Abstract

Oceanic radiance model inversion methods are used to develop a comprehensive algorithm for retrieval of the absorption coefficients of phycourobilin (PUB) pigment, type I phycoerythrobilin (PEB) pigment rich in PUB, and type II PEB deficient in PUB pigment (together with the usual “big three” inherent optical properties: the total backscattering coefficient and the absorption coefficients of chromophoric dissolved organic matter (CDOM)–detritus and phytoplankton). This fully modeled inversion algorithm is then simplified to yield a hybrid modeled–unmodeled inversion algorithm in which the phycoerythrin (PE) absorption coefficient is retrieved as unmodeled 488-nm absorption (which exceeds the modeled phytoplankton and the CDOM–detritus absorption coefficients). Each algorithm was applied to water-leaving radiances, but only hybrid modeled–unmodeled inversions yielded viable retrievals of the PE absorption coefficient. Validation of the PE absorption coefficient retrieval was achieved by relative comparison with airborne laser-induced PEB fluorescence. The modeled–unmodeled retrieval of four inherent optical properties by direct matrix inversion is rapid and well conditioned, but the accuracy is strongly limited by the accuracy of the three principal inherent optical property models across all four spectral bands. Several research areas are identified to enhance the radiance-model-based retrievals: (a) improved PEB and PUB absorption coefficient models, (b) PE spectral shifts induced by PUB chromophore substitution at chromophore binding sites, (c) specific absorption-sensitive phytoplankton absorption modeling, (d) total constituent backscattering modeling, (e) unmodeled carotinoid and phycocyanin absorption that are not now accounted for in the chlorophyll-dominated phytoplankton absorption coefficient model, and (f) iterative inversion techniques to solve for six constituents with only five radiances. Although considerable progress has been made toward the satellite recovery of PE absorption, the maturity of the retrieval is presently insufficient for routine global application. Instead it must currently be used on a regional basis where localized ship and aircraft validation can be made available. The algorithm was developed for the MODIS (Moderate-Resolution Imaging Spectroradiometer) sensor but is applicable to any sensor having comparable band locations.

© 1999 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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  29. F. E. Hoge, A. Vodacek, R. N. Swift, J. Y. Yungel, N. V. Blough, “Inherent optical properties of the ocean: retrieval of the absorption coefficient of chromophoric dissolved organic matter from airborne laser spectral fluorescence measurements,” Appl. Opt. 34, 7032–7038 (1995).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  35. R. A. Maffione, D. R. Dana, “In-situ characterization of optical backscattering and attenuation for lidar applications,” in Laser Remote Sensing of Natural Waters: from Theory to Practice: CIS Selected Papers, V. I. Feigels, Y. I. Kopelevich, eds., Proc. SPIE2964, 152–163 (1996).
    [CrossRef]
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1999 (1)

1998 (2)

F. E. Hoge, C. W. Wright, T. M. Kana, R. N. Swift, J. K. Yungel, “Spatial variability of oceanic phycoerythrin spectral types derived from airborne laser-induced fluorescence measurements,” Appl. Opt. 37, 4744–4749 (1998).
[CrossRef]

A. M. Wood, D. A. Phinney, C. S. Yentsch, “Water column transparency and the distribution of spectrally distinct forms of phycoerythrin-containing organisms,” Mar. Ecol. Prog. Ser. 162, 25–31 (1998).
[CrossRef]

1997 (3)

1996 (1)

F. E. Hoge, P. E. Lyon, “Satellite retrieval of inherent optical properties by linear matrix inversion of oceanic radiance models: an analysis of model and radiance measurement errors,” J. Geophys. Res. 101, 16,631–16,648 (1996).
[CrossRef]

1995 (2)

1994 (2)

Z. P. Lee, K. L. Carder, S. K. Hawes, R. G. Steward, T. G. Peacock, C. O. Davis, “Model for the interpretation of hyperspectral remote-sensing reflectance,” Appl. Opt. 33, 5721–5732 (1994).
[CrossRef] [PubMed]

M. E. Culver, M. J. Perry, “Detection of phycoerythrin fluorescence in upwelling irradiance spectra,” Eos Trans. Am. Geophys. Union 75, 233 (1994).

1993 (3)

N. Hoepffner, S. Sathyendranath, “Determination of the major groups of phytoplankton pigments from the absorption spectra of total particulate matter,” J. Geophys. Res. 98, 22,789–22,803 (1993).
[CrossRef]

F. E. Hoge, A. Vodacek, N. V. Blough, “Inherent optical properties of the ocean: retrieval of the absorption coefficient of chromophoric dissolved organic matter from fluorescence measurements,” Limnol. Oceanogr. 38, 1394–1402 (1993).

S. M. Wilbanks, A. Glazer, “Rod structure of a phycoerythrin II-containing phycobilisome. I. Organization and sequence of the gene cluster encoding the major phycobiliprotein rod components in the genome of marine Synechococcus SP WH8020,” J. Biol. Chem. 268, 1226–1235 (1993).
[PubMed]

1992 (1)

T. M. Kana, N. L. Feiwel, L. C. Flynn, “Nitrogen starvation in marine Synechococcus strains: clonal differences in phycobiliprotien breakdown and energy coupling,” Mar. Ecol. Prog. Ser. 88, 75–82 (1992).
[CrossRef]

1991 (3)

L. J. Ong, A. N. Glazer, “Phycoerythrins of marine unicellular cyanobacteria. I. Bilin types and locations and energy transfer pathways in Synechococcus spp. phycoerythrins,” J. Biol. Chem. 266, 9515–9527 (1991).
[PubMed]

R. V. Swanson, L. J. Ong, S. M. Wilbanks, A. Glazer, “Phycoerythrins of marine unicellular cyanobacteria. II. Characterization of phycobiliprotiens with unusually high phycourobilin,” J. Biol. Chem. 266, 9528–9534 (1991).
[PubMed]

S. M. Wilbanks, R. de Lorimier, A. Glazer, “Phycoerythrins of marine unicellular cyanobacteria. III. Sequence of a class II phycoerythrin,” J. Biol. Chem. 266, 9535–9539 (1991).
[PubMed]

1990 (3)

F. E. Hoge, R. N. Swift, “Phytoplankton accessory pigments: evidence for the influence of phycoerythrin on the submarine light field,” Remote Sens. Environ. 34, 19–25 (1990).
[CrossRef]

R. J. Olson, S. W. Chisholm, E. R. Zettler, E. V. Armbrust, “Pigments, size, and distribution of Synechococcus in the North Atlantic and Pacific Oceans,” Limnol. Oceanogr. 35, 45–58 (1990).

