Abstract

It is shown that the oceanic beam attenuation coefficient can be retrieved from airborne laser-induced and depth-resolved chromophoric dissolved organic matter (CDOM) fluorescence. The radiative transfer equation (RTE) retrieval methodology does not require a laser beam spread function model since two CDOM fluorescence bands are used in conjunction with a beam attenuation spectral model, is self-normalizing since the CDOM absorption coefficient and laser beam irradiance are common to both fluorescence observational channels, and is enabled by the known isotropic phase function for CDOM fluorescence. Although this RTE analytical inversion theory is exact, the retrieval uncertainty is reduced by configuring the proposed lidar in the multiple-field-of-view beam attenuation mode to significantly diminish observation of multiple scattering. The theory can be applied over wide regions of the ocean's continental margins, estuaries, lakes, and rivers that are known to have sufficient CDOM.

© 2006 Optical Society of America

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2003 (2)

2002 (2)

L. Bissonnette, G. Roy, L. Poutier, S. G. Cober, and G. A. Isaac, "Multiple-scattering lidar retrieval method: tests on Monte Carlo simulations and comparisons with in situ measurements," Appl. Opt. 41, 6307-6324 (2002).
[CrossRef] [PubMed]

C. D. Clark, J. Jimenez-Morais, G. Jones, E. Zanardi-Lamardo, C. A. Moore, and R. G. Zika, "A time-resolved fluorescence study of dissolved organic matter in a riverine to marine transition zone," Mar. Chem. 78, 121-135 (2002).
[CrossRef]

2001 (2)

C. W. Wright, F. E. Hoge, R. N. Swift, J. K. Yungel, and C. R. Schirtzinger, "Next-generation NASA airborne oceanographic lidar system," Appl. Opt. 40, 336-342 (2001).
[CrossRef]

F. E. Hoge, C. W. Wright, P. E. Lyon, R. N. Swift, and J. K. Yungel, "Inherent optical properties imagery of the western North Atlantic Ocean: horizontal spatial variability of the upper mixed layer," J. Geophys. Res. 106, 31129-31140 (2001).
[CrossRef]

2000 (1)

1999 (6)

1998 (1)

A. H. Bernard, W. S. Pegau, and J. R. V. Zaneveld, "Global relationships of the inherent optical properties of the oceans," J. Geophys. Res 103, 24955-24968 (1998).
[CrossRef]

1997 (1)

1995 (2)

F. E. Hoge, A. Vodacek, R. N. Swift, J. K. Yungel, and 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, M. E. Williams, R. N. Swift, J. K. Yungel, and A. Vodacek, "Satellite retrieval of the absorption coefficient of chromophoric dissolved organic matter in continental margins," J. Geophys. Res. 100, 24847-24854 (1995).
[CrossRef]

1994 (1)

1993 (3)

F. E. Hoge, R. N. Swift, J. K. Yungel, and A. Vodacek, "Fluorescence of dissolved organic matter: a comparison of North Pacific and North Atlantic Oceans during April 1991," J. Geophys. Res. 98, 22779-22787 (1993).
[CrossRef]

Y. Ge, H. R. Gordon, and K. J. Voss, "Simulation of inelastic-scattering contributions to the irradiance field in the ocean: variation in Fraunhofer line depths," Appl. Opt. 32, 4028-4036 (1993).
[PubMed]

F. E. Hoge, A. Vodacek, and 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).
[CrossRef]

1992 (1)

K. J. Voss, "A spectral model of the beam attenuation coefficient in the ocean and coastal areas," Limnol. Oceanogr. 37, 501-509 (1992).
[CrossRef]

1990 (1)

1986 (2)

1983 (3)

1982 (1)

H. R. Gordon, "Interpretation of airborne oceanic lidar: effects of multiple scattering," Appl. Opt 21, 2996-3001 (1982).
[CrossRef] [PubMed]

1981 (1)

A. Bricaud, A. Morel, and 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]

Bastille, C.

