Abstract

A model based on a matrix-operator theory capable of simulating underwater daylight in the ocean is presented. The main focus is on gelbstoff and chlorophyll fluorescence as well as water Raman scattering as sources of inelastic scattering and their effect on underwater daylight and relevance for the remote sensing of ocean color. Any combination of inelastic sources can be investigated, including differences in simulated underwater daylight in the absence and the presence of these sources. To our knowledge, it is the first matrix-operator model to include all these inelastic sources. The model allows simulations for case 1 and case 2 waters. Calculations can be done with highly anisotropic phase functions as they are observed in the ocean, and every order of multiple scattering is considered. A detailed mathematical description of inelastic sources is given, and a special treatment of the depth dependency of these sources is presented. The model is validated by comparison with depth-dependent and spectrally resolved measurements of downward irradiance in the open ocean. The differences between measured and simulated data are within the error of the radiometric measurements. Water Raman scattering has been found to contribute significantly to water-leaving radiance. The inelastic fraction depends on the water Raman scattering coefficient, on the ratio of the total attenuation coefficient at excitation and emission wavelengths, and on the spectral course of the irradiance incident on the ocean. For clear ocean waters the inelastic fraction can reach values of more than 17% [C = 0.03 mg m-3, ay (440 nm) = 0.01 m-1] at wavelengths relevant for the remote sensing of ocean color. The inelastic fraction of gelbstoff fluorescence can reach or even exceed the relevance of water Raman scattering at short wavelengths. In the water column, depending on optically active substances and on actual depth, water Raman scattering can provide 100% of the light field at wavelengths greater than 580 nm. The effect of gelbstoff fluorescence on depth-dependent irradiances is less significant than the effect of water Raman scattering in all cases considered, except for near surface levels and high gelbstoff concentrations.

© 2003 Optical Society of America

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2002 (1)

M. Babin, D. Stramski, “Light absorption by aquatic particles in the near-infrared spectral region,” Limnol. Oceanogr. 47, 911–915 (2002).
[CrossRef]

2001 (2)

K. G. Ruddick, H. J. Gons, M. Rijkeboer, G. Tilstone, “Optical remote sensing of chlorophyll a in case 2 waters by use of an adaptive two-band algorithm with optimal error properties,” Appl. Opt. 40, 3575–3585 (2001).
[CrossRef]

F. Fell, J. Fischer, “Numerical simulations of the light field in the atmosphere-ocean system using the matrix-operator theory,” J. Quant. Spectrosc. Radiat. Transfer 69, 351–388 (2001).
[CrossRef]

2000 (3)

1999 (1)

1998 (2)

J. S. Bartlett, K. J. Voss, S. Sathyendranath, A. Vodacek, “Raman scattering by pure water and seawater,” Appl. Opt. 37, 3324–3332 (1998).
[CrossRef]

G. Thuillier, M. Herse, P. C. Simon, D. Labs, H. Mandel, D. Gillotay, T. Foujols, “The visible solar spectral irradiance from 350 to 850 nm as measured by the SOLSPEC spectrometer during the ATLAS-1 mission,” Sol. Phys. 177, 41–61 (1998).
[CrossRef]

1997 (3)

1996 (1)

P. G. Coble, “Characterization of marine and terrestrial DOM in seawater using excitation-emission matrix spectroscopy,” Mar. Chem. 51, 325–346 (1996).
[CrossRef]

1995 (1)

K. J. Waters, “Effects of Raman scattering on the water-leaving radiance,” J. Geophys. Res. 100, 13151–13161 (1995).
[CrossRef]

1994 (2)

Z. Jin, K. Stamnes, “Radiative transfer in nonuniformly refracting layered media: atmosphere-ocean system,” Appl. Opt. 33, 431–442 (1994).
[CrossRef] [PubMed]

S. A. Green, N. V. Blough, “Optical absorption and fluorescence properties of chromorphic dissolved organic matter in natural waters,” Limnol. Oceanogr. 39, 1903–1916 (1994).
[CrossRef]

1993 (4)

1990 (2)

B. R. Marshall, R. C. Smith, “Raman scattering and in-water ocean properties,” Appl. Opt. 29, 71–84 (1990).
[CrossRef] [PubMed]

J. Fischer, U. Kronfeld, “Sun-stimulated chlorophyll fluorescence. 1: Influence of oceanic properties,” Int. J. Remote Sens. 11, 2125–2147 (1990).
[CrossRef]

1989 (1)

D. A. Kiefer, W. S. Chamberlin, C. R. Booth, “Natural fluorescence of chlorophyll a: relationship to photosynthesis and chlorophyll concentration in the western South Pacific gyre,” Limnol. Oceanogr. 34, 868–881 (1989).
[CrossRef]

1988 (1)

1987 (1)

R. Doerffer, J. Fischer, “Measurements and model simulations of Sun-stimulated chlorophyll fluorescence within a daily cycle,” Adv. Space Res. 7, 117–120 (1987).
[CrossRef]

1986 (1)

1981 (3)

A. Bricaud, A. Morel, L. Prieur, “Absorption by dissolved organic matter of the sea (yellow substance) in the UV and visible domains,” Limnol. Oceanogr. 26, 43–53 (1981).
[CrossRef]

R. C. Smith, K. S. Baker, “Optical properties of the clearest natural waters (200–800 nm),” Appl. Opt. 20, 177–184 (1981).
[CrossRef] [PubMed]

L. Prieur, S. Sathyendranath, “An optical classification of coastal and oceanic waters based on the specific spectral absorption curves of phytoplankton pigments, dissolved organic matter, and other particulate materials,” Limnol. Oceanogr. 26, 671–689 (1981).
[CrossRef]

1979 (1)

1973 (1)

1970 (1)

J. F. Potter, “The delta function approximation in radiative transfer theory,” J. Atmos. Sci. 27, 943–949 (1970).
[CrossRef]

1969 (3)

E. D. Traganza, “Fluorescence excitation and emission spectra of dissolved organic matter in sea water,” Bull. Mar. Sci. 19, 897–904 (1969).