M. Vernet, B. G. Mitchell, O. Holm-Hansen, “Adaptation of synechococcus in situ determined by variability in intracellular phycoerythrin-543 at a coastal station off the Southern California coast, USA,” Mar. Ecol. 63, 9–16 (1990).
[CrossRef]

1989 (2)

C. S. Roesler, M. J. Perry, K. L. Carder, “Modeling in situ phytoplankton from total absorption spectra in productive inland marine waters,” Limnol. Oceanogr. 34, 1510–1523 (1989).

S. Sathyendranath, L. Prieur, A. Morel, “A three-component model of ocean colour and its application to remote sensing of phytoplankton pigment in coastal waters,” Int. J. Remote Sens. 10, 1373–1394 (1989).
[CrossRef]

1988 (2)

A. Morel, “Optical modeling of the upper ocean in relation to its biogenous matter content (case I waters),” J. Geophys. Res. 93, 10,749–10,768 (1988).
[CrossRef]

H. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, D. K. Clark, “A semianalytic radiance model of ocean color,” J. Geophys. Res. 93, 10,909–10,924 (1988).
[CrossRef]

1987 (1)

T. M. Kana, P. M. Glibert, “Effect of irradiances up to 2000 µE m-2 s-1 on marine Synechococcus WH7803: I. Growth, pigmentation, and cell composition,” Deep-Sea Res. 34, 479–495 (1987).
[CrossRef]

1986 (1)

1981 (2)

F. E. Hoge, R. N. Swift, “Airborne simultaneous spectroscopic detection of laser-induced water-Raman backscatter and fluorescence from chlorophyll a and other naturally occurring pigments,” Appl. Opt. 20, 3197–3205 (1981).
[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).

1979 (2)

J. B. Waterbury, S. W. Watson, R. R. R. Guillard, L. E. Brand, “Widespread occurrence of a unicellular, marine, planktonic cyanobacterium,” Nature (London) 277, 293–294 (1979).
[CrossRef]

C. S. Yentsch, C. M. Yentsch, “Fluorescence spectral signatures: the characterization of phytoplankton populations by the use of excitation and emission spectra,” J. Mar. Res. 37, 471–483 (1979).

Armbrust, E. V.

R. J. Olson, S. W. Chisholm, E. R. Zettler, E. V. Armbrust, “Pigments, size, and distribution of Synechococcus in the North Atlantic and Pacific Oceans,” Limnol. Oceanogr. 35, 45–58 (1990).

Baker, K. S.

H. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, D. K. Clark, “A semianalytic radiance model of ocean color,” J. Geophys. Res. 93, 10,909–10,924 (1988).
[CrossRef]

Bergman, B.

D. G. Capone, J. P. Zehr, H. W. Paerl, B. Bergman, E. J. Carpenter, “Trichodesmium, a globally significant marine cyanobacterium,” Science 276, 1221–1229 (1997).
[CrossRef]

Bidigare, R. R.

R. R. Bidigare, M. E. Ondrusek, J. H. Morrow, D. A. Kiefer, “In vivo absorption properties of algal pigments,” in Ocean Optics X, R. W. Spinrad, ed., Proc. SPIE1302, 290–302 (1990).
[CrossRef]

Blough, N. V.

F. E. Hoge, A. Vodacek, R. N. Swift, J. Y. Yungel, N. V. Blough, “Inherent optical properties of the ocean: retrieval of the absorption coefficient of chromophoric dissolved organic matter from airborne laser spectral fluorescence measurements,” Appl. Opt. 34, 7032–7038 (1995).
[CrossRef] [PubMed]

F. E. Hoge, A. Vodacek, N. V. Blough, “Inherent optical properties of the ocean: retrieval of the absorption coefficient of chromophoric dissolved organic matter from fluorescence measurements,” Limnol. Oceanogr. 38, 1394–1402 (1993).

Brand, L. E.

J. B. Waterbury, S. W. Watson, R. R. R. Guillard, L. E. Brand, “Widespread occurrence of a unicellular, marine, planktonic cyanobacterium,” Nature (London) 277, 293–294 (1979).
[CrossRef]

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).

Brown, J. W.

H. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, D. K. Clark, “A semianalytic radiance model of ocean color,” J. Geophys. Res. 93, 10,909–10,924 (1988).
[CrossRef]

Brown, O. B.

H. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, D. K. Clark, “A semianalytic radiance model of ocean color,” J. Geophys. Res. 93, 10,909–10,924 (1988).
[CrossRef]

Capone, D. G.

D. G. Capone, J. P. Zehr, H. W. Paerl, B. Bergman, E. J. Carpenter, “Trichodesmium, a globally significant marine cyanobacterium,” Science 276, 1221–1229 (1997).
[CrossRef]

Carder, K. L.

Z. P. Lee, K. L. Carder, S. K. Hawes, R. G. Steward, T. G. Peacock, C. O. Davis, “Model for the interpretation of hyperspectral remote-sensing reflectance,” Appl. Opt. 33, 5721–5732 (1994).
[CrossRef] [PubMed]

C. S. Roesler, M. J. Perry, K. L. Carder, “Modeling in situ phytoplankton from total absorption spectra in productive inland marine waters,” Limnol. Oceanogr. 34, 1510–1523 (1989).

Carpenter, E. J.

D. G. Capone, J. P. Zehr, H. W. Paerl, B. Bergman, E. J. Carpenter, “Trichodesmium, a globally significant marine cyanobacterium,” Science 276, 1221–1229 (1997).
[CrossRef]

Chisholm, S. W.

R. J. Olson, S. W. Chisholm, E. R. Zettler, E. V. Armbrust, “Pigments, size, and distribution of Synechococcus in the North Atlantic and Pacific Oceans,” Limnol. Oceanogr. 35, 45–58 (1990).

Clark, D. K.

H. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, D. K. Clark, “A semianalytic radiance model of ocean color,” J. Geophys. Res. 93, 10,909–10,924 (1988).
[CrossRef]

Culver, M. E.

M. E. Culver, M. J. Perry, “Detection of phycoerythrin fluorescence in upwelling irradiance spectra,” Eos Trans. Am. Geophys. Union 75, 233 (1994).

Dana, D. R.

