2002), PDF 194.

Gurganus, E. A.

Haltrin, V. I.

V. I. Haltrin, M. E. Lee, E. B. Shybanov, R. A. Arnone, A. D. Weidermann, V. I. Mankovsky, W. S. Pegau, S. D. Ladner, “Relation between backscattering and beam scattering coefficients derived from measurements of light scattering phase function,” in Ocean Optics XVI(CD-ROM) (Office of Naval Research, Washington, D.C., 2002), PDF 094.

S. D. Ladner, R. A. Arnone, R. W. Gould, A. D. Weidermann, V. I. Haltrin, Z. Lee, P. Martinolich, T. Bergmann, “Variability in the backscattering to scattering and f/Q ratios observed in natural waters,” in Ocean Optics XVI(CD-ROM) (Office of Naval Research, Washington, D.C., 2002), PDF 194.

Houghton, W. M.

Jacobs, M. M.

Jerome, J. H.

J. H. Jerome, R. P. Bukata, J. R. Miller, “Remote sensing and its relationship to optical properties on natural waters,” Int. J. Remote Sens. 17, 3135–3155 (1996).
[CrossRef]

Ladner, S. D.

S. D. Ladner, R. A. Arnone, R. W. Gould, A. D. Weidermann, V. I. Haltrin, Z. Lee, P. Martinolich, T. Bergmann, “Variability in the backscattering to scattering and f/Q ratios observed in natural waters,” in Ocean Optics XVI(CD-ROM) (Office of Naval Research, Washington, D.C., 2002), PDF 194.

V. I. Haltrin, M. E. Lee, E. B. Shybanov, R. A. Arnone, A. D. Weidermann, V. I. Mankovsky, W. S. Pegau, S. D. Ladner, “Relation between backscattering and beam scattering coefficients derived from measurements of light scattering phase function,” in Ocean Optics XVI(CD-ROM) (Office of Naval Research, Washington, D.C., 2002), PDF 094.

Lee, M. E.

V. I. Haltrin, M. E. Lee, E. B. Shybanov, R. A. Arnone, A. D. Weidermann, V. I. Mankovsky, W. S. Pegau, S. D. Ladner, “Relation between backscattering and beam scattering coefficients derived from measurements of light scattering phase function,” in Ocean Optics XVI(CD-ROM) (Office of Naval Research, Washington, D.C., 2002), PDF 094.

Lee, Z.

S. D. Ladner, R. A. Arnone, R. W. Gould, A. D. Weidermann, V. I. Haltrin, Z. Lee, P. Martinolich, T. Bergmann, “Variability in the backscattering to scattering and f/Q ratios observed in natural waters,” in Ocean Optics XVI(CD-ROM) (Office of Naval Research, Washington, D.C., 2002), PDF 194.

Mankovsky, V. I.

V. I. Haltrin, M. E. Lee, E. B. Shybanov, R. A. Arnone, A. D. Weidermann, V. I. Mankovsky, W. S. Pegau, S. D. Ladner, “Relation between backscattering and beam scattering coefficients derived from measurements of light scattering phase function,” in Ocean Optics XVI(CD-ROM) (Office of Naval Research, Washington, D.C., 2002), PDF 094.

Martinolich, P.

S. D. Ladner, R. A. Arnone, R. W. Gould, A. D. Weidermann, V. I. Haltrin, Z. Lee, P. Martinolich, T. Bergmann, “Variability in the backscattering to scattering and f/Q ratios observed in natural waters,” in Ocean Optics XVI(CD-ROM) (Office of Naval Research, Washington, D.C., 2002), PDF 194.

Miller, J. R.

J. H. Jerome, R. P. Bukata, J. R. Miller, “Remote sensing and its relationship to optical properties on natural waters,” Int. J. Remote Sens. 17, 3135–3155 (1996).
[CrossRef]

Mobley, C. D.

C. D. Mobley, “Inverse methods,” in Light and Water (Academic, San Diego, Calif., 1994), pp. 473–497.

Morel, A.