I. Grant, G. Hunt, “Discrete space theory of radiative transfer I + II: fundamentals and stability and non-negativity,” Proc. R. Soc. London Ser. A 313, 183–197, 199–216 (1969).
[CrossRef]

G. E. Walrafen, “Continuum model of water—an erroneous interpretation,” J. Chem. Phys. 50, 567–569 (1969).
[CrossRef]

1967 (1)

G. E. Walrafen, “Raman spectral studies of the effects of temperature on water structure,” J. Chem. Phys. 47, 114–126 (1967).
[CrossRef]

1966 (1)

1962 (1)

R. Redheffer, “On the relation of transmission-line theory to scattering and transfer,” J. Math. Phys. 41, 1–41 (1962).

1943 (1)

V. A. Ambarzumian, “Diffusion of light by a foggy medium,” C. R. Acad. Sci. USSR 38, 229–232 (1943).

1908 (1)

G. Mie, “Beiträge zur Optik trüber Medien, speziell kolloidaler Metall-Lösungen,” Ann. Phys. 25, 377–445 (1908).
[CrossRef]

1862 (1)

G. G. Stokes, “On the intensity of the light reflected from or transmitted through a pile of plates,” Proc. R. Soc. London 11, 545–556 (1862).
[CrossRef]

Ambarzumian, V. A.

V. A. Ambarzumian, “Diffusion of light by a foggy medium,” C. R. Acad. Sci. USSR 38, 229–232 (1943).

Arnone, R. A.

R. W. Gould, R. A. Arnone, “Remote sensing estimates of inherent optical properties in a coastal environment,” Remote Sens. Environ. 61, 290–301 (1997).
[CrossRef]

Babin, M.

M. Babin, D. Stramski, “Light absorption by aquatic particles in the near-infrared spectral region,” Limnol. Oceanogr. 47, 911–915 (2002).
[CrossRef]

Baker, K. S.

Bartlett, J. S.

Bartsch, B.

Blough, N. V.

S. A. Green, N. V. Blough, “Optical absorption and fluorescence properties of chromorphic dissolved organic matter in natural waters,” Limnol. Oceanogr. 39, 1903–1916 (1994).
[CrossRef]

Booth, C. R.

D. A. Kiefer, W. S. Chamberlin, C. R. Booth, “Natural fluorescence of chlorophyll a: relationship to photosynthesis and chlorophyll concentration in the western South Pacific gyre,” Limnol. Oceanogr. 34, 868–881 (1989).
[CrossRef]

Braeske, T.

Breves, W.

W. Breves, R. Reuter, “Bio-optical observations of gelbstoff in the Arabian Sea at the onset of the southwest monsoon,” Proc. Indian Acad. Sci. (Earth Planet. Sci.) 109, 415–425 (2000).

W. Breves, R. Heuermann, R. Reuter, “Enhanced red fluorescence emission in the oxygen minimum zone of the Arabian Sea,” Ocean Dyn. (to be published).

Bricaud, A.

A. Bricaud, A. Morel, L. Prieur, “Absorption by dissolved organic matter of the sea (yellow substance) in the UV and visible domains,” Limnol. Oceanogr. 26, 43–53 (1981).
[CrossRef]

Carder, C. K.

S. K. Hawes, C. K. Carder, G. R. Harvey, “Quantum fluorescence efficiencies of fulvic and humic acids: effects on ocean color and fluorometric detection,” in Ocean Optics XI, G. D. Gilbert, ed., Proc. SPIE1750, 212–223 (1992).
[CrossRef]

Catchings, F. E.

Chamberlin, W. S.

D. A. Kiefer, W. S. Chamberlin, C. R. Booth, “Natural fluorescence of chlorophyll a: relationship to photosynthesis and chlorophyll concentration in the western South Pacific gyre,” Limnol. Oceanogr. 34, 868–881 (1989).
[CrossRef]

Chandrasekhar, S.

S. Chandrasekhar, Radiative Transfer (Dover, New York, 1960).

Chang, A. H.

A. H. Chang, L. A. Young, “Seawater temperature measurement from Raman spectra,” , (AVCO Everett Research Laboratory, Everett, Mass., 1974), pp. 82.

Coble, P. G.

P. G. Coble, “Characterization of marine and terrestrial DOM in seawater using excitation-emission matrix spectroscopy,” Mar. Chem. 51, 325–346 (1996).
[CrossRef]

Doerffer, R.

R. Doerffer, J. Fischer, “Measurements and model simulations of Sun-stimulated chlorophyll fluorescence within a daily cycle,” Adv. Space Res. 7, 117–120 (1987).
[CrossRef]

J. Fischer, R. Doerffer, H. Grassl, “Factor analysis of multispectral radiances over coastal and open ocean water based on radiative-transfer calculations,” Appl. Opt. 25, 448–456 (1986).
[CrossRef] [PubMed]

R. Doerffer, H. Schiller, “Pigment index, sediment and gelbstoff retrieval from directional water-leaving radiance reflectances using inverse modeling techniques,” (ESA—European Space Research and Technology Center, Nordweijk, Netherlands, 1997).

Ernst, D.

K. Günther, D. Ernst, M. Maske, “Biophysical process of chlorophyll a fluorescence,” in The Use of Chlorophyll Fluorescence Measurements from Space for Separating Constituents of Seawater, European Space Agency contract RFQ 3-5059/84/NL/MD, Vol. II [Gesellschaft zur Kernenergieverwertung in Schiffbau und Schifffahrt (GKSS), Forschungszentrum Geesthacht, Geesthacht, Germany, 1986].

Fell, F.

F. Fell, J. Fischer, “Numerical simulations of the light field in the atmosphere-ocean system using the matrix-operator theory,” J. Quant. Spectrosc. Radiat. Transfer 69, 351–388 (2001).
[CrossRef]

Fischer, J.