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]

R. A. Maffione, D. R. Dana, J. M. Voss, “Spectral dependence of optical backscattering in the ocean,” presented at the OSA Annual Meeting, Portland, Ore., 10–15 September 1995, Paper MDD4.

R. A. Maffione, D. R. Dana, “In-situ characterization of optical backscattering and attenuation for lidar applications,” in Laser Remote Sensing of Natural Waters: from Theory to Practice: CIS Selected Papers, V. I. Feigels, Y. I. Kopelevich, eds., Proc. SPIE2964, 152–163 (1996).
[CrossRef]

Davis, C. O.

de Lorimier, R.

S. M. Wilbanks, R. de Lorimier, A. Glazer, “Phycoerythrins of marine unicellular cyanobacteria. III. Sequence of a class II phycoerythrin,” J. Biol. Chem. 266, 9535–9539 (1991).
[PubMed]

Evans, R. H.

H. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, D. K. Clark, “A semianalytic radiance model of ocean color,” J. Geophys. Res. 93, 10,909–10,924 (1988).
[CrossRef]

Feiwel, N. L.

T. M. Kana, N. L. Feiwel, L. C. Flynn, “Nitrogen starvation in marine Synechococcus strains: clonal differences in phycobiliprotien breakdown and energy coupling,” Mar. Ecol. Prog. Ser. 88, 75–82 (1992).
[CrossRef]

Flynn, L. C.

T. M. Kana, N. L. Feiwel, L. C. Flynn, “Nitrogen starvation in marine Synechococcus strains: clonal differences in phycobiliprotien breakdown and energy coupling,” Mar. Ecol. Prog. Ser. 88, 75–82 (1992).
[CrossRef]

Franks, D. G.

J. B. Waterbury, S. W. Watson, F. W. Valois, D. G. Franks, “Biological and ecological characterization of the marine unicellular cyanobacterium synechococcus,” in Photosynthetic Picoplankton, T. Platt, W. K. W. Li, eds., Canadian Bulletin of Fisheries and Aquatic Sciences No. 214 (Fisheries Research Board of Canada, Ottawa, Ontario, Canada, 1986).

Fry, E. S.

Glazer, A.

S. M. Wilbanks, A. Glazer, “Rod structure of a phycoerythrin II-containing phycobilisome. I. Organization and sequence of the gene cluster encoding the major phycobiliprotein rod components in the genome of marine Synechococcus SP WH8020,” J. Biol. Chem. 268, 1226–1235 (1993).
[PubMed]

R. V. Swanson, L. J. Ong, S. M. Wilbanks, A. Glazer, “Phycoerythrins of marine unicellular cyanobacteria. II. Characterization of phycobiliprotiens with unusually high phycourobilin,” J. Biol. Chem. 266, 9528–9534 (1991).
[PubMed]

S. M. Wilbanks, R. de Lorimier, A. Glazer, “Phycoerythrins of marine unicellular cyanobacteria. III. Sequence of a class II phycoerythrin,” J. Biol. Chem. 266, 9535–9539 (1991).
[PubMed]

L. J. Ong, A. Glazer, “Structural studies of phycobiliprotiens in unicellular marine cyanobacteria,” in Light-Energy Transduction in Photosynthesis: Higher Plant and Bacterial Models, S. E. Stevens, D. A. Bryant, eds. (American Society of Plant Physiologists, Rockville, Md., 1988), pp. 102–121.

Glazer, A. N.

L. J. Ong, A. N. Glazer, “Phycoerythrins of marine unicellular cyanobacteria. I. Bilin types and locations and energy transfer pathways in Synechococcus spp. phycoerythrins,” J. Biol. Chem. 266, 9515–9527 (1991).
[PubMed]

Glibert, P. M.

T. M. Kana, P. M. Glibert, “Effect of irradiances up to 2000 µE m-2 s-1 on marine Synechococcus WH7803: I. Growth, pigmentation, and cell composition,” Deep-Sea Res. 34, 479–495 (1987).
[CrossRef]

Gordon, H.

H. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, D. K. Clark, “A semianalytic radiance model of ocean color,” J. Geophys. Res. 93, 10,909–10,924 (1988).
[CrossRef]

Guillard, R. R. R.

J. B. Waterbury, S. W. Watson, R. R. R. Guillard, L. E. Brand, “Widespread occurrence of a unicellular, marine, planktonic cyanobacterium,” Nature (London) 277, 293–294 (1979).
[CrossRef]

Hawes, S. K.

Hoepffner, N.

N. Hoepffner, S. Sathyendranath, “Determination of the major groups of phytoplankton pigments from the absorption spectra of total particulate matter,” J. Geophys. Res. 98, 22,789–22,803 (1993).
[CrossRef]

Hoge, F. E.

F. E. Hoge, C. W. Wright, P. E. Lyon, R. N. Swift, J. K. Yungel, “Satellite retrieval of inherent optical properties by inversion of an oceanic radiance model: a preliminary algorithm,” Appl. Opt. 38, 495–504 (1999).
[CrossRef]

F. E. Hoge, C. W. Wright, T. M. Kana, R. N. Swift, J. K. Yungel, “Spatial variability of oceanic phycoerythrin spectral types derived from airborne laser-induced fluorescence measurements,” Appl. Opt. 37, 4744–4749 (1998).
[CrossRef]

F. E. Hoge, P. E. Lyon, “Satellite retrieval of inherent optical properties by linear matrix inversion of oceanic radiance models: an analysis of model and radiance measurement errors,” J. Geophys. Res. 101, 16,631–16,648 (1996).
[CrossRef]

F. E. Hoge, A. Vodacek, R. N. Swift, J. Y. Yungel, N. V. Blough, “Inherent optical properties of the ocean: retrieval of the absorption coefficient of chromophoric dissolved organic matter from airborne laser spectral fluorescence measurements,” Appl. Opt. 34, 7032–7038 (1995).
[CrossRef] [PubMed]

F. E. Hoge, R. N. Swift, J. K. Yungel, “Oceanic radiance model development and validation: application of airborne active–passive ocean color spectral measurements,” Appl. Opt. 34, 3468–3476 (1995).
[CrossRef] [PubMed]

F. E. Hoge, A. Vodacek, N. V. Blough, “Inherent optical properties of the ocean: retrieval of the absorption coefficient of chromophoric dissolved organic matter from fluorescence measurements,” Limnol. Oceanogr. 38, 1394–1402 (1993).

