Abstract

Multiangle, multispectral photopolarimetry of atmosphere–ocean systems provides the fullest set of remote sensing information possible on the scattering properties of aerosols and on the color of the ocean. Recent studies have shown that inverting such data allows for the potential of separating the retrieval of aerosol properties from ocean color monitoring in the visible part of the spectrum. However, the data in these studies were limited to those principal plane observations where the polarization of water-leaving radiances could be ignored. Examining similar potentials for off-principal plane observations requires the ability to assess realistic variations in both the reflectance for and bidirectionality of polarized water-leaving radiances for such viewing geometries. We provide hydrosol models for use in underwater light scattering computations to study such variations. The model consists of two components whose refractive indices resemble those of detritus–minerallike and planktonlike particles, whose size distributions are constrained by underwater light linear polarization signatures, and whose mixing ratios change as a function of particulate backscattering efficiency. Multiple scattering computations show that these models are capable of reproducing realistic underwater light albedos for wavelengths ranging from 400 to 600  nm, and for chlorophyll a concentrations ranging from 0.03 to 3 .0  mg/m 3. Numerical results for spaceborne observations of the reflectance for total and polarized water-leaving radiances are provided as a function of polar angles, and the change in these reflectances with wavelength, chlorophyll a concentration, and hydrosol model are discussed in detail for case 1 (open ocean) waters.

© 2006 Optical Society of America

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2005 (6)

O. P. Hasekamp and J. Landgraf, "Retrieval of aerosol properties over the ocean from multispectral single-viewing-angle measurements of intensity and polarization: Retrieval approach, information content, and sensitivity study," J. Geophys. Res. 110, D20207, doi: (2005).
[CrossRef]

B. Gérard, J.-L. Deuzé, M. Herman, Y. J. Kaufman, P. Lallart, C. Oudard, L. A. Remer, B. Roger, B. Six, and D. Tanré, "Comparisons between POLDER 2 and MODIS/Terra aerosol retrievals over ocean," J. Geophys. Res. 110, D24211, doi: (2005).
[CrossRef]

J. Chowdhary, B. Cairns, M. I. Mishchenko, P. V. Hobbs, G. F. Cota, J. Redemann, K. Rutledge, B. N. Holben, and E. Russel, "Retrievals of aerosol scattering and absorption properties from photo-polarimetric observations over the ocean during the CLAMS experiment," J. Atmos. Sci. 62, 1093-1117 (2005).
[CrossRef]

D. Stramski and S. B. Wozniak, "On the role of colloidal particles in light scattering in the ocean," Limnol. Oceanogr. 50, 1581-1591 (2005).
[CrossRef]

H. R. Gordon, "Normalized water-leaving radiance: revisiting the influence of surface roughness," Appl. Opt. 44, 241-248 (2005).
[CrossRef] [PubMed]

M. Stramska and D. Stramski, "Effects of a nonuniform profile of chlorophyll concentration on remote-sensing reflectance of the ocean," Appl. Opt. 44, 1735-1747 (2005).
[CrossRef] [PubMed]

2004 (4)

S. Wozniak and D. Stramski, "Modeling the optical properties of mineral particles suspended in seawater and their influence on ocean reflectance and chlorophyll estimation from remote sensing algorithms," Appl. Opt. 43, 3489-3503 (2004).
[CrossRef] [PubMed]

M. I. Mishchenko, B. Cairns, J. E. Hansen, L. D. Travis, R. Burg, Y. J. Kaufman, J. V. Martins, and E. P. Shettle, "Monitoring of aerosol forcing of climate from space: analysis of measurement requirements," J. Quant. Spectrosc. Radiat. Transfer 88, 149-161 (2004).
[CrossRef]

D. Stramski, E. Boss, D. Bogucki, and K. J. Voss, "The role of seawater constituents in light backscattering in the ocean," Prog. Oceanog. 61, 27-56 (2004).
[CrossRef]

A. Quirantes and S. Benard, "Light scattering by marine algae: two-layer spherical and nonspherical models," J. Quant. Spectrosc. Radiat. Transfer 89, 311-321 (2004).
[CrossRef]