F. Fell, J. Fischer, “Numerical simulations of the light field in the atmosphere-ocean system using the matrix-operator theory,” J. Quant. Spectrosc. Radiat. Transfer 69, 351–388 (2001).
[CrossRef]

J. Fischer, U. Kronfeld, “Sun-stimulated chlorophyll fluorescence. 1: Influence of oceanic properties,” Int. J. Remote Sens. 11, 2125–2147 (1990).
[CrossRef]

R. Doerffer, J. Fischer, “Measurements and model simulations of Sun-stimulated chlorophyll fluorescence within a daily cycle,” Adv. Space Res. 7, 117–120 (1987).
[CrossRef]

J. Fischer, R. Doerffer, H. Grassl, “Factor analysis of multispectral radiances over coastal and open ocean water based on radiative-transfer calculations,” Appl. Opt. 25, 448–456 (1986).
[CrossRef] [PubMed]

Foujols, T.

G. Thuillier, M. Herse, P. C. Simon, D. Labs, H. Mandel, D. Gillotay, T. Foujols, “The visible solar spectral irradiance from 350 to 850 nm as measured by the SOLSPEC spectrometer during the ATLAS-1 mission,” Sol. Phys. 177, 41–61 (1998).
[CrossRef]

Freeman, C. G.

Fry, E. S.

Ge, Y.

Gentili, B.

Gillotay, D.

G. Thuillier, M. Herse, P. C. Simon, D. Labs, H. Mandel, D. Gillotay, T. Foujols, “The visible solar spectral irradiance from 350 to 850 nm as measured by the SOLSPEC spectrometer during the ATLAS-1 mission,” Sol. Phys. 177, 41–61 (1998).
[CrossRef]

Gons, H. J.

Gordon, H. R.

Gordon, R. H.

Gould, R. W.

R. W. Gould, R. A. Arnone, “Remote sensing estimates of inherent optical properties in a coastal environment,” Remote Sens. Environ. 61, 290–301 (1997).
[CrossRef]

Grant, I.

I. Grant, G. Hunt, “Discrete space theory of radiative transfer I + II: fundamentals and stability and non-negativity,” Proc. R. Soc. London Ser. A 313, 183–197, 199–216 (1969).
[CrossRef]

Grassl, H.

Green, S. A.

S. A. Green, N. V. Blough, “Optical absorption and fluorescence properties of chromorphic dissolved organic matter in natural waters,” Limnol. Oceanogr. 39, 1903–1916 (1994).
[CrossRef]

Günther, K.

K. Günther, D. Ernst, M. Maske, “Biophysical process of chlorophyll a fluorescence,” in The Use of Chlorophyll Fluorescence Measurements from Space for Separating Constituents of Seawater, European Space Agency contract RFQ 3-5059/84/NL/MD, Vol. II [Gesellschaft zur Kernenergieverwertung in Schiffbau und Schifffahrt (GKSS), Forschungszentrum Geesthacht, Geesthacht, Germany, 1986].

Haltrin, V. I.

V. I. Haltrin, G. W. Kattawar, “Self-consistent solution to the equation of transfer with elastic and inelastic scattering in ocean optics: 1. Model,” Appl. Opt. 32, 5357–5367 (1993).
[CrossRef]

Harvey, G. R.

S. K. Hawes, C. K. Carder, G. R. Harvey, “Quantum fluorescence efficiencies of fulvic and humic acids: effects on ocean color and fluorometric detection,” in Ocean Optics XI, G. D. Gilbert, ed., Proc. SPIE1750, 212–223 (1992).
[CrossRef]

Hawes, S. K.

S. K. Hawes, C. K. Carder, G. R. Harvey, “Quantum fluorescence efficiencies of fulvic and humic acids: effects on ocean color and fluorometric detection,” in Ocean Optics XI, G. D. Gilbert, ed., Proc. SPIE1750, 212–223 (1992).
[CrossRef]

Hecht, A.

A. Hecht, Optik (Addison-Wesley, Bonn, Germany, 1989).

Herse, M.

G. Thuillier, M. Herse, P. C. Simon, D. Labs, H. Mandel, D. Gillotay, T. Foujols, “The visible solar spectral irradiance from 350 to 850 nm as measured by the SOLSPEC spectrometer during the ATLAS-1 mission,” Sol. Phys. 177, 41–61 (1998).
[CrossRef]

Heuermann, R.

R. Heuermann, R. Reuter, R. Willkomm, “RAMSES: a modular multispectral radiometer for light measurements in the UV and VIS,” in Environmental Sensing and Applications, M. Carleer, M. Hilton, T. Lamp, R. Reuter, K. Schaefer, G. M. Russwurm, K. Weber, K. Weitkamp, J. Wolf, L. Woppowa, eds., Proc. SPIE3821, 279–285 (1999).
[CrossRef]

W. Breves, R. Heuermann, R. Reuter, “Enhanced red fluorescence emission in the oxygen minimum zone of the Arabian Sea,” Ocean Dyn. (to be published).

Hu, C.

Hunt, G.

I. Grant, G. Hunt, “Discrete space theory of radiative transfer I + II: fundamentals and stability and non-negativity,” Proc. R. Soc. London Ser. A 313, 183–197, 199–216 (1969).
[CrossRef]

Iqbal, M.

M. Iqbal, An Introduction to Solar Radiation (Academic, New York, 1983).

Jin, Z.

Kattawar, G. W.

Kenneth, J.

Kiefer, D. A.

D. A. Kiefer, W. S. Chamberlin, C. R. Booth, “Natural fluorescence of chlorophyll a: relationship to photosynthesis and chlorophyll concentration in the western South Pacific gyre,” Limnol. Oceanogr. 34, 868–881 (1989).
[CrossRef]

D. A. Kiefer, R. A. Reynolds, “Advances in understanding phytoplankton fluorescence and photosynthesis,” in Primary Productivity and Biogeochemical Cycles in the Sea, P. G. Falkowski, A. D. Woodhead, eds. (Plenum, New York, 1992), pp. 155–174.
[CrossRef]

Kirk, J. T. O.

J. T. O. Kirk, Light and Photosynthesis in Aquatic Ecosystems (Cambridge University, Cambridge, England, 1994).
[CrossRef]

Kronfeld, U.