F. E. Hoge, R. N. Swift, “Phytoplankton accessory pigments: evidence for the influence of phycoerythrin on the submarine light field,” Remote Sens. Environ. 34, 19–25 (1990).
[CrossRef]

F. E. Hoge, R. N. Swift, “Active-passive correlation spectroscopy: a new technique for identifying ocean color algorithm spectral regions,” Appl. Opt. 25, 2571–2583 (1986).
[CrossRef] [PubMed]

F. E. Hoge, R. N. Swift, “Airborne simultaneous spectroscopic detection of laser-induced water-Raman backscatter and fluorescence from chlorophyll a and other naturally occurring pigments,” Appl. Opt. 20, 3197–3205 (1981).
[CrossRef] [PubMed]

Holm-Hansen, O.

M. Vernet, B. G. Mitchell, O. Holm-Hansen, “Adaptation of synechococcus in situ determined by variability in intracellular phycoerythrin-543 at a coastal station off the Southern California coast, USA,” Mar. Ecol. 63, 9–16 (1990).
[CrossRef]

Kana, T. M.

F. E. Hoge, C. W. Wright, T. M. Kana, R. N. Swift, J. K. Yungel, “Spatial variability of oceanic phycoerythrin spectral types derived from airborne laser-induced fluorescence measurements,” Appl. Opt. 37, 4744–4749 (1998).
[CrossRef]

T. M. Kana, N. L. Feiwel, L. C. Flynn, “Nitrogen starvation in marine Synechococcus strains: clonal differences in phycobiliprotien breakdown and energy coupling,” Mar. Ecol. Prog. Ser. 88, 75–82 (1992).
[CrossRef]

T. M. Kana, P. M. Glibert, “Effect of irradiances up to 2000 µE m-2 s-1 on marine Synechococcus WH7803: I. Growth, pigmentation, and cell composition,” Deep-Sea Res. 34, 479–495 (1987).
[CrossRef]

Kiefer, D. A.

R. R. Bidigare, M. E. Ondrusek, J. H. Morrow, D. A. Kiefer, “In vivo absorption properties of algal pigments,” in Ocean Optics X, R. W. Spinrad, ed., Proc. SPIE1302, 290–302 (1990).
[CrossRef]

Lee, Z. P.

Lyon, P. E.

F. E. Hoge, C. W. Wright, P. E. Lyon, R. N. Swift, J. K. Yungel, “Satellite retrieval of inherent optical properties by inversion of an oceanic radiance model: a preliminary algorithm,” Appl. Opt. 38, 495–504 (1999).
[CrossRef]

F. E. Hoge, P. E. Lyon, “Satellite retrieval of inherent optical properties by linear matrix inversion of oceanic radiance models: an analysis of model and radiance measurement errors,” J. Geophys. Res. 101, 16,631–16,648 (1996).
[CrossRef]

Maffione, R. A.

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]

R. A. Maffione, D. R. Dana, J. M. Voss, “Spectral dependence of optical backscattering in the ocean,” presented at the OSA Annual Meeting, Portland, Ore., 10–15 September 1995, Paper MDD4.

R. A. Maffione, D. R. Dana, “In-situ characterization of optical backscattering and attenuation for lidar applications,” in Laser Remote Sensing of Natural Waters: from Theory to Practice: CIS Selected Papers, V. I. Feigels, Y. I. Kopelevich, eds., Proc. SPIE2964, 152–163 (1996).
[CrossRef]

Mitchell, B. G.

M. Vernet, B. G. Mitchell, O. Holm-Hansen, “Adaptation of synechococcus in situ determined by variability in intracellular phycoerythrin-543 at a coastal station off the Southern California coast, USA,” Mar. Ecol. 63, 9–16 (1990).
[CrossRef]

Morel, A.

S. Sathyendranath, L. Prieur, A. Morel, “A three-component model of ocean colour and its application to remote sensing of phytoplankton pigment in coastal waters,” Int. J. Remote Sens. 10, 1373–1394 (1989).
[CrossRef]

A. Morel, “Optical modeling of the upper ocean in relation to its biogenous matter content (case I waters),” J. Geophys. Res. 93, 10,749–10,768 (1988).
[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).

Morrow, J. H.

R. R. Bidigare, M. E. Ondrusek, J. H. Morrow, D. A. Kiefer, “In vivo absorption properties of algal pigments,” in Ocean Optics X, R. W. Spinrad, ed., Proc. SPIE1302, 290–302 (1990).
[CrossRef]

Olson, R. J.

R. J. Olson, S. W. Chisholm, E. R. Zettler, E. V. Armbrust, “Pigments, size, and distribution of Synechococcus in the North Atlantic and Pacific Oceans,” Limnol. Oceanogr. 35, 45–58 (1990).

Ondrusek, M. E.

R. R. Bidigare, M. E. Ondrusek, J. H. Morrow, D. A. Kiefer, “In vivo absorption properties of algal pigments,” in Ocean Optics X, R. W. Spinrad, ed., Proc. SPIE1302, 290–302 (1990).
[CrossRef]

Ong, L. J.

R. V. Swanson, L. J. Ong, S. M. Wilbanks, A. Glazer, “Phycoerythrins of marine unicellular cyanobacteria. II. Characterization of phycobiliprotiens with unusually high phycourobilin,” J. Biol. Chem. 266, 9528–9534 (1991).
[PubMed]

L. J. Ong, A. N. Glazer, “Phycoerythrins of marine unicellular cyanobacteria. I. Bilin types and locations and energy transfer pathways in Synechococcus spp. phycoerythrins,” J. Biol. Chem. 266, 9515–9527 (1991).
[PubMed]

L. J. Ong, A. Glazer, “Structural studies of phycobiliprotiens in unicellular marine cyanobacteria,” in Light-Energy Transduction in Photosynthesis: Higher Plant and Bacterial Models, S. E. Stevens, D. A. Bryant, eds. (American Society of Plant Physiologists, Rockville, Md., 1988), pp. 102–121.

Paerl, H. W.

D. G. Capone, J. P. Zehr, H. W. Paerl, B. Bergman, E. J. Carpenter, “Trichodesmium, a globally significant marine cyanobacterium,” Science 276, 1221–1229 (1997).
[CrossRef]

Peacock, T. G.

Perry, M. J.

M. E. Culver, M. J. Perry, “Detection of phycoerythrin fluorescence in upwelling irradiance spectra,” Eos Trans. Am. Geophys. Union 75, 233 (1994).