Bernard, A. H.

A. H. Bernard, W. S. Pegau, and J. R. V. Zaneveld, "Global relationships of the inherent optical properties of the oceans," J. Geophys. Res 103, 24955-24968 (1998).
[CrossRef]

Berry, R. E.

Bishop, J. K. B.

J. K. B. Bishop, "Transmissometer measurement of POC," Deep-Sea Res. I 46, 353-369 (1999).
[CrossRef]

J. K. B. Bishop, S. E. Calvert, and M. Y. S. Moon, "Spatial variability of POC in the northeast Subarctic Pacific," Deep-Sea Res. II 46, 2699-2733 (1999).
[CrossRef]

Bisonnette, L. R.

Bissonnette, L.

Bissonnette, L. R.

Blough, N. V.

F. E. Hoge, A. Vodacek, R. N. Swift, J. K. Yungel, and 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, and 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).
[CrossRef]

Boynton, G. C.

Bricaud, A.

A. Bricaud, A. Morel, and 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]

Calvert, S. E.

J. K. B. Bishop, S. E. Calvert, and M. Y. S. Moon, "Spatial variability of POC in the northeast Subarctic Pacific," Deep-Sea Res. II 46, 2699-2733 (1999).
[CrossRef]

Clark, C. D.

C. D. Clark, J. Jimenez-Morais, G. Jones, E. Zanardi-Lamardo, C. A. Moore, and R. G. Zika, "A time-resolved fluorescence study of dissolved organic matter in a riverine to marine transition zone," Mar. Chem. 78, 121-135 (2002).
[CrossRef]

Cober, S. G.

Durand, L.

Esaias, W.

Exton, R. J.

Farmer, F. H.

Flannery, B. P.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipies in Fortran, 2nd ed. (Cambridge U. Press, 1992).

Ge, Y.

Gordon, H. R.

Harriss, R. C.

Hoge, F. E.

F. E. Hoge, "Validation of satellite-retrieved oceanic inherent optical properties: proposed two-color elastic backscatter lidar and retrieval theory," Appl. Opt. 42, 7191-7196 (2003).
[CrossRef]

C. W. Wright, F. E. Hoge, R. N. Swift, J. K. Yungel, and C. R. Schirtzinger, "Next-generation NASA airborne oceanographic lidar system," Appl. Opt. 40, 336-342 (2001).
[CrossRef]

F. E. Hoge, C. W. Wright, P. E. Lyon, R. N. Swift, and J. K. Yungel, "Inherent optical properties imagery of the western North Atlantic Ocean: horizontal spatial variability of the upper mixed layer," J. Geophys. Res. 106, 31129-31140 (2001).
[CrossRef]

F. E. Hoge, C. W. Wright, P. E. Lyon, R. N. Swift, and 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, P. E. Lyon, R. N. Swift, and J. K. Yungel, "Satellite retrieval of the absorption coefficient of phytoplankton phycoerythrin pigment: theory and feasibility status," Appl. Opt. 38, 7431-7441 (1999).
[CrossRef]

F. E. Hoge, A. Vodacek, R. N. Swift, J. K. Yungel, and 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, M. E. Williams, R. N. Swift, J. K. Yungel, and A. Vodacek, "Satellite retrieval of the absorption coefficient of chromophoric dissolved organic matter in continental margins," J. Geophys. Res. 100, 24847-24854 (1995).
[CrossRef]

F. E. Hoge, A. Vodacek, and 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).
[CrossRef]

F. E. Hoge, R. N. Swift, J. K. Yungel, and A. Vodacek, "Fluorescence of dissolved organic matter: a comparison of North Pacific and North Atlantic Oceans during April 1991," J. Geophys. Res. 98, 22779-22787 (1993).
[CrossRef]

F. E. Hoge, R. E. Berry, and R. N. Swift, "Active-passive airborne ocean color measurement. 1: Instrumentation," Appl. Opt. 25, 39-47 (1986).
[CrossRef] [PubMed]