J. Fischer, U. Kronfeld, “Sun-stimulated chlorophyll fluorescence. 1: Influence of oceanic properties,” Int. J. Remote Sens. 11, 2125–2147 (1990).
[CrossRef]

Labs, D.

G. Thuillier, M. Herse, P. C. Simon, D. Labs, H. Mandel, D. Gillotay, T. Foujols, “The visible solar spectral irradiance from 350 to 850 nm as measured by the SOLSPEC spectrometer during the ATLAS-1 mission,” Sol. Phys. 177, 41–61 (1998).
[CrossRef]

Litjens, R. A. J.

Mandel, H.

G. Thuillier, M. Herse, P. C. Simon, D. Labs, H. Mandel, D. Gillotay, T. Foujols, “The visible solar spectral irradiance from 350 to 850 nm as measured by the SOLSPEC spectrometer during the ATLAS-1 mission,” Sol. Phys. 177, 41–61 (1998).
[CrossRef]

Marshall, B. R.

Maske, M.

K. Günther, D. Ernst, M. Maske, “Biophysical process of chlorophyll a fluorescence,” in The Use of Chlorophyll Fluorescence Measurements from Space for Separating Constituents of Seawater, European Space Agency contract RFQ 3-5059/84/NL/MD, Vol. II [Gesellschaft zur Kernenergieverwertung in Schiffbau und Schifffahrt (GKSS), Forschungszentrum Geesthacht, Geesthacht, Germany, 1986].

Mie, G.

G. Mie, “Beiträge zur Optik trüber Medien, speziell kolloidaler Metall-Lösungen,” Ann. Phys. 25, 377–445 (1908).
[CrossRef]

Mobley, A. D.

Mobley, C. D.

C. D. Mobley, Light and Water (Academic, San Diego, Calif., 1994).

Morel, A.

A. 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]

A. Bricaud, A. Morel, L. Prieur, “Absorption by dissolved organic matter of the sea (yellow substance) in the UV and visible domains,” Limnol. Oceanogr. 26, 43–53 (1981).
[CrossRef]

H. R. Gordon, A. Morel, “Remote assessment of ocean color for interpretation with satellite visible imagery, a review,” in Lecture Notes on Coastal and Estuarine Studies, Vol. 4, M. Bowman, ed. (Springer-Verlag, New York, 1983), pp. 1–114.
[CrossRef]

A. Morel, “Diffusion de la lumier par le aux de mer. Resultats Experimentaux et approche theorique,” in Light in the Sea, J. E. Tyler, ed. (Dowden, Hutchinson and Ross, Stroudsberg, Pa., 1977), pp. 65–97.

Ovidio, F.

K. G. Ruddick, F. Ovidio, D. Van den Eynde, A. Vasilkov, “The distribution and dynamics of suspended particulate matter in the Belgian coastal waters derived from AVHRR imagery,” in Proceedings of the Ninth Conference on Satellite Meteorology and Oceanography, Paris, France, 25–29 May 1998 (American Meteorological Society, Boston, Mass., 1998) Vol. 2, pp. 626–629.

Petzold, T. J.

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

Plass, G. N.

Pope, R. M.

Porto, S. P. S.

Potter, J. F.

J. F. Potter, “The delta function approximation in radiative transfer theory,” J. Atmos. Sci. 27, 943–949 (1970).
[CrossRef]

Preisendorfer, R. W.

R. W. Preisendorfer, Radiative Transfer on Discrete Spaces (Pergamon, New York, 1965).

Prieur, L.

A. Bricaud, A. Morel, L. Prieur, “Absorption by dissolved organic matter of the sea (yellow substance) in the UV and visible domains,” Limnol. Oceanogr. 26, 43–53 (1981).
[CrossRef]

L. Prieur, S. Sathyendranath, “An optical classification of coastal and oceanic waters based on the specific spectral absorption curves of phytoplankton pigments, dissolved organic matter, and other particulate materials,” Limnol. Oceanogr. 26, 671–689 (1981).
[CrossRef]

Quickenden, T. I.

Redheffer, R.

R. Redheffer, “On the relation of transmission-line theory to scattering and transfer,” J. Math. Phys. 41, 1–41 (1962).

Reinersman, P.

Reuter, R.

W. Breves, R. Reuter, “Bio-optical observations of gelbstoff in the Arabian Sea at the onset of the southwest monsoon,” Proc. Indian Acad. Sci. (Earth Planet. Sci.) 109, 415–425 (2000).

B. Bartsch, T. Braeske, R. Reuter, “Oceanic lidar: radiative transfer in the atmosphere at operating altitudes from 100 m to 100 km,” Appl. Opt. 32, 6732–6741 (1993).
[CrossRef] [PubMed]

R. Heuermann, R. Reuter, R. Willkomm, “RAMSES: a modular multispectral radiometer for light measurements in the UV and VIS,” in Environmental Sensing and Applications, M. Carleer, M. Hilton, T. Lamp, R. Reuter, K. Schaefer, G. M. Russwurm, K. Weber, K. Weitkamp, J. Wolf, L. Woppowa, eds., Proc. SPIE3821, 279–285 (1999).
[CrossRef]

W. Breves, R. Heuermann, R. Reuter, “Enhanced red fluorescence emission in the oxygen minimum zone of the Arabian Sea,” Ocean Dyn. (to be published).

Reynolds, R. A.

D. A. Kiefer, R. A. Reynolds, “Advances in understanding phytoplankton fluorescence and photosynthesis,” in Primary Productivity and Biogeochemical Cycles in the Sea, P. G. Falkowski, A. D. Woodhead, eds. (Plenum, New York, 1992), pp. 155–174.
[CrossRef]

Rijkeboer, M.

Ruddick, K. G.

K. G. Ruddick, H. J. Gons, M. Rijkeboer, G. Tilstone, “Optical remote sensing of chlorophyll a in case 2 waters by use of an adaptive two-band algorithm with optimal error properties,” Appl. Opt. 40, 3575–3585 (2001).
[CrossRef]

K. G. Ruddick, F. Ovidio, D. Van den Eynde, A. Vasilkov, “The distribution and dynamics of suspended particulate matter in the Belgian coastal waters derived from AVHRR imagery,” in Proceedings of the Ninth Conference on Satellite Meteorology and Oceanography, Paris, France, 25–29 May 1998 (American Meteorological Society, Boston, Mass., 1998) Vol. 2, pp. 626–629.