C. S. Roesler, M. J. Perry, K. L. Carder, “Modeling in situ phytoplankton from total absorption spectra in productive inland marine waters,” Limnol. Oceanogr. 34, 1510–1523 (1989).

Phinney, D. A.

A. M. Wood, D. A. Phinney, C. S. Yentsch, “Water column transparency and the distribution of spectrally distinct forms of phycoerythrin-containing organisms,” Mar. Ecol. Prog. Ser. 162, 25–31 (1998).
[CrossRef]

Pope, R. M.

Prieur, L.

S. Sathyendranath, L. Prieur, A. Morel, “A three-component model of ocean colour and its application to remote sensing of phytoplankton pigment in coastal waters,” Int. J. Remote Sens. 10, 1373–1394 (1989).
[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).

Roesler, C. S.

C. S. Roesler, M. J. Perry, K. L. Carder, “Modeling in situ phytoplankton from total absorption spectra in productive inland marine waters,” Limnol. Oceanogr. 34, 1510–1523 (1989).

Sathyendranath, S.

N. Hoepffner, S. Sathyendranath, “Determination of the major groups of phytoplankton pigments from the absorption spectra of total particulate matter,” J. Geophys. Res. 98, 22,789–22,803 (1993).
[CrossRef]

S. Sathyendranath, L. Prieur, A. Morel, “A three-component model of ocean colour and its application to remote sensing of phytoplankton pigment in coastal waters,” Int. J. Remote Sens. 10, 1373–1394 (1989).
[CrossRef]

Smith, R. C.

H. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, D. K. Clark, “A semianalytic radiance model of ocean color,” J. Geophys. Res. 93, 10,909–10,924 (1988).
[CrossRef]

Steward, R. G.

Swanson, R. V.

R. V. Swanson, L. J. Ong, S. M. Wilbanks, A. Glazer, “Phycoerythrins of marine unicellular cyanobacteria. II. Characterization of phycobiliprotiens with unusually high phycourobilin,” J. Biol. Chem. 266, 9528–9534 (1991).
[PubMed]

Swift, R. N.

F. E. Hoge, C. W. Wright, P. E. Lyon, R. N. Swift, J. K. Yungel, “Satellite retrieval of inherent optical properties by inversion of an oceanic radiance model: a preliminary algorithm,” Appl. Opt. 38, 495–504 (1999).
[CrossRef]

F. E. Hoge, C. W. Wright, T. M. Kana, R. N. Swift, J. K. Yungel, “Spatial variability of oceanic phycoerythrin spectral types derived from airborne laser-induced fluorescence measurements,” Appl. Opt. 37, 4744–4749 (1998).
[CrossRef]

F. E. Hoge, R. N. Swift, J. K. Yungel, “Oceanic radiance model development and validation: application of airborne active–passive ocean color spectral measurements,” Appl. Opt. 34, 3468–3476 (1995).
[CrossRef] [PubMed]

F. E. Hoge, A. Vodacek, R. N. Swift, J. Y. Yungel, N. V. Blough, “Inherent optical properties of the ocean: retrieval of the absorption coefficient of chromophoric dissolved organic matter from airborne laser spectral fluorescence measurements,” Appl. Opt. 34, 7032–7038 (1995).
[CrossRef] [PubMed]

F. E. Hoge, R. N. Swift, “Phytoplankton accessory pigments: evidence for the influence of phycoerythrin on the submarine light field,” Remote Sens. Environ. 34, 19–25 (1990).
[CrossRef]

F. E. Hoge, R. N. Swift, “Active-passive correlation spectroscopy: a new technique for identifying ocean color algorithm spectral regions,” Appl. Opt. 25, 2571–2583 (1986).
[CrossRef] [PubMed]

F. E. Hoge, R. N. Swift, “Airborne simultaneous spectroscopic detection of laser-induced water-Raman backscatter and fluorescence from chlorophyll a and other naturally occurring pigments,” Appl. Opt. 20, 3197–3205 (1981).
[CrossRef] [PubMed]

Valois, F. W.

J. B. Waterbury, S. W. Watson, F. W. Valois, D. G. Franks, “Biological and ecological characterization of the marine unicellular cyanobacterium synechococcus,” in Photosynthetic Picoplankton, T. Platt, W. K. W. Li, eds., Canadian Bulletin of Fisheries and Aquatic Sciences No. 214 (Fisheries Research Board of Canada, Ottawa, Ontario, Canada, 1986).

Vernet, M.

M. Vernet, B. G. Mitchell, O. Holm-Hansen, “Adaptation of synechococcus in situ determined by variability in intracellular phycoerythrin-543 at a coastal station off the Southern California coast, USA,” Mar. Ecol. 63, 9–16 (1990).
[CrossRef]

Vodacek, A.

F. E. Hoge, A. Vodacek, R. N. Swift, J. Y. Yungel, N. V. Blough, “Inherent optical properties of the ocean: retrieval of the absorption coefficient of chromophoric dissolved organic matter from airborne laser spectral fluorescence measurements,” Appl. Opt. 34, 7032–7038 (1995).
[CrossRef] [PubMed]

F. E. Hoge, A. Vodacek, N. V. Blough, “Inherent optical properties of the ocean: retrieval of the absorption coefficient of chromophoric dissolved organic matter from fluorescence measurements,” Limnol. Oceanogr. 38, 1394–1402 (1993).

Voss, J. M.

R. A. Maffione, D. R. Dana, J. M. Voss, “Spectral dependence of optical backscattering in the ocean,” presented at the OSA Annual Meeting, Portland, Ore., 10–15 September 1995, Paper MDD4.

Waterbury, J. B.

J. B. Waterbury, S. W. Watson, R. R. R. Guillard, L. E. Brand, “Widespread occurrence of a unicellular, marine, planktonic cyanobacterium,” Nature (London) 277, 293–294 (1979).
[CrossRef]

J. B. Waterbury, S. W. Watson, F. W. Valois, D. G. Franks, “Biological and ecological characterization of the marine unicellular cyanobacterium synechococcus,” in Photosynthetic Picoplankton, T. Platt, W. K. W. Li, eds., Canadian Bulletin of Fisheries and Aquatic Sciences No. 214 (Fisheries Research Board of Canada, Ottawa, Ontario, Canada, 1986).

Watson, S. W.