2003 (1)

M. E. Lee and M. R. Lewis, "A new method for the measurement of the optical volume scattering function in the upper ocean," J. Atmos. Ocean. Technol. 20, 563-571 (2003).
[CrossRef]

2002 (9)

Z. Jin, T. P. Charlock, and K. Rutledge, "Analysis of broadband solar radiation and albedo over the ocean surface at COVE," J. Atmos. Ocean. Technol. 19, 1585-1601 (2002).
[CrossRef]

J. Chowdhary, B. Cairns, and L. D. Travis, "Case studies of aerosol retrievals over the ocean from multiangle, multispectral photopolarimetric remote sensing data," J. Atmos. Sci. 59, 383-397 (2002).
[CrossRef]

V. I. Haltrin, "One-parameter two-term Henyey-Greenstein phase function for light scattering in seawater," Appl. Opt. 41, 1022-1028 (2002).
[CrossRef] [PubMed]

C. D. Mobley, L. K. Sundman, and E. Boss, "Phase function effects on oceanic light fields," Appl. Opt. 41, 1035-1050 (2002).
[CrossRef] [PubMed]

J. T. Adams, E. Aas, N. K. Højerslev, and B. Lundgren, "Comparison of radiance and polarization values observed in the Mediterranean Sea and simulated in a Monte Carlo model," Appl. Opt. 41, 2724-2733 (2002).
[CrossRef] [PubMed]

A. Morel, D. Antoine, and B. Gentili, "Bidirectional reflectance of oceanic waters: Accounting for Raman emission and varying particle scattering phase function," Appl. Opt. 41, 6289-6306 (2002).
[CrossRef] [PubMed]

H. Mehrtens and T. Martin, "Remote sensing of oligotrophic waters: model divergence at low chlorophyll concentrations," Appl. Opt. 41, 7058-7067 (2002).
[CrossRef] [PubMed]

D. Risovic, "Effect of suspended particulate-size distribution on the backscattering ratio in the remote sensing of seawater," Appl. Opt. 41, 7092-7100 (2002).
[CrossRef] [PubMed]

M. I. Mishchenko, "Vector radiative transfer equation for arbitrary shaped and arbitrary oriented particles: a microphysical derivation from statistical electromagnetics," Appl. Opt. 41, 7114-7134 (2002).
[CrossRef] [PubMed]

2001 (6)

H. Loisel, D. Stramski, B. G. Mitchel, F. Fell, V. Fournier-Sicre, B. Lemasle, and M. Babin, "Comparison of the ocean inherent properties obtained from measurements and inverse modeling," Appl. Opt. 40, 2384-2397 (2001).
[CrossRef]

M. Chami, R. Santer, and E. Dillegeard, "Radiative transfer model for the computation of radiance and polarization in an atmosphere-ocean system: polarization properties of suspended matter for remote sensing," Appl. Opt. 40, 2398-2416 (2001).
[CrossRef]

D. Stramski, A. Bricaud, and A. Morel, "Modeling the inherent optical properties of the ocean based on the detailed composition of the planktonic community," Appl. Opt. 40, 2929-2945 (2001).
[CrossRef]

J. Chowdhary, B. Cairns, M. I. Mishchenko, and L. D. Travis, "Retrieval of aerosol properties over the ocean using multispectral and multiangle photopolarimetric measurements from the Research Scanning Polarimeter," Geophys. Res. Lett. 28, 243-246 (2001).
[CrossRef]

M. S. Twardowski, E. Boss, J. B. Macdonald, W. S. Pegau, A. H. Bernard, and J. R. V. Zaneveld, "A model for estimating bulk refractive index from the optical backscattering efficiency ratio and the implications for understanding particle composition in case I and II waters," J. Geophys. Res. 106, 14129-14142 (2001).
[CrossRef]

A. Morel and S. Maritorena, "Bio-optical properties of oceanic waters: a reappraisal," J. Geophys. Res. 106, 7163-7180 (2001).
[CrossRef]

1999 (4)