Sathyendranath, S.

J. S. Bartlett, K. J. Voss, S. Sathyendranath, A. Vodacek, “Raman scattering by pure water and seawater,” Appl. Opt. 37, 3324–3332 (1998).
[CrossRef]

L. Prieur, S. Sathyendranath, “An optical classification of coastal and oceanic waters based on the specific spectral absorption curves of phytoplankton pigments, dissolved organic matter, and other particulate materials,” Limnol. Oceanogr. 26, 671–689 (1981).
[CrossRef]

Schiller, H.

R. Doerffer, H. Schiller, “Pigment index, sediment and gelbstoff retrieval from directional water-leaving radiance reflectances using inverse modeling techniques,” (ESA—European Space Research and Technology Center, Nordweijk, Netherlands, 1997).

Secrest, D.

A. H. Stroud, D. Secrest, Gaussian Quadrature Formulas (Prentice-Hill, Englewood Cliffs, N.J., 1966).

Simon, P. C.

G. Thuillier, M. Herse, P. C. Simon, D. Labs, H. Mandel, D. Gillotay, T. Foujols, “The visible solar spectral irradiance from 350 to 850 nm as measured by the SOLSPEC spectrometer during the ATLAS-1 mission,” Sol. Phys. 177, 41–61 (1998).
[CrossRef]

Smith, R. C.

Stamnes, K.

Stavn, R. H.

Stokes, G. G.

G. G. Stokes, “On the intensity of the light reflected from or transmitted through a pile of plates,” Proc. R. Soc. London 11, 545–556 (1862).
[CrossRef]

Stramski, D.

M. Babin, D. Stramski, “Light absorption by aquatic particles in the near-infrared spectral region,” Limnol. Oceanogr. 47, 911–915 (2002).
[CrossRef]

Stroud, A. H.

A. H. Stroud, D. Secrest, Gaussian Quadrature Formulas (Prentice-Hill, Englewood Cliffs, N.J., 1966).

Thuillier, G.

G. Thuillier, M. Herse, P. C. Simon, D. Labs, H. Mandel, D. Gillotay, T. Foujols, “The visible solar spectral irradiance from 350 to 850 nm as measured by the SOLSPEC spectrometer during the ATLAS-1 mission,” Sol. Phys. 177, 41–61 (1998).
[CrossRef]

Tilstone, G.

Traganza, E. D.

E. D. Traganza, “Fluorescence excitation and emission spectra of dissolved organic matter in sea water,” Bull. Mar. Sci. 19, 897–904 (1969).

Van den Eynde, D.

K. G. Ruddick, F. Ovidio, D. Van den Eynde, A. Vasilkov, “The distribution and dynamics of suspended particulate matter in the Belgian coastal waters derived from AVHRR imagery,” in Proceedings of the Ninth Conference on Satellite Meteorology and Oceanography, Paris, France, 25–29 May 1998 (American Meteorological Society, Boston, Mass., 1998) Vol. 2, pp. 626–629.

Vasilkov, A.

K. G. Ruddick, F. Ovidio, D. Van den Eynde, A. Vasilkov, “The distribution and dynamics of suspended particulate matter in the Belgian coastal waters derived from AVHRR imagery,” in Proceedings of the Ninth Conference on Satellite Meteorology and Oceanography, Paris, France, 25–29 May 1998 (American Meteorological Society, Boston, Mass., 1998) Vol. 2, pp. 626–629.

Vodacek, A.

Voss, K. J.

Walrafen, G. E.

G. E. Walrafen, “Continuum model of water—an erroneous interpretation,” J. Chem. Phys. 50, 567–569 (1969).
[CrossRef]

G. E. Walrafen, “Raman spectral studies of the effects of temperature on water structure,” J. Chem. Phys. 47, 114–126 (1967).
[CrossRef]

Waters, K. J.

K. J. Waters, “Effects of Raman scattering on the water-leaving radiance,” J. Geophys. Res. 100, 13151–13161 (1995).
[CrossRef]

Weidemann, A. D.

Willkomm, R.

R. Heuermann, R. Reuter, R. Willkomm, “RAMSES: a modular multispectral radiometer for light measurements in the UV and VIS,” in Environmental Sensing and Applications, M. Carleer, M. Hilton, T. Lamp, R. Reuter, K. Schaefer, G. M. Russwurm, K. Weber, K. Weitkamp, J. Wolf, L. Woppowa, eds., Proc. SPIE3821, 279–285 (1999).
[CrossRef]

Young, L. A.

A. H. Chang, L. A. Young, “Seawater temperature measurement from Raman spectra,” , (AVCO Everett Research Laboratory, Everett, Mass., 1974), pp. 82.

Adv. Space Res. (1)

R. Doerffer, J. Fischer, “Measurements and model simulations of Sun-stimulated chlorophyll fluorescence within a daily cycle,” Adv. Space Res. 7, 117–120 (1987).
[CrossRef]

Ann. Phys. (1)

G. Mie, “Beiträge zur Optik trüber Medien, speziell kolloidaler Metall-Lösungen,” Ann. Phys. 25, 377–445 (1908).
[CrossRef]

Appl. Opt. (18)

B. Bartsch, T. Braeske, R. Reuter, “Oceanic lidar: radiative transfer in the atmosphere at operating altitudes from 100 m to 100 km,” Appl. Opt. 32, 6732–6741 (1993).
[CrossRef] [PubMed]

R. M. Pope, E. S. Fry, “Absorption spectrum (380–700 nm) of pure water. II. Integrating cavity measurements,” Appl. Opt. 36, 8710–8723 (1997).
[CrossRef]

R. C. Smith, K. S. Baker, “Optical properties of the clearest natural waters (200–800 nm),” Appl. Opt. 20, 177–184 (1981).
[CrossRef] [PubMed]