F. E. Hoge, R. N. Swift, and J. K. Yungel, "Active-passive airborne ocean color measurement. 2: Applications," Appl. Opt. 25, 48-57 (1986).
[CrossRef] [PubMed]

F. E. Hoge and R. N. Swift, "Airborne detection of oceanic turbidity cell structure using depth-resolved laser-induced water Raman backscatter," Appl. Opt. 22, 3778-3786 (1983).
[CrossRef] [PubMed]

F. E. Hoge and R. N. Swift, "Experimental feasibility of the airborne measurement of absolute oil fluorescence spectral conversion efficiency," Appl. Opt. 22, 37-47 (1983).
[CrossRef] [PubMed]

F. E. Hoge is preparing a manuscript with the title "Oceanic beam attenuation coefficient retrieval by radiative transfer equation inversion of airborne water Raman backscattering. 1: Theory."

Houghton, W. M.

Hunt, D. L.

Hutt, D. L.

Isaac, G. A.

Jimenez-Morais, J.

C. D. Clark, J. Jimenez-Morais, G. Jones, E. Zanardi-Lamardo, C. A. Moore, and R. G. Zika, "A time-resolved fluorescence study of dissolved organic matter in a riverine to marine transition zone," Mar. Chem. 78, 121-135 (2002).
[CrossRef]

Jones, G.

C. D. Clark, J. Jimenez-Morais, G. Jones, E. Zanardi-Lamardo, C. A. Moore, and R. G. Zika, "A time-resolved fluorescence study of dissolved organic matter in a riverine to marine transition zone," Mar. Chem. 78, 121-135 (2002).
[CrossRef]

Katzev, I.

Lyon, P. E.

Malinka, A. V.

Mobley, C. D.

C. D. Mobley, Light and Water, Radiative Transfer in Natural Waters (Academic, 1994), Chap. 5. The errata can be found at ftp.sequoiasci.com within the file /pub/outgoing/LightandWaterErrata.pdf. Note: at the time of publication, Mobley's Light and Water is now available on CD, with the errors corrected. The CD is available from Mobley, or the contents of the CD can be downloaded from http://www.curtismobley.com/curts_work.htm or from http://www.curtismobley.com/LightandWater.zip.

Moon, M. Y. S.

J. K. B. Bishop, S. E. Calvert, and M. Y. S. Moon, "Spatial variability of POC in the northeast Subarctic Pacific," Deep-Sea Res. II 46, 2699-2733 (1999).
[CrossRef]

Moore, C. A.

C. D. Clark, J. Jimenez-Morais, G. Jones, E. Zanardi-Lamardo, C. A. Moore, and R. G. Zika, "A time-resolved fluorescence study of dissolved organic matter in a riverine to marine transition zone," Mar. Chem. 78, 121-135 (2002).
[CrossRef]

Morel, A.

A. Bricaud, A. Morel, and 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]

Pegau, W. S.

A. H. Bernard, W. S. Pegau, and J. R. V. Zaneveld, "Global relationships of the inherent optical properties of the oceans," J. Geophys. Res 103, 24955-24968 (1998).
[CrossRef]

Polansky, I.

Poutier, L.

Press, W. H.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipies in Fortran, 2nd ed. (Cambridge U. Press, 1992).

Prieur, L.

A. Bricaud, A. Morel, and 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]

Prikhach, A.

Roy, G.

Schirtzinger, C. R.

Swift, R. N.