A. Morel, J. V. Voss, B. Gentili, “Bidirectional reflectance of oceanic water: a comparison of modeled and measured upward radiance,” J. Geophys. Res. 100, 143–151 (1995).
[CrossRef]

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

Morris, W. D.

Pegau, W. S.

V. I. Haltrin, M. E. Lee, E. B. Shybanov, R. A. Arnone, A. D. Weidermann, V. I. Mankovsky, W. S. Pegau, S. D. Ladner, “Relation between backscattering and beam scattering coefficients derived from measurements of light scattering phase function,” in Ocean Optics XVI(CD-ROM) (Office of Naval Research, Washington, D.C., 2002), PDF 094.

Petzold, T. J.

T. J. Petzold, “Volume scattering functions for selected ocean waters,” Report SIO Ref. 72–78 (Visibility Laboratory, Scripps Institution of Oceanography, San Diego, Calif., 1972), p. 79.

Poole, L. R.

Prieur, L.

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

Roesler, C. S.

C. S. Roesler, E. Boss, “A novel reflectance inversion model: retrieval of beam attenuation coefficients and particle size distributions from ocean color” in Ocean Optics XVI (CD-ROM) (Office of Naval Research, Washington, D.C., 2002), PDF 099.

Shybanov, E. B.

V. I. Haltrin, M. E. Lee, E. B. Shybanov, R. A. Arnone, A. D. Weidermann, V. I. Mankovsky, W. S. Pegau, S. D. Ladner, “Relation between backscattering and beam scattering coefficients derived from measurements of light scattering phase function,” in Ocean Optics XVI(CD-ROM) (Office of Naval Research, Washington, D.C., 2002), PDF 094.

Shybavov, E. B.

E. B. Shybavov , “Method for retrieval of the spectral properties of optically active substances from measurement of water’s reflectance,” Ph.D. dissertation (Marine Hydrophysical Institute, National Academy of Ukraine, Sevastopol, Ukraine, 2002).

Sydor, M.

M. Sydor, D. B. Wolz, A. M. Thralow, “Spectral analysis of bulk reflectance from coastal waters,” J. Coastal Res. 18, 352–361 (2002).

M. Sydor, “Treatment of reflectance from coastal waters in terms of the probability for multiple scattering,” in Ocean Optics XVI(CD-ROM) (Office of Naval Research, Washington, D.C., 2002), PDF 049.

Thralow, A. M.

M. Sydor, D. B. Wolz, A. M. Thralow, “Spectral analysis of bulk reflectance from coastal waters,” J. Coastal Res. 18, 352–361 (2002).

Usry, J. W.

Voss, J. V.

A. Morel, J. V. Voss, B. Gentili, “Bidirectional reflectance of oceanic water: a comparison of modeled and measured upward radiance,” J. Geophys. Res. 100, 143–151 (1995).
[CrossRef]

Weidermann, A. D.

V. I. Haltrin, M. E. Lee, E. B. Shybanov, R. A. Arnone, A. D. Weidermann, V. I. Mankovsky, W. S. Pegau, S. D. Ladner, “Relation between backscattering and beam scattering coefficients derived from measurements of light scattering phase function,” in Ocean Optics XVI(CD-ROM) (Office of Naval Research, Washington, D.C., 2002), PDF 094.

S. D. Ladner, R. A. Arnone, R. W. Gould, A. D. Weidermann, V. I. Haltrin, Z. Lee, P. Martinolich, T. Bergmann, “Variability in the backscattering to scattering and f/Q ratios observed in natural waters,” in Ocean Optics XVI(CD-ROM) (Office of Naval Research, Washington, D.C., 2002), PDF 194.

Whitlock, C. H.

Witte, W. G.

Wolz, D. B.

M. Sydor, D. B. Wolz, A. M. Thralow, “Spectral analysis of bulk reflectance from coastal waters,” J. Coastal Res. 18, 352–361 (2002).

Appl. Opt. (2)

Int. J. Remote Sens. (1)

J. H. Jerome, R. P. Bukata, J. R. Miller, “Remote sensing and its relationship to optical properties on natural waters,” Int. J. Remote Sens. 17, 3135–3155 (1996).
[CrossRef]

J. Coastal Res. (1)

M. Sydor, D. B. Wolz, A. M. Thralow, “Spectral analysis of bulk reflectance from coastal waters,” J. Coastal Res. 18, 352–361 (2002).