J. S. Bartlett, K. J. Voss, S. Sathyendranath, A. Vodacek, “Raman scattering by pure water and seawater,” Appl. Opt. 37, 3324–3332 (1998).
[CrossRef]

T. I. Quickenden, C. G. Freeman, R. A. J. Litjens, “Some comments on the paper by Edward S. Fry on the visible and near-ultraviolet absorption spectrum of liquid water,” Appl. Opt. 39, 2740–2742 (2000).
[CrossRef]

E. S. Fry, “Reply to criticisms of the Pope and Fry paper on pure water absorption made in a comment by T. I. Qickenden, C. G. Freeman, and R. A. J. Litjens,” Appl. Opt. 39, 5843–5846 (2000).
[CrossRef]

A. 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]

J. Fischer, R. Doerffer, H. Grassl, “Factor analysis of multispectral radiances over coastal and open ocean water based on radiative-transfer calculations,” Appl. Opt. 25, 448–456 (1986).
[CrossRef] [PubMed]

H. R. Gordon, “Diffuse reflection of the ocean: the theory of its augmentation by chlorophyll a fluorescence at 685 nm,” Appl. Opt. 18, 1161–1166 (1979).
[CrossRef] [PubMed]

Y. Ge, H. R. Gordon, K. J. Voss, J. Kenneth, “Simulation of inelastic scattering contributions to the irradiance field in the ocean: variations in Fraunhofer line depths,” Appl. Opt. 32, 4028–4036 (1993).
[CrossRef] [PubMed]

V. I. Haltrin, G. W. Kattawar, “Self-consistent solution to the equation of transfer with elastic and inelastic scattering in ocean optics: 1. Model,” Appl. Opt. 32, 5357–5367 (1993).
[CrossRef]

B. R. Marshall, R. C. Smith, “Raman scattering and in-water ocean properties,” Appl. Opt. 29, 71–84 (1990).
[CrossRef] [PubMed]

C. Hu, K. J. Voss, “In situ measurements of Raman scattering in clear ocean water,” Appl. Opt. 36, 6962–6967 (1997).
[CrossRef]

R. H. Gordon, “Contribution of Raman scattering to water-leaving radiance: a reexamination,” Appl. Opt. 38, 3166–3174 (1999).
[CrossRef]

K. G. Ruddick, H. J. Gons, M. Rijkeboer, G. Tilstone, “Optical remote sensing of chlorophyll a in case 2 waters by use of an adaptive two-band algorithm with optimal error properties,” Appl. Opt. 40, 3575–3585 (2001).
[CrossRef]

Z. Jin, K. Stamnes, “Radiative transfer in nonuniformly refracting layered media: atmosphere-ocean system,” Appl. Opt. 33, 431–442 (1994).
[CrossRef] [PubMed]

R. H. Stavn, A. D. Weidemann, “Optical modeling of clear ocean light fields: Raman scattering effects,” Appl. Opt. 27, 4002–4011 (1988).
[CrossRef] [PubMed]

G. N. Plass, G. W. Kattawar, F. E. Catchings, “Matrix operator theory of radiative transfer. 1: Rayleigh scattering,” Appl. Opt. 12, 314–329 (1973).
[CrossRef] [PubMed]

Bull. Mar. Sci. (1)

E. D. Traganza, “Fluorescence excitation and emission spectra of dissolved organic matter in sea water,” Bull. Mar. Sci. 19, 897–904 (1969).

C. R. Acad. Sci. USSR (1)

V. A. Ambarzumian, “Diffusion of light by a foggy medium,” C. R. Acad. Sci. USSR 38, 229–232 (1943).

Int. J. Remote Sens. (1)

J. Fischer, U. Kronfeld, “Sun-stimulated chlorophyll fluorescence. 1: Influence of oceanic properties,” Int. J. Remote Sens. 11, 2125–2147 (1990).
[CrossRef]

J. Atmos. Sci. (1)

J. F. Potter, “The delta function approximation in radiative transfer theory,” J. Atmos. Sci. 27, 943–949 (1970).
[CrossRef]

J. Chem. Phys. (2)

G. E. Walrafen, “Continuum model of water—an erroneous interpretation,” J. Chem. Phys. 50, 567–569 (1969).
[CrossRef]

G. E. Walrafen, “Raman spectral studies of the effects of temperature on water structure,” J. Chem. Phys. 47, 114–126 (1967).
[CrossRef]

J. Geophys. Res. (1)

K. J. Waters, “Effects of Raman scattering on the water-leaving radiance,” J. Geophys. Res. 100, 13151–13161 (1995).
[CrossRef]

J. Math. Phys. (1)

R. Redheffer, “On the relation of transmission-line theory to scattering and transfer,” J. Math. Phys. 41, 1–41 (1962).

J. Opt. Soc. Am. (1)

J. Quant. Spectrosc. Radiat. Transfer (1)

F. Fell, J. Fischer, “Numerical simulations of the light field in the atmosphere-ocean system using the matrix-operator theory,” J. Quant. Spectrosc. Radiat. Transfer 69, 351–388 (2001).
[CrossRef]

Limnol. Oceanogr. (5)

S. A. Green, N. V. Blough, “Optical absorption and fluorescence properties of chromorphic dissolved organic matter in natural waters,” Limnol. Oceanogr. 39, 1903–1916 (1994).
[CrossRef]

D. A. Kiefer, W. S. Chamberlin, C. R. Booth, “Natural fluorescence of chlorophyll a: relationship to photosynthesis and chlorophyll concentration in the western South Pacific gyre,” Limnol. Oceanogr. 34, 868–881 (1989).
[CrossRef]

L. Prieur, S. Sathyendranath, “An optical classification of coastal and oceanic waters based on the specific spectral absorption curves of phytoplankton pigments, dissolved organic matter, and other particulate materials,” Limnol. Oceanogr. 26, 671–689 (1981).
[CrossRef]

M. Babin, D. Stramski, “Light absorption by aquatic particles in the near-infrared spectral region,” Limnol. Oceanogr. 47, 911–915 (2002).
[CrossRef]

A. Bricaud, A. Morel, L. Prieur, “Absorption by dissolved organic matter of the sea (yellow substance) in the UV and visible domains,” Limnol. Oceanogr. 26, 43–53 (1981).
[CrossRef]

Mar. Chem. (1)

P. G. Coble, “Characterization of marine and terrestrial DOM in seawater using excitation-emission matrix spectroscopy,” Mar. Chem. 51, 325–346 (1996).
[CrossRef]

Proc. Indian Acad. Sci. (Earth Planet. Sci.) (1)

W. Breves, R. Reuter, “Bio-optical observations of gelbstoff in the Arabian Sea at the onset of the southwest monsoon,” Proc. Indian Acad. Sci. (Earth Planet. Sci.) 109, 415–425 (2000).