C. W. Wright, F. E. Hoge, R. N. Swift, J. K. Yungel, and C. R. Schirtzinger, "Next-generation NASA airborne oceanographic lidar system," Appl. Opt. 40, 336-342 (2001).
[CrossRef]

F. E. Hoge, C. W. Wright, P. E. Lyon, R. N. Swift, and J. K. Yungel, "Inherent optical properties imagery of the western North Atlantic Ocean: horizontal spatial variability of the upper mixed layer," J. Geophys. Res. 106, 31129-31140 (2001).
[CrossRef]

F. E. Hoge, C. W. Wright, P. E. Lyon, R. N. Swift, and 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, P. E. Lyon, R. N. Swift, and J. K. Yungel, "Satellite retrieval of the absorption coefficient of phytoplankton phycoerythrin pigment: theory and feasibility status," Appl. Opt. 38, 7431-7441 (1999).
[CrossRef]

F. E. Hoge, A. Vodacek, R. N. Swift, J. K. Yungel, and 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, M. E. Williams, R. N. Swift, J. K. Yungel, and A. Vodacek, "Satellite retrieval of the absorption coefficient of chromophoric dissolved organic matter in continental margins," J. Geophys. Res. 100, 24847-24854 (1995).
[CrossRef]

F. E. Hoge, R. N. Swift, J. K. Yungel, and A. Vodacek, "Fluorescence of dissolved organic matter: a comparison of North Pacific and North Atlantic Oceans during April 1991," J. Geophys. Res. 98, 22779-22787 (1993).
[CrossRef]

F. E. Hoge, R. E. Berry, and R. N. Swift, "Active-passive airborne ocean color measurement. 1: Instrumentation," Appl. Opt. 25, 39-47 (1986).
[CrossRef] [PubMed]

F. E. Hoge, R. N. Swift, and J. K. Yungel, "Active-passive airborne ocean color measurement. 2: Applications," Appl. Opt. 25, 48-57 (1986).
[CrossRef] [PubMed]

F. E. Hoge and R. N. Swift, "Airborne detection of oceanic turbidity cell structure using depth-resolved laser-induced water Raman backscatter," Appl. Opt. 22, 3778-3786 (1983).
[CrossRef] [PubMed]

F. E. Hoge and R. N. Swift, "Experimental feasibility of the airborne measurement of absolute oil fluorescence spectral conversion efficiency," Appl. Opt. 22, 37-47 (1983).
[CrossRef] [PubMed]

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipies in Fortran, 2nd ed. (Cambridge U. Press, 1992).

Vallee, G.

Vetterling, W. T.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipies in Fortran, 2nd ed. (Cambridge U. Press, 1992).

Vodacek, A.

F. E. Hoge, M. E. Williams, R. N. Swift, J. K. Yungel, and A. Vodacek, "Satellite retrieval of the absorption coefficient of chromophoric dissolved organic matter in continental margins," J. Geophys. Res. 100, 24847-24854 (1995).
[CrossRef]

F. E. Hoge, A. Vodacek, R. N. Swift, J. K. Yungel, and 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, and 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).
[CrossRef]

F. E. Hoge, R. N. Swift, J. K. Yungel, and A. Vodacek, "Fluorescence of dissolved organic matter: a comparison of North Pacific and North Atlantic Oceans during April 1991," J. Geophys. Res. 98, 22779-22787 (1993).
[CrossRef]

Voss, K. J.

White, H. H.

Williams, M. E.

F. E. Hoge, M. E. Williams, R. N. Swift, J. K. Yungel, and A. Vodacek, "Satellite retrieval of the absorption coefficient of chromophoric dissolved organic matter in continental margins," J. Geophys. Res. 100, 24847-24854 (1995).
[CrossRef]

Wright, C. W.

Yungel, J. K.