J. Geophys. Res. (1)

A. Morel, J. V. Voss, B. Gentili, “Bidirectional reflectance of oceanic water: a comparison of modeled and measured upward radiance,” J. Geophys. Res. 100, 143–151 (1995).
[CrossRef]

Limn. Oceanogr. (1)

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

Other (7)

S. D. Ladner, R. A. Arnone, R. W. Gould, A. D. Weidermann, V. I. Haltrin, Z. Lee, P. Martinolich, T. Bergmann, “Variability in the backscattering to scattering and f/Q ratios observed in natural waters,” in Ocean Optics XVI(CD-ROM) (Office of Naval Research, Washington, D.C., 2002), PDF 194.

V. I. Haltrin, M. E. Lee, E. B. Shybanov, R. A. Arnone, A. D. Weidermann, V. I. Mankovsky, W. S. Pegau, S. D. Ladner, “Relation between backscattering and beam scattering coefficients derived from measurements of light scattering phase function,” in Ocean Optics XVI(CD-ROM) (Office of Naval Research, Washington, D.C., 2002), PDF 094.

M. Sydor, “Treatment of reflectance from coastal waters in terms of the probability for multiple scattering,” in Ocean Optics XVI(CD-ROM) (Office of Naval Research, Washington, D.C., 2002), PDF 049.

T. J. Petzold, “Volume scattering functions for selected ocean waters,” Report SIO Ref. 72–78 (Visibility Laboratory, Scripps Institution of Oceanography, San Diego, Calif., 1972), p. 79.

C. D. Mobley, “Inverse methods,” in Light and Water (Academic, San Diego, Calif., 1994), pp. 473–497.

C. S. Roesler, E. Boss, “A novel reflectance inversion model: retrieval of beam attenuation coefficients and particle size distributions from ocean color” in Ocean Optics XVI (CD-ROM) (Office of Naval Research, Washington, D.C., 2002), PDF 099.

E. B. Shybavov , “Method for retrieval of the spectral properties of optically active substances from measurement of water’s reflectance,” Ph.D. dissertation (Marine Hydrophysical Institute, National Academy of Ukraine, Sevastopol, Ukraine, 2002).

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Figures (10)

Fig. 1
Fig. 1

Spectral absorption coefficients derived from relation (4) applied in sequential fit to Rrs(λ) off the coast of South Africa before the onset of phytoplankton bloom. 1, 2, 3, Predicted a y , a p , a ph, respectively. Rrs(λ) was traced from enlarged figures shown by Roesler and Boss.2 Solid and filled triangles and circles, a y and a p , respectively, taken from Roesler and Boss. The wavelength dependence of the surrogate a ph*(λ) used in the sequential fit was based on a ph(λ) measured in the waters of the Mississippi Sound (Ref. 11). The magnitude of a ph(λ) shown here corresponds roughly to 0.038a ph*(λ). No attempt was made to back out the actual a ph(λ) spectrum off the coast of South Africa. We assumed that a w (λ) dominated a(λ) for λ > 650 nm. This assumption is justified because at 650 nm a w650 ∼ 0.35 m-1, which is far greater than the combined values of a d , a ph, and a y at 650 nm reported by Roesler and Boss.

Fig. 2
Fig. 2

Filled squares, Rrs(λ) off the coast of South Africa taken from Ref. 2. Solid curve, sequential fit to Rrs(λ) based on relation (4) with C b = 0.0011 and b(λ) = 0.39(730/λ)1.1.

Fig. 3
Fig. 3

Solid line, r 2 = 0.99 correlation between sequentially simulated Rrs(λ) and reported Rrs(λ) (filled squares from Fig. 2).