J. B. Waterbury, S. W. Watson, R. R. R. Guillard, L. E. Brand, “Widespread occurrence of a unicellular, marine, planktonic cyanobacterium,” Nature (London) 277, 293–294 (1979).
[CrossRef]

J. B. Waterbury, S. W. Watson, F. W. Valois, D. G. Franks, “Biological and ecological characterization of the marine unicellular cyanobacterium synechococcus,” in Photosynthetic Picoplankton, T. Platt, W. K. W. Li, eds., Canadian Bulletin of Fisheries and Aquatic Sciences No. 214 (Fisheries Research Board of Canada, Ottawa, Ontario, Canada, 1986).

Wilbanks, S. M.

S. M. Wilbanks, A. Glazer, “Rod structure of a phycoerythrin II-containing phycobilisome. I. Organization and sequence of the gene cluster encoding the major phycobiliprotein rod components in the genome of marine Synechococcus SP WH8020,” J. Biol. Chem. 268, 1226–1235 (1993).
[PubMed]

R. V. Swanson, L. J. Ong, S. M. Wilbanks, A. Glazer, “Phycoerythrins of marine unicellular cyanobacteria. II. Characterization of phycobiliprotiens with unusually high phycourobilin,” J. Biol. Chem. 266, 9528–9534 (1991).
[PubMed]

S. M. Wilbanks, R. de Lorimier, A. Glazer, “Phycoerythrins of marine unicellular cyanobacteria. III. Sequence of a class II phycoerythrin,” J. Biol. Chem. 266, 9535–9539 (1991).
[PubMed]

Wood, A. M.

A. M. Wood, D. A. Phinney, C. S. Yentsch, “Water column transparency and the distribution of spectrally distinct forms of phycoerythrin-containing organisms,” Mar. Ecol. Prog. Ser. 162, 25–31 (1998).
[CrossRef]

Wright, C. W.

Yentsch, C. M.

C. S. Yentsch, C. M. Yentsch, “Fluorescence spectral signatures: the characterization of phytoplankton populations by the use of excitation and emission spectra,” J. Mar. Res. 37, 471–483 (1979).

Yentsch, C. S.

A. M. Wood, D. A. Phinney, C. S. Yentsch, “Water column transparency and the distribution of spectrally distinct forms of phycoerythrin-containing organisms,” Mar. Ecol. Prog. Ser. 162, 25–31 (1998).
[CrossRef]

C. S. Yentsch, C. M. Yentsch, “Fluorescence spectral signatures: the characterization of phytoplankton populations by the use of excitation and emission spectra,” J. Mar. Res. 37, 471–483 (1979).

Yungel, J. K.

Yungel, J. Y.

Zehr, J. P.

D. G. Capone, J. P. Zehr, H. W. Paerl, B. Bergman, E. J. Carpenter, “Trichodesmium, a globally significant marine cyanobacterium,” Science 276, 1221–1229 (1997).
[CrossRef]

Zettler, E. R.

R. J. Olson, S. W. Chisholm, E. R. Zettler, E. V. Armbrust, “Pigments, size, and distribution of Synechococcus in the North Atlantic and Pacific Oceans,” Limnol. Oceanogr. 35, 45–58 (1990).

Appl. Opt. (9)

F. E. Hoge, R. N. Swift, “Airborne simultaneous spectroscopic detection of laser-induced water-Raman backscatter and fluorescence from chlorophyll a and other naturally occurring pigments,” Appl. Opt. 20, 3197–3205 (1981).
[CrossRef] [PubMed]

F. E. Hoge, R. N. Swift, “Active-passive correlation spectroscopy: a new technique for identifying ocean color algorithm spectral regions,” Appl. Opt. 25, 2571–2583 (1986).
[CrossRef] [PubMed]

Z. P. Lee, K. L. Carder, S. K. Hawes, R. G. Steward, T. G. Peacock, C. O. Davis, “Model for the interpretation of hyperspectral remote-sensing reflectance,” Appl. Opt. 33, 5721–5732 (1994).
[CrossRef] [PubMed]

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]

F. E. Hoge, C. W. Wright, P. E. Lyon, R. N. Swift, J. K. Yungel, “Satellite retrieval of inherent optical properties by inversion of an oceanic radiance model: a preliminary algorithm,” Appl. Opt. 38, 495–504 (1999).
[CrossRef]

F. E. Hoge, R. N. Swift, J. K. Yungel, “Oceanic radiance model development and validation: application of airborne active–passive ocean color spectral measurements,” Appl. Opt. 34, 3468–3476 (1995).
[CrossRef] [PubMed]

F. E. Hoge, A. Vodacek, R. N. Swift, J. Y. Yungel, N. V. Blough, “Inherent optical properties of the ocean: retrieval of the absorption coefficient of chromophoric dissolved organic matter from airborne laser spectral fluorescence measurements,” Appl. Opt. 34, 7032–7038 (1995).
[CrossRef] [PubMed]

F. E. Hoge, C. W. Wright, T. M. Kana, R. N. Swift, J. K. Yungel, “Spatial variability of oceanic phycoerythrin spectral types derived from airborne laser-induced fluorescence measurements,” Appl. Opt. 37, 4744–4749 (1998).
[CrossRef]

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]

Deep-Sea Res. (1)

T. M. Kana, P. M. Glibert, “Effect of irradiances up to 2000 µE m-2 s-1 on marine Synechococcus WH7803: I. Growth, pigmentation, and cell composition,” Deep-Sea Res. 34, 479–495 (1987).
[CrossRef]

Eos Trans. Am. Geophys. Union (1)

M. E. Culver, M. J. Perry, “Detection of phycoerythrin fluorescence in upwelling irradiance spectra,” Eos Trans. Am. Geophys. Union 75, 233 (1994).