A. Bricaud, A. Morel, M. Babin, K. Allali, H. Claustre, Erratum: "Variations of light absorption by suspended particles with chlorophyll a concentration in oceanic (case 1) waters: analysis and implications for bio-optical models," J. Geophys. Res. 104, 8025 (1999).
[CrossRef]

B. Cairns, L. D. Travis, and E. E. Russel, "The Research Scanning Polarimeter: calibration and ground-based measurements," in Polarization: Measurements, Analysis, and Remote Sensing II, D. H. Goldstein and D. H. Chenault, eds., Proc. SPIE 3754, 186-196 (1999).
[CrossRef]

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

V. I. Haltrin, "Chlorophyll-based model of seawater optical properties," Appl. Opt. 38, 6826-6832 (1999).
[CrossRef]

1998 (5)

A. Kouzoubov, M. J. Brennan, and J. C. Thomas, "Treatment of polarization in laser remote sensing," Appl. Opt. 37, 3873-3885 (1998).
[CrossRef]

H. Volten, J. F. de Haan, J. W. Hovenier, R. Schreurs, W. Vassen, A. G. Dekker, H. J. Hoogenboom, and F. Charlton, "Laboratory measurements of angular distributions of light scattering by phytoplankton and silt," Limnol. Oceanogr. 43, 1180-1197 (1998).
[CrossRef]

A. Bricaud, A. Morel, M. Babin, K. Allali, and H. Claustre, "Variations of light absorption by suspended particles with chlorophyll a concentration in oceanic (case 1) waters: analysis and implications for bio-optical models," J. Geophys. Res. 103, 31033-31044 (1998).
[CrossRef]

H. Loisel and A. Morel, "Light scattering and chlorophyll concentration in case 1 waters: a reexamination," Limnol. Oceanogr. 43, 847-858 (1998).
[CrossRef]

A. Morel and H. Loisel, "Apparent optical properties of oceanic water: dependence on the molecular scattering contribution," Appl. Opt. 21, 4765-4776 (1998).
[CrossRef]

1997 (5)

D. Stramski and C. D. Mobley, "Effects of microbial particles on ocean optics: a database of single-particle optical properties," Limnol. Oceanogr. 42, 538-549 (1997).
[CrossRef]

M. I. Mishchenko and L. D. Travis, "Satellite retrieval of aerosol properties over the ocean using polarization as well as intensity of reflected sunlight," J. Geophys. Res. 102, 16989-17013 (1997).
[CrossRef]

H. R. Gordon, "Atmospheric correction of ocean color imagery in the Earth Observing System era," J. Geophys. Res. 102, 17081-17106 (1997).
[CrossRef]

H. R. Gordon and G. C. Boynton, "Radiance-irradiance inversion algorithm for estimating the absorption and backscattering coefficients of natural waters: homogeneous water," Appl. Opt. 36, 2636-2641 (1997).
[CrossRef] [PubMed]

R. M. Pope and E. S. Fry, "Absorption spectrum (380-700 nm) of pure water. II. Integration cavity measurements," Appl. Opt. 36, 8710-8723 (1997).
[CrossRef]

1996 (3)

A. Morel and B. Gentilli, "Diffuse reflectance of oceanic waters. III. Implication of bidirectionality for the remote-sensing problem," Appl. Opt. 35, 4850-4862 (1996).
[CrossRef] [PubMed]

E. Aas, "Refractive index of phytoplankton derived from its metabolite composition," J. Plankton. Res. 18, 2223-2249 (1996).
[CrossRef]

R. Frouin, M. Schindling, and P.-Y. Deschamps, "Spectral reflectance of sea-foam in the visible and near-infrared: In-situ measurements and remote sensing applications," J. Geophys. Res. 101, 14361-14371 (1996).
[CrossRef]

1995 (1)

1994 (1)

1993 (2)

D. Risovic, "Two-component model of sea particle size distribution," Deep-Sea Res. I 40, 1459-1473 (1993).
[CrossRef]

A. Morel and B. Gentilli, "Diffuse reflectance of oceanic waters. II. Bidirectional aspects," Appl. Opt. 32, 6864-6878 (1993).
[CrossRef] [PubMed]

1992 (2)