C. W. Wright, F. E. Hoge, R. N. Swift, J. K. Yungel, and C. R. Schirtzinger, "Next-generation NASA airborne oceanographic lidar system," Appl. Opt. 40, 336-342 (2001).
[CrossRef]

F. E. Hoge, C. W. Wright, P. E. Lyon, R. N. Swift, and J. K. Yungel, "Inherent optical properties imagery of the western North Atlantic Ocean: horizontal spatial variability of the upper mixed layer," J. Geophys. Res. 106, 31129-31140 (2001).
[CrossRef]

F. E. Hoge, C. W. Wright, P. E. Lyon, R. N. Swift, and 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, P. E. Lyon, R. N. Swift, and J. K. Yungel, "Satellite retrieval of the absorption coefficient of phytoplankton phycoerythrin pigment: theory and feasibility status," Appl. Opt. 38, 7431-7441 (1999).
[CrossRef]

F. E. Hoge, A. Vodacek, R. N. Swift, J. K. Yungel, and 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, M. E. Williams, R. N. Swift, J. K. Yungel, and A. Vodacek, "Satellite retrieval of the absorption coefficient of chromophoric dissolved organic matter in continental margins," J. Geophys. Res. 100, 24847-24854 (1995).
[CrossRef]

F. E. Hoge, R. N. Swift, J. K. Yungel, and A. Vodacek, "Fluorescence of dissolved organic matter: a comparison of North Pacific and North Atlantic Oceans during April 1991," J. Geophys. Res. 98, 22779-22787 (1993).
[CrossRef]

F. E. Hoge, R. N. Swift, and J. K. Yungel, "Active-passive airborne ocean color measurement. 2: Applications," Appl. Opt. 25, 48-57 (1986).
[CrossRef] [PubMed]

Zanardi-Lamardo, E.

C. D. Clark, J. Jimenez-Morais, G. Jones, E. Zanardi-Lamardo, C. A. Moore, and R. G. Zika, "A time-resolved fluorescence study of dissolved organic matter in a riverine to marine transition zone," Mar. Chem. 78, 121-135 (2002).
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Zaneveld, J. R. V.

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Zege, E. P.

Zika, R. G.

C. D. Clark, J. Jimenez-Morais, G. Jones, E. Zanardi-Lamardo, C. A. Moore, and R. G. Zika, "A time-resolved fluorescence study of dissolved organic matter in a riverine to marine transition zone," Mar. Chem. 78, 121-135 (2002).
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Appl. Opt (1)

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G. Roy, L. R. Bissonnette, C. Bastille, and G. Vallee, "Retrieval of droplet-size density distribution from multiple-field-of-view cross-polarized lidar signals: theory and experimental validation," Appl. Opt. 38, 5202-5211 (1999).
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L. Bissonnette, G. Roy, L. Poutier, S. G. Cober, and G. A. Isaac, "Multiple-scattering lidar retrieval method: tests on Monte Carlo simulations and comparisons with in situ measurements," Appl. Opt. 41, 6307-6324 (2002).
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H. R. Gordon, "Contribution of Raman scattering to water-leaving radiance: a reexamination," Appl. Opt. 38, 3166-3174 (1999).
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F. E. Hoge, C. W. Wright, P. E. Lyon, R. N. Swift, and J. K. Yungel, "Satellite retrieval of the absorption coefficient of phytoplankton phycoerythrin pigment: theory and feasibility status," Appl. Opt. 38, 7431-7441 (1999).
[CrossRef]

F. E. Hoge, A. Vodacek, R. N. Swift, J. K. Yungel, and 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).
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Deep-Sea Res. I (1)

J. K. B. Bishop, "Transmissometer measurement of POC," Deep-Sea Res. I 46, 353-369 (1999).
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Deep-Sea Res. II (1)

J. K. B. Bishop, S. E. Calvert, and M. Y. S. Moon, "Spatial variability of POC in the northeast Subarctic Pacific," Deep-Sea Res. II 46, 2699-2733 (1999).
[CrossRef]

J. Geophys. Res (1)

A. H. Bernard, W. S. Pegau, and J. R. V. Zaneveld, "Global relationships of the inherent optical properties of the oceans," J. Geophys. Res 103, 24955-24968 (1998).
[CrossRef]