Int. J. Remote Sens. (1)

S. Sathyendranath, L. Prieur, A. Morel, “A three-component model of ocean colour and its application to remote sensing of phytoplankton pigment in coastal waters,” Int. J. Remote Sens. 10, 1373–1394 (1989).
[CrossRef]

J. Biol. Chem. (4)

S. M. Wilbanks, A. Glazer, “Rod structure of a phycoerythrin II-containing phycobilisome. I. Organization and sequence of the gene cluster encoding the major phycobiliprotein rod components in the genome of marine Synechococcus SP WH8020,” J. Biol. Chem. 268, 1226–1235 (1993).
[PubMed]

L. J. Ong, A. N. Glazer, “Phycoerythrins of marine unicellular cyanobacteria. I. Bilin types and locations and energy transfer pathways in Synechococcus spp. phycoerythrins,” J. Biol. Chem. 266, 9515–9527 (1991).
[PubMed]

R. V. Swanson, L. J. Ong, S. M. Wilbanks, A. Glazer, “Phycoerythrins of marine unicellular cyanobacteria. II. Characterization of phycobiliprotiens with unusually high phycourobilin,” J. Biol. Chem. 266, 9528–9534 (1991).
[PubMed]

S. M. Wilbanks, R. de Lorimier, A. Glazer, “Phycoerythrins of marine unicellular cyanobacteria. III. Sequence of a class II phycoerythrin,” J. Biol. Chem. 266, 9535–9539 (1991).
[PubMed]

J. Geophys. Res. (4)

F. E. Hoge, P. E. Lyon, “Satellite retrieval of inherent optical properties by linear matrix inversion of oceanic radiance models: an analysis of model and radiance measurement errors,” J. Geophys. Res. 101, 16,631–16,648 (1996).
[CrossRef]

H. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, D. K. Clark, “A semianalytic radiance model of ocean color,” J. Geophys. Res. 93, 10,909–10,924 (1988).
[CrossRef]

N. Hoepffner, S. Sathyendranath, “Determination of the major groups of phytoplankton pigments from the absorption spectra of total particulate matter,” J. Geophys. Res. 98, 22,789–22,803 (1993).
[CrossRef]

A. Morel, “Optical modeling of the upper ocean in relation to its biogenous matter content (case I waters),” J. Geophys. Res. 93, 10,749–10,768 (1988).
[CrossRef]

J. Mar. Res. (1)

C. S. Yentsch, C. M. Yentsch, “Fluorescence spectral signatures: the characterization of phytoplankton populations by the use of excitation and emission spectra,” J. Mar. Res. 37, 471–483 (1979).

Limnol. Oceanogr. (4)

C. S. Roesler, M. J. Perry, K. L. Carder, “Modeling in situ phytoplankton from total absorption spectra in productive inland marine waters,” Limnol. Oceanogr. 34, 1510–1523 (1989).

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).

F. E. Hoge, A. Vodacek, N. V. Blough, “Inherent optical properties of the ocean: retrieval of the absorption coefficient of chromophoric dissolved organic matter from fluorescence measurements,” Limnol. Oceanogr. 38, 1394–1402 (1993).

R. J. Olson, S. W. Chisholm, E. R. Zettler, E. V. Armbrust, “Pigments, size, and distribution of Synechococcus in the North Atlantic and Pacific Oceans,” Limnol. Oceanogr. 35, 45–58 (1990).

Mar. Ecol. (1)

M. Vernet, B. G. Mitchell, O. Holm-Hansen, “Adaptation of synechococcus in situ determined by variability in intracellular phycoerythrin-543 at a coastal station off the Southern California coast, USA,” Mar. Ecol. 63, 9–16 (1990).
[CrossRef]

Mar. Ecol. Prog. Ser. (2)

A. M. Wood, D. A. Phinney, C. S. Yentsch, “Water column transparency and the distribution of spectrally distinct forms of phycoerythrin-containing organisms,” Mar. Ecol. Prog. Ser. 162, 25–31 (1998).
[CrossRef]

T. M. Kana, N. L. Feiwel, L. C. Flynn, “Nitrogen starvation in marine Synechococcus strains: clonal differences in phycobiliprotien breakdown and energy coupling,” Mar. Ecol. Prog. Ser. 88, 75–82 (1992).
[CrossRef]

Nature (London) (1)

J. B. Waterbury, S. W. Watson, R. R. R. Guillard, L. E. Brand, “Widespread occurrence of a unicellular, marine, planktonic cyanobacterium,” Nature (London) 277, 293–294 (1979).
[CrossRef]

Remote Sens. Environ. (1)

F. E. Hoge, R. N. Swift, “Phytoplankton accessory pigments: evidence for the influence of phycoerythrin on the submarine light field,” Remote Sens. Environ. 34, 19–25 (1990).
[CrossRef]

Science (1)

D. G. Capone, J. P. Zehr, H. W. Paerl, B. Bergman, E. J. Carpenter, “Trichodesmium, a globally significant marine cyanobacterium,” Science 276, 1221–1229 (1997).
[CrossRef]

Other (5)

R. R. Bidigare, M. E. Ondrusek, J. H. Morrow, D. A. Kiefer, “In vivo absorption properties of algal pigments,” in Ocean Optics X, R. W. Spinrad, ed., Proc. SPIE1302, 290–302 (1990).
[CrossRef]

J. B. Waterbury, S. W. Watson, F. W. Valois, D. G. Franks, “Biological and ecological characterization of the marine unicellular cyanobacterium synechococcus,” in Photosynthetic Picoplankton, T. Platt, W. K. W. Li, eds., Canadian Bulletin of Fisheries and Aquatic Sciences No. 214 (Fisheries Research Board of Canada, Ottawa, Ontario, Canada, 1986).

L. J. Ong, A. Glazer, “Structural studies of phycobiliprotiens in unicellular marine cyanobacteria,” in Light-Energy Transduction in Photosynthesis: Higher Plant and Bacterial Models, S. E. Stevens, D. A. Bryant, eds. (American Society of Plant Physiologists, Rockville, Md., 1988), pp. 102–121.

R. A. Maffione, D. R. Dana, J. M. Voss, “Spectral dependence of optical backscattering in the ocean,” presented at the OSA Annual Meeting, Portland, Ore., 10–15 September 1995, Paper MDD4.

R. A. Maffione, D. R. Dana, “In-situ characterization of optical backscattering and attenuation for lidar applications,” in Laser Remote Sensing of Natural Waters: from Theory to Practice: CIS Selected Papers, V. I. Feigels, Y. I. Kopelevich, eds., Proc. SPIE2964, 152–163 (1996).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

(a) Excitation (absorption) spectra of PUB and PEB having various degrees of PUB substitution at chromophore binding sites. PEB excitation (absorption) spectra of three cultures of phytoplankton having PE: PUB rich (PEBI), PUB intermediate (PEBI), and PUB deficient (PEBII). The peak of the PEB excitation (absorption) spectrum shifts ∼15 nm toward the blue when PUB chromophores are substituted within the hexameric protein aggregate. The vertical bars illustrate the location of the 412-, 488-, 531-, and 551-nm MODIS bands. (b) Gaussian model fit to the absorption spectrum of PEB that is deficient in PUB substitution. The optimum fit is chosen to occur at the MODIS band positions, not the peak wavelength. (c) Same as (b) except for PEB that is rich in PUB substitution. (d) Gaussian model fit to the absorption spectrum of PUB. The optimum fit is chosen to occur at the 488-nm MODIS band position.