Proc. R. Soc. London (1)

G. G. Stokes, “On the intensity of the light reflected from or transmitted through a pile of plates,” Proc. R. Soc. London 11, 545–556 (1862).
[CrossRef]

Proc. R. Soc. London Ser. A (1)

I. Grant, G. Hunt, “Discrete space theory of radiative transfer I + II: fundamentals and stability and non-negativity,” Proc. R. Soc. London Ser. A 313, 183–197, 199–216 (1969).
[CrossRef]

Remote Sens. Environ. (1)

R. W. Gould, R. A. Arnone, “Remote sensing estimates of inherent optical properties in a coastal environment,” Remote Sens. Environ. 61, 290–301 (1997).
[CrossRef]

Sol. Phys. (1)

G. Thuillier, M. Herse, P. C. Simon, D. Labs, H. Mandel, D. Gillotay, T. Foujols, “The visible solar spectral irradiance from 350 to 850 nm as measured by the SOLSPEC spectrometer during the ATLAS-1 mission,” Sol. Phys. 177, 41–61 (1998).
[CrossRef]

Other (18)

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

A. Hecht, Optik (Addison-Wesley, Bonn, Germany, 1989).

R. Heuermann, R. Reuter, R. Willkomm, “RAMSES: a modular multispectral radiometer for light measurements in the UV and VIS,” in Environmental Sensing and Applications, M. Carleer, M. Hilton, T. Lamp, R. Reuter, K. Schaefer, G. M. Russwurm, K. Weber, K. Weitkamp, J. Wolf, L. Woppowa, eds., Proc. SPIE3821, 279–285 (1999).
[CrossRef]

H. R. Gordon, A. Morel, “Remote assessment of ocean color for interpretation with satellite visible imagery, a review,” in Lecture Notes on Coastal and Estuarine Studies, Vol. 4, M. Bowman, ed. (Springer-Verlag, New York, 1983), pp. 1–114.
[CrossRef]

W. Breves, R. Heuermann, R. Reuter, “Enhanced red fluorescence emission in the oxygen minimum zone of the Arabian Sea,” Ocean Dyn. (to be published).

M. Iqbal, An Introduction to Solar Radiation (Academic, New York, 1983).

A. Morel, “Diffusion de la lumier par le aux de mer. Resultats Experimentaux et approche theorique,” in Light in the Sea, J. E. Tyler, ed. (Dowden, Hutchinson and Ross, Stroudsberg, Pa., 1977), pp. 65–97.

K. Günther, D. Ernst, M. Maske, “Biophysical process of chlorophyll a fluorescence,” in The Use of Chlorophyll Fluorescence Measurements from Space for Separating Constituents of Seawater, European Space Agency contract RFQ 3-5059/84/NL/MD, Vol. II [Gesellschaft zur Kernenergieverwertung in Schiffbau und Schifffahrt (GKSS), Forschungszentrum Geesthacht, Geesthacht, Germany, 1986].

K. G. Ruddick, F. Ovidio, D. Van den Eynde, A. Vasilkov, “The distribution and dynamics of suspended particulate matter in the Belgian coastal waters derived from AVHRR imagery,” in Proceedings of the Ninth Conference on Satellite Meteorology and Oceanography, Paris, France, 25–29 May 1998 (American Meteorological Society, Boston, Mass., 1998) Vol. 2, pp. 626–629.

R. Doerffer, H. Schiller, “Pigment index, sediment and gelbstoff retrieval from directional water-leaving radiance reflectances using inverse modeling techniques,” (ESA—European Space Research and Technology Center, Nordweijk, Netherlands, 1997).

J. T. O. Kirk, Light and Photosynthesis in Aquatic Ecosystems (Cambridge University, Cambridge, England, 1994).
[CrossRef]

C. D. Mobley, Light and Water (Academic, San Diego, Calif., 1994).

A. H. Stroud, D. Secrest, Gaussian Quadrature Formulas (Prentice-Hill, Englewood Cliffs, N.J., 1966).

A. H. Chang, L. A. Young, “Seawater temperature measurement from Raman spectra,” , (AVCO Everett Research Laboratory, Everett, Mass., 1974), pp. 82.

S. Chandrasekhar, Radiative Transfer (Dover, New York, 1960).

R. W. Preisendorfer, Radiative Transfer on Discrete Spaces (Pergamon, New York, 1965).

S. K. Hawes, C. K. Carder, G. R. Harvey, “Quantum fluorescence efficiencies of fulvic and humic acids: effects on ocean color and fluorometric detection,” in Ocean Optics XI, G. D. Gilbert, ed., Proc. SPIE1750, 212–223 (1992).
[CrossRef]

D. A. Kiefer, R. A. Reynolds, “Advances in understanding phytoplankton fluorescence and photosynthesis,” in Primary Productivity and Biogeochemical Cycles in the Sea, P. G. Falkowski, A. D. Woodhead, eds. (Plenum, New York, 1992), pp. 155–174.
[CrossRef]

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Figures (16)

Fig. 1
Fig. 1

Introduction of matrix operators.

Fig. 2
Fig. 2

Composition of, solid curve, the redistribution function of water Raman scattering of, dashed curves, four Gauss functions for an examplary excitation wavelength of 400 nm.

Fig. 3
Fig. 3

Raman redistribution function for three different excitation wavelengths.

Fig. 4
Fig. 4

Maxima of the redistribution function fR of water Raman scattering for three different wavelength increments.