J. Geophys. Res. (3)

F. E. Hoge, M. E. Williams, R. N. Swift, J. K. Yungel, and A. Vodacek, "Satellite retrieval of the absorption coefficient of chromophoric dissolved organic matter in continental margins," J. Geophys. Res. 100, 24847-24854 (1995).
[CrossRef]

F. E. Hoge, R. N. Swift, J. K. Yungel, and A. Vodacek, "Fluorescence of dissolved organic matter: a comparison of North Pacific and North Atlantic Oceans during April 1991," J. Geophys. Res. 98, 22779-22787 (1993).
[CrossRef]

F. E. Hoge, C. W. Wright, P. E. Lyon, R. N. Swift, and J. K. Yungel, "Inherent optical properties imagery of the western North Atlantic Ocean: horizontal spatial variability of the upper mixed layer," J. Geophys. Res. 106, 31129-31140 (2001).
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J. Opt. Soc. Am. A (1)

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F. E. Hoge, A. Vodacek, and 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).
[CrossRef]

Mar. Chem. (1)

C. D. Clark, J. Jimenez-Morais, G. Jones, E. Zanardi-Lamardo, C. A. Moore, and R. G. Zika, "A time-resolved fluorescence study of dissolved organic matter in a riverine to marine transition zone," Mar. Chem. 78, 121-135 (2002).
[CrossRef]

Other (3)

C. D. Mobley, Light and Water, Radiative Transfer in Natural Waters (Academic, 1994), Chap. 5. The errata can be found at ftp.sequoiasci.com within the file /pub/outgoing/LightandWaterErrata.pdf. Note: at the time of publication, Mobley's Light and Water is now available on CD, with the errors corrected. The CD is available from Mobley, or the contents of the CD can be downloaded from http://www.curtismobley.com/curts_work.htm or from http://www.curtismobley.com/LightandWater.zip.

F. E. Hoge is preparing a manuscript with the title "Oceanic beam attenuation coefficient retrieval by radiative transfer equation inversion of airborne water Raman backscattering. 1: Theory."

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipies in Fortran, 2nd ed. (Cambridge U. Press, 1992).

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Equations (23)