H. R. Gordon, "Diffuse reflectance of the ocean: influence of nonuniform phytoplankton pigment profile," Appl. Opt. 31, 2116-2129 (1992).
[CrossRef] [PubMed]

J. C. Kitchen and J. R. V. Zaneveld, "A three-layered sphere model of optical properties of phytoplankton," Limnol. Oceanogr. 37, 1680-1690 (1992).
[CrossRef]

1991 (2)

1989 (3)

M. S. Quinby-Hunt, A. J. Hunt, K. Lofftus, and D. Shapiro, "Polarized-light scattering studies of marine Chlorella," Limnol. Oceanogr. 34, 1587-1600 (1989).
[CrossRef]

G. W. Kattawar, and C. N. Adams, "Stokes vector calculations of the submarine light field in an atmosphere-ocean with scattering according to a Rayleigh phase matrix: effect of interface refractive index on radiance and polarization," Limnol. Oceanogr. 34, 1453-1472 (1989).
[CrossRef]

P. Stamnes, J. F. de Haan, and J. W. Hovenier, "The polarized internal radiation field of a planetary atmosphere," Astron. Astrophys. 225, 239-259 (1989).

1988 (4)

K. Masuda and T. Takashima, "Dependence of the radiation just above and below the ocean surface on atmospheric and oceanic parameters," Appl. Opt. 23, 4891-4898 (1988).
[CrossRef]

K. Masuda and T. Takashima, "Sensitivity of radiation absorbed in the ocean to atmospheric and oceanic parameters in the short wavelengths region. Part 1. Cloudless atmosphere," J. Meteorol. Soc. Japan 66, 617-628 (1988).

H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, and D. K. Clark, "A semianalytical radiance model of ocean color," J. Geophys. Res. 93, 10909-10924 (1988).
[CrossRef]

A. Morel, "Optical modeling of the upper ocean in relation to its biogenous matter content (case I waters)," J. Geophys. Res. 93, 10749-10768 (1988).
[CrossRef]

1987 (2)

M. Jonasz, "Nonsphericity of suspended marine particles and its influence on light scattering," Limnol. Oceanogr. 32, 1059-1065 (1987).
[CrossRef]

J. F. de Haan, P. B. Bosma, and J. W. Hovenier, "The adding method for multiple scattering computations of polarized light," Astron. Astrophys. 183, 371-391 (1987).

1986 (3)

M. Jonasz and H. Prandke, "Comparison of measured and computed light scattering in the Baltic," Tellus , Ser. B 38B, 144-157 (1986).
[CrossRef]

R. W. Preisendorfer and C. D. Mobley, "Albedos and glitter patterns of a wind-roughened sea surface," J. Phys. Oceanogr. 16, 1293-1316 (1986).
[CrossRef]

R. W. Spinrad and J. F. Brown, "Relative real refractive index of marine microorganisms: a technique for flow cytometric estimation," Appl. Opt. 25, 1930-1934 (1986).
[CrossRef] [PubMed]

1985 (4)

D. Spitzer and R. W. J. Dirk, "Contamination of the reflectance of natural waters by solar-induced fluorescence of dissolved organic matter," Appl. Opt. 24, 444-445 (1985).
[CrossRef] [PubMed]

J. W. Hovenier and J. F. de Haan, "Polarized light in planetary atmospheres for perpendicular directions," Astron. Astrophys. 146, 185-191 (1985).

T. Takashima, "Polarization effect on radiative transfer in planetary atmospheres with interacting surfaces," Earth , Moon, Planets 33, 59-97 (1985).

E. S. Fry and K. J. Voss, "Measurement of the Mueller matrix for phytoplankton," Limnol. Oceanogr. 30, 1322-1326 (1985).
[CrossRef]

1984 (5)

J. Fischer and H. Grassl, "Radiative transfer in an atmosphere-ocean system: an azimuthal dependent matrix-operator approach," Appl. Opt. 23, 1023-1039 (1984).
[CrossRef]

W. A. de Rooij and C. C. A. H. van der Stap, "Expansion of Mie scattering matrices in generalized spherical functions," Astron. Astrophys. 131, 237-248 (1984).