Fig. 5
Fig. 5

Location of station 12.

Fig. 6
Fig. 6

Measured temperature and salinity at station 12.

Fig. 7
Fig. 7

Measured gelbstoff and chlorophyll fluorescence at station 12.

Fig. 8
Fig. 8

Comparison of the measured and the simulated downward irradiance Ed at 429 nm.

Fig. 9
Fig. 9

Comparison of the measured and the simulated downward irradiance Ed at 489 nm.

Fig. 10
Fig. 10

Comparison of the measured and the simulated downward irradiance Ed at 555 nm.

Fig. 11
Fig. 11

Comparison of the measured and the simulated downward irradiance Ed at 641 nm.

Fig. 12
Fig. 12

Wavelength dependency of the inelastic fraction JR,C for the upward nadir radiance just below the ocean surface determined at four different gelbstoff absorptions at 440 nm (C = 0.03 mg m-3).

Fig. 13
Fig. 13

Wavelength dependency of the inelastic fraction JR,C for the upward nadir radiance just below the ocean surface determined at five different phytoplankton concentrations [ay (440 nm) = 0.1 m-1].

Fig. 14
Fig. 14

Wavelength dependency of the inelastic fraction JY for the upward nadir radiance just below the ocean surface determined at three different combinations of the gelbstoff absorption (the first value in the legend) and the phytoplankton concentration (the second value in the legend).

Fig. 15
Fig. 15

Depth dependency of the inelastic fraction for the upward irradiance at five different wavelengths [C = 0.5 mg m-3, ay (440 nm) = 0.1 m-1].

Fig. 16
Fig. 16

Depth dependency of the inelastic fraction for the downward irradiance at five different wavelengths [C = 0.5 mg m-3, ay (440 nm) = 0.1 m-1].

Tables (3)

Tables Icon

Table 1 Set of User Defined Parameters Taken as a Model Input

Tables Icon

Table 2 Measured Phytoplankton Concentration and Gelbstoff Absorption (Lambda 18)

Tables Icon

Table 3 Parameterization of βP with bPa

Equations (48)

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

 t01μμL0+μdμ=t01L0+
Li+=E-ri0rij-1ri0tjiLj-+t0iL0++ri0Jji-+J0i+,
Li-=E-rijri0-1rijt0iL0++tjiLj-+rijJ0i++Jji-,
rj0=rji+tijE-ri0rij-1ri0tji,
t0j=tijE-ri0rij-1t0i,
J0j+=Jij++tijE-ri0rij-1ri0Jji-+J0i+.
r02=r20=r2=r1+t1E-r1r1-1r1t1,
t02=t20=t2=t1E-r1r1-1t1,
J02+=J12++t1E-r1r1-1r1J21-+J01+,
J20-=J10-+t1E-r1r1-1r1J01++J21-.
μ dLτ; ξ; λdτ=-Lτ; ξ; λ+ω0Ξ β˜τ; ξξ; λ×Lτ; ξ; λdΩξ+ω0β˜τ; ξ0ξ; λF0 exp-τ/μ0+1c L*Iτ; ξ; λ,
01 fμdμ=i=1N fμici+RN.
t10=t01=t=E-ΔτM-1E-ω02πβ˜++C,
r10=r01=r=Δτω02πM-1β˜-+C,
JC,Yξ; λ=1cλΛC,YΞ βC,Yξξ; λ×Lξ; λdΩξdλ,
bC,Yλλ=aC,YλfC,Yλλ,
bC,Yλλ=aC,YλΦC,YλgC,YλhC,Yλλλ,
JC,Yλ=ΦC,YhC,Yλ4πcλλΛC,Y aC,YλgC,YλE0λλdλ=ΦC,YhC,Yλ4πcλλ AC,Yλ.
JC,YΔτ; τ; λ=Δτ ΦC,YhC,Yλ4πcλ; τλM-1AC,Yλ; τ.
bRλλ=aRλfRλλ,
aRλ=a0Rλ0λ0λn.
fRλλ=107λ212π1/2i=14αiσii=14 αi×exp-107λ-107λ-Δv˜i22σi2.
βRψ; λλ=316π1+3ρ1+2ρ×1+γ cos2ψbRλλ,
βRψ; λλ=316π1+3ρ1+2ρ1+13 γ+23 γP2cos ψbRλλ,
βRψ; λλ=14πl=0N blRλλPlcos ψ,
b0Rλλ=bRλλ,
b2Rλλ=121-ρ1+2ρbRλλ.
JRμ; λ=14πcλΛR bRλλE0λ+121-ρ1+2ρ E2μ; λP2μdλ=14πcλ ARμ; λ.
JRΔτ; τ; μ; λ=Δτ 14πcλ; τM-1ARλ; μ; τ.
J02+μi; λ=f2μi; λJ01+μi; λ.
J24+μi; λ=f2μi; λJ23+μi; λ.
J04+μi; λ=f4μi; λJ01+μi; λ,
J48+μi; λ=f4μi; λJ45+μi; λ.
bPλ=bP400 nmλ400 nm3-cj.
ayλ=ay440 nmexp-sλ-440 nm.
i=1NEdMzi-fEdSzi/EdM(zi
bPλ=0.3550 nmλC0.62.
β˜ψ; λ=ibiλbλ β˜iψ,
2π -11 β˜μ; λdμ=1.
β˜μμ; λ=αλδ1, μ+1-αλβ˜μμ; λ,
12π-i=1Nβ˜μ1μi; λ+β˜μ1-μi; λci<ε.
β˜HGg; ψ=1-g24π1+g2-2g cos ψ3/2,
β˜μjμj; λ=β˜μjμj; λ+ΔEμj; λcj.
ΔEμj; λ=12π-i=1Nβ˜μjμi; λ+β˜μj-μi; λci.
rOO=ROOμi; nO/nAμiO1, μC1μiOμC, 0,
rAA=RAAμi; nA/nO μiA1, 0,
tOA=TOAμi; nA/nOnAnO2μiO1, μC0μiOμC, 0,
tAO=TAOμi; nO/nAnOnA2 μiA1, 0.

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