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d L ( t = 2 z m / ν ; θ , ϕ ; λ F ) d z = P S W F d L ( z ; θ , ϕ ; λ F ) d z ,
F = F 0 exp ( 1 τ ) ,
d L ( z ; θ , ϕ ; λ F ) d z c ( z ; λ F ) L ( z ; θ , ϕ ; λ F ) + a F ( z , λ L ) f F ( λ L λ F ) β ˜ F ( ψ ) 0 2 π 0 π L ( z ; θ , ϕ ; λ L )     sin θ d θ d ϕ .
d L ( z ; θ , ϕ ; λ Y 1 ) d z c ( z ; λ Y 1 ) L ( z ; θ , ϕ ; λ Y 1 ) + a Y ( z , λ L ) f Y ( λ L λ Y 1 ) β ˜ Y ( ψ ) 0 2 π 0 π L ( z ; θ , ϕ ; λ L )     sin θ d θ d ϕ ,
d L ( z ; θ , ϕ ; λ Y 2 ) d z c ( z ; λ Y 2 ) L ( z ; θ , ϕ ; λ Y 2 ) + a Y ( z , λ L ) f Y ( λ L λ Y 2 ) β ˜ Y ( ψ ) 0 2 π 0 π L ( z ; θ , ϕ ; λ L )     sin θ d θ d ϕ ,
c ( λ , z ) c w ( λ , z ) = [ c ( λ r e f , z ) c w ( λ r e f , z ) ] ( A + B λ ) ,
c ( λ ref , z ) c w ( λ ref , z ) = f 1 ( c w 2 L 2 D 2 ) f 2 ( c w 1 L 1 D 1 ) l 1 L 1 f 2 l 2 L 2 f 1 ,
c ( λ ref , z ) c w ( λ ref , z ) = p ( c w 2 L 2 D 2 ) ( c w 1 L 1 D 1 ) l 1 L 1 p l 2 L 2 .
cos θ d L ( z ; θ , ϕ ; λ ) d z = c ( z ; λ ) L ( z ; θ , ϕ ; λ )
+ 0 2 π 0 π β ( z ; θ , ϕ θ , ϕ ; λ ) L ( z ; θ , ϕ ; λ ) sin θ d θ d ϕ + λ 0 2 π 0 π β F ( z ; θ , ϕ θ , ϕ ; λ λ ) L ( z ; θ , ϕ ; λ ) sin θ d θ d ϕ d λ ,
L * F ( z ; θ , ϕ ; λ ) = 0 2 π 0 π β F ( z ; θ , ϕ θ , ϕ ; λ λ ) L ( z ; θ , ϕ ; λ ) sin θ d θ d ϕ .
+ L * F ( z ; θ , ϕ ; λ ) δ ( λ λ L ) d λ = L * F ( z ; θ , ϕ ; λ L ) .
cos θ d L ( z ; θ , ϕ ; λ ) d z = c ( z ; λ ) L ( z ; θ , ϕ ; λ )
+ 0 2 π 0 π β ( z ; θ , ϕ θ , ϕ ; λ ) L ( z ; θ , ϕ ; λ ) sin θ d θ d ϕ + 0 2 π 0 π β F ( z ; θ , ϕ θ , ϕ ; λ L λ ) L ( z ; θ , ϕ ; λ L ) sin θ d θ d ϕ .
cos θ d L ( z ; θ , ϕ ; λ F ) d z = c ( z ; λ F ) L ( z ; θ , ϕ ; λ F )
+ 0 2 π 0 π β ( z ; θ , ϕ θ , ϕ ; λ F ) L ( z ; θ , ϕ ; λ F ) sin θ d θ d ϕ + 0 2 π 0 π β F ( z ; θ , ϕ θ , ϕ ; λ L λ F ) L ( z ; θ , ϕ ; λ L ) sin θ d θ d ϕ .
L ( z ; θ , ϕ ; λ F ) = L solar ( z ; θ , ϕ ; λ F ) + L sky ( z ; θ , ϕ ; λ F ) + L fluorescence ( z ; θ , ϕ ; λ F ) .
cos θ d L ( z ; θ , ϕ ; λ F ) d z = c ( z ; λ F ) L ( z ; θ , ϕ ; λ F )
+ 0 2 π 0 π β ( z ; θ , ϕ θ , ϕ ; λ F ) L fluorescence ( z ; θ , ϕ ; λ F ) sin θ d θ d ϕ + 0 2 π 0 π β F ( z ; θ , ϕ θ , ϕ ; λ L λ F ) L ( z ; θ , ϕ ; λ L ) sin θ d θ d ϕ ,
cos θ d L ( z ; θ , ϕ ; λ F ) d z = c ( z ; λ F ) L ( z ; θ , ϕ ; λ F ) + 0 2 π 0 π β R ( θ , ϕ θ , ϕ ; λ L λ F ) L ( z ; θ , ϕ ; λ L ) sin θ d θ d ϕ .
β F ( z ; θ , ϕ θ , ϕ ; λ L λ F ) = a F ( z , λ L ) f F ( λ L λ F ) β ˜ F ( θ , ϕ θ , ϕ ) ,
L * F ( z ; θ , ϕ ; λ L ) = a F ( z , λ L ) f F ( λ L λ F ) 0 2 π 0 π β ˜ F ( θ , ϕ θ , ϕ ) L ( z ; θ , ϕ ; λ L ) sin θ d θ d ϕ .
d L ( z ; θ , ϕ ; λ F ) d z = c ( z ; λ F ) L ( z ; θ , ϕ ; λ F ) + a F ( z , λ L ) f F ( λ L λ F ) β ˜ F ( ψ ) 0 2 π 0 π L ( z ; θ , ϕ ; λ L ) sin θ d θ d ϕ .

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