Fig. 2
Fig. 2

(a) Phytoplankton model analytically represented by a single Gaussian, (b) the CDOM and detritus exponential model, and (c) the total constituent backscattering (TCB) wavelength ratio model.

Fig. 3
Fig. 3

Outbound flight track of the NASA P3-B aircraft with Airborne Oceanographic Lidar and passive radiometric subsystems on 3 April 1995. (The inbound flight track data were not available for analyses because of other experiments.)

Fig. 4
Fig. 4

(a) Comparison of the airborne laser-induced PEB pigment fluorescence with the passively retrieved unmodeled absorption coefficient at 488 nm [a PE(488)]. The laser-induced fluorescence was scaled and offset to provide improved agreement with the passively retrieved absorption coefficient. (b) Comparison of the standard airborne laser-derived CDOM absorption coefficient with the passively retrieved CDOM and detritus absorption coefficient at 412 nm [a d (412)]. (c) Comparison of the airborne laser-derived phytoplankton absorption coefficient with the passively retrieved phytoplankton absorption coefficient at 412 nm [a ph(412)]. (d) The passively retrieved TCB coefficient at 412 nm [b bt(412)]. The total backscattering can be obtained by adding the backscattering of water at 412 nm [b bw(412)]. No airborne laser instrumentation is yet available to provide truth for the retrieved backscattering product.

Fig. 5
Fig. 5

(a) Two segments, A and B, displaying negative correlation between laser-induced PEB fluorescence and chlorophyll fluorescence. These negative correlation regions are important validation regions for illustrating PE absorption coefficient retrieval in the presence of normally correlated phytoplankton chlorophyll. (b) Two segments, A′ and B′, displaying correlation of the retrieved unmodeled PE absorption coefficient a PE(488) and the PEB fluorescence. (c) Two segments, A″ and B″, displaying the correlation of the retrieved phytoplankton absorption coefficient a ph(412) and the chlorophyll fluorescence. Comparing segments A, A′, and A″ the data strongly suggest that the multiband model inversion is simultaneously retrieving both the PE absorption coefficient and the phytoplankton absorption coefficient. Similarly, comparing segments B, B′, and B″ the data suggest, but less convincingly, that the multiband model inversion is concurrently retrieving both the PE and the phytoplankton absorption coefficients.

Equations (17)

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Gλi, λg,k, gk=exp-λi-λg,k2/2gk2,
GN,λrλi, λg,k, gk=exp-λi-λg,k2/2gk2/exp-λr-λg,k2/2gk2,
apebIIλi=apebIIλr,pebIIGN,λrλi, λg,pebII, gpebII,
apebIλi=apebIλr,pebIGN,λrλi, λg,pebI, gpebI.
apubλi=apubλr,pubGN,λrλi, λg,pub, gpub.
aphλi=aphλr,phGN,λrλi, λg,ph, gph.
adλi=adλdexp-Sλi-λd,
bbtλi=bbtλbλb/λin,
n=a1L412/L551+a2.
apubλi+apebIIλi+apebIλi+aphλi+adλi+bbtλivλi=hλi,
apubλr,pubGN,λrλi, λg,pub, gpub+apebIIλr,pebIIGN,λrλi, λg,pebII, gpebII+apebIλr,pebIGN,λrλi, λg,pebI, gpebI+aphλrGN,λrλi, λg,ph, gph+adλd×exp-Sλi-λd+bbtλbλb/λinvλi=-awλi-bbwλivλi.
Dp=h.
h=-awλ1-bbwλ1vλ1-awλ2-bbwλ2vλ2-awλ3-bbwλ3vλ3-awλ4-bbwλ4vλ4-awλ5-bbwλ5vλ5-awλ6-bbwλ6vλ6.
p=apubλr,pub, apebIIλr,pebII, apebIλr,pebI,×aphλr,ph, adλd, bbtλbT,
p=D-1h,
0GN,λrλ1, λg,ph, gphexp-Sλ1-λdλb/λ1nvλi1GN,λrλ2, λg,ph, gphexp-Sλ2-λdλb/λ2nvλi0GN,λrλ3, λg,ph, gphexp-Sλ3-λdλb/λ3nvλi0GN,λrλ4, λg,ph, gphexp-Sλ4-λdλb/λ4nvλi×aPE488aphλr,phadλdbbtλb=-awλ1-bbwλ1vλ1-awλ2-bbwλ2vλ2-awλ3-bbwλ3vλ3-awλ4-bbwλ4vλ4.
GN,λrλ1, λg,pub, gpubGN,λrλ1, λg,pebII, gpebIIGN,λrλ1, λg,pebI, gpebIGN,λrλ1, λg,ph, gphexp-Sλ1-λdλb/λ1nvλ1GN,λrλ2, λg,pub, gpubGN,λrλ2, λg,pebII, gpebIIGN,λrλ2, λg,pebI, gpebIGN,λrλ2, λg,ph, gphexp-Sλ2-λdλb/λ2nvλ2GN,λrλ3, λg,pub, gpubGN,λrλ3, λg,pebII, gpebIIGN,λrλ3, λg,pebI, gpebIGN,λrλ3, λg,ph, gphexp-Sλ3-λdλb/λ3nvλ3GN,λrλ4, λg,pub, gpubGN,λrλ4, λg,pebII, gpebIIGN,λrλ4, λg,pebI, gpebIGN,λrλ4, λg,ph, gphexp-Sλ4-λdλb/λ4nvλ4GN,λrλ5, λg,pub, gpubGN,λrλ5, λg,pebII, gpebIIGN,λrλ5, λg,pebI, gpebIGN,λrλ5, λg,ph, gphexp-Sλ5-λdλb/λ5nvλ5GN,λrλ6, λg,pub, gpubGN,λrλ6, λg,pebII, gpebIIGN,λrλ6, λg,pebI, gpebIGN,λrλ6, λg,ph, gphexp-Sλ6-λdλb/λ6nvλ6×apubλr,pubapebIIλr,pebIIapebIλr,pebIaphλr,phadλdbbtλb=-awλ1-bbwλ1vλ1-awλ2-bbwλ2vλ2-awλ3-bbwλ3vλ3-awλ4-bbwλ4vλ4-awλ5-bbwλ5vλ5-awλ6-bbwλ6vλ6.

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