Fig. 4
Fig. 4

Filled squares, reflectance R(λ) off the coast of Oregon. The data were traced from Roesler and Boss.2 Close fits to this R(λ) can be obtained by use of real and false sets of IOP parameters. Dotted curve, first-order sequential fit without any iteration. Solid curve, sequential parameter fit by iteration to find the best fit. Dashed curve, example of an ad hoc parameter fit. The contrived ad hoc fit departs from the experimental R(λ) at longer wavelengths where a w dominates the absorption and thereby limits the possibility of a false fit. Curve 1, fit from use of 0.0065b/ a w alone, indicating that in this case 1/(λa w ) determines the spectral shape of R(λ) for λ > 500 nm.

Fig. 5
Fig. 5

Curve 1, b(λ) determined from R(λ) versus C b ′/a w in the λ > 560 nm region of R(λ) shown by the filled squares in Fig. 4. Curve 2, b(λ) for the false ad hoc fit to R(λ). b(λ) obtained in the ad hoc fit is deemed unlikely, as its magnitude increases with λ. Nonetheless, the ad hoc b(λ) produces a close fit to R(λ) as long as a d (λ) and a y (λ) are adjusted accordingly.

Fig. 6
Fig. 6

The solid trace and curve 2 show a p (λ) from the sequential and the ad hoc fits, respectively, to R(λ) off the Oregon Coast (filled squares in Fig. 4). Curve 3, a d (λ), the detrital component of a p (λ). Most of the absorption by suspended particles off the Coast of Oregon is attributable to a ph(λ), whose magnitude here was 0.0035a ph*(λ) of the waters of the Mississippi Sound. The lone upward-pointing triangle shows an experimental point for a p reported by Roesler and Boss.2 Curves A and B, a y (λ) for the sequential and the ad hoc fits, respectively. The downward-pointing triangle shows the lone a y point reported by Roesler and Boss.2 We assumed that a w dominates the absorption in the tail of R(λ) for λ > 560 nm. Curve 1 of Fig. 4 shows that this assumption was justified. The pure-water tail, where a w (λ) ∼ a(λ), shifts toward the shorter wavelengths when the concentration of suspended particles and CDOM is low.

Fig. 7
Fig. 7

Wavelength dependence of Rrs(λ) for turbid waters of Pearl River, Miss. Solid and dashed curves, two (independently) surface corrected values of Rrs(λ) for Pearl River. The triangles show that b b /(a + b b ) does not follow the measured Rrs(λ); the filled squares show that (b/ a)(1 - 2πRrs) follows the spectral shape of Rrs(λ) quite closely. To compare their spectral dependence we normalized both cases to the measured Rrs at 620 nm. The dotted curve shows that the sequential fit to Rrs(λ) has the correct magnitude and displays the fine spectral features exhibited in the measured Rrs(λ).

Fig. 8
Fig. 8

Filled squares, b(λ) for Pearl River determined with an ac9 instrument. Stars, b b (λ) measured with Hydroscat (multiplied here by a factor of 14 to permit its wavelength dependence to be compared with that of b(λ)). Solid curve, b(λ) obtained from a sequential fit by use of relation (4) and C b = 0.0012 sr-1.

Fig. 9
Fig. 9

Downward-pointing triangles a(λ) (without a w ) for the waters of Pearl River, Miss. Upward-pointing triangles, the sum of a y (λ) measured with a 0.045-μm pore filter at the intake of the ac9 meter plus a p (λ) determined from a filter-pad transmission measurement. Solid curve, a(λ) obtained from the sequential fit from relation (4).

Fig. 10
Fig. 10

In the linear limit of Rrs ≪ 1 and constant b b /b < 0.03, Eq. (3) and relation (4) give comparable results for Rrs(λ). Downward-pointing triangles, Rrs(λ) obtained from Eq. (3) by Hydroscat b b (λ) and ac9 measurement of a(λ). Upward-pointing triangles, Rrs(λ) predicted by relation (4) from ac9-determined b(λ) and a(λ). Solid curve, measured Rrs(λ).

Equations (4)

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

R=fbb/a+bb,
Rrsw=f/Qbb/a+bb,
Rrs=f/Qtt/nR2bb/a+bb sr-1,
Rrs/1-2πRrsCbb/a,

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