P. Koepke, "Effective reflectance of oceanic whitecaps," Appl. Opt. 23, 1816-1842 (1984).
[CrossRef] [PubMed]

K. J. Voss and E. S. Fry, "Measurement of the Mueller matrix for ocean water," Appl. Opt. 23, 4427-4439 (1984).
[CrossRef] [PubMed]

G. Kullenberg, "Observations of light scattering in two oceanic areas," Deep-Sea Res. 31, 295-316 (1984).
[CrossRef]

1983 (2)

M. Jonasz, "Particle-size distributions in the Baltic," Tellus , Ser. B 35, 346-35 (1983).

J. W. Hovenier and C. V. M. van der Mee, "Fundamental relationships relevant to the transfer of polarized light in a scattering atmosphere," Astron. Astrophys. 128, 1-16 (1983).

1981 (2)

L. Prieur and 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 matter," Limnol. Oceanogr. 26, 671-689 (1981).
[CrossRef]

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

1979 (1)

1977 (2)

A. Morel and I. Prieur, "Analysis of variations in ocean color," Limnol. Oceanogr. 22, 709-722 (1977).
[CrossRef]

M. Tanaka and T. Nakajima, "Effects of oceanic turbidity and index of refraction of hydrosols on the flux of solar radiation in the atmosphere-ocean system," J. Quant. Spectrosc. Radiat. Transfer 18, 93-111 (1977).
[CrossRef]

1975 (2)

H. R. Gordon and W. R. McCluney, "Estimation of the depth of sunlight penetration in the sea for remote sensing," Appl. Opt. 14, 413-416 (1975).
[CrossRef] [PubMed]

G. W. Kattawar, "A three-parameter analytical phase function for multiple scattering calculations," J. Quant. Spectros. Radiat. Transfer 15, 839-849 (1975).
[CrossRef]

1974 (2)

J. E. Hansen and L. D. Travis, "Light scattering in planetary atmospheres," Space Sci. Rev. 16, 527-610 (1974).
[CrossRef]

J. R. Zaneveld, D. M. Roach, and H. Pak, "The determination of the index of refraction distribution of oceanic particles," J. Geophys. Res. 79, 4091-4095 (1974).
[CrossRef]

1973 (3)

G. W. Kattawar, G. N. Plass, and J. A. Guinn, Jr., "Monte Carlo calculations of the polarization of radiation in the Earth's atmosphere-ocean system," J. Phys. Oceanogr. 3, 353-372 (1973).
[CrossRef]

Y. A. Kad'shevich and Y. S. Lyubovtseva, "Certain characteristics of ocean hydrosols from scattering matrices," Izv. , Acad. Sci., USSR, Atmos. Oceanic. Phys. 9, 659-663 (1973).

O. B. Brown and H. R. Gordon, "Two component Mie scattering models of Sargasso Sea particles," Appl. Opt. 12, 2461-2465 (1973).
[CrossRef] [PubMed]

1972 (2)

G. W. Kattawar and G. N. Plass, "Radiative transfer in the Earth's atmosphere-ocean system: II. Radiance in the atmosphere and ocean," J. Phys. Oceanogr. 2, 146-156 (1972).
[CrossRef]

G. N. Plass and G. W. Kattawar, "Monte Carlo calculations of radiative transfer in the Earth's atmosphere-ocean system: I. Flux in the atmosphere and ocean," J. Phys. Oceanogr. 2, 139-145 (1972).
[CrossRef]

1971 (1)

J. E. Hansen, "Multiple scattering of polarized light in planetary atmospheres. Part II. Sunlight reflected by terrestrial clouds," J. Atmos. Sci. 28, 1400-1426 (1971).
[CrossRef]

1969 (2)

J. W. Hovenier, "Symmetry relationships for scattering of polarized light in a slab of randomly oriented particles," J. Atmos. Sci. 26, 488-499 (1969).
[CrossRef]

M. I. Sancer, "Shadow-corrected electromagnetic scattering from a randomly-rough ocean surface," IEEE Trans. Antennas Propag. 17, 557-585 (1969).
[CrossRef]

1954 (1)

C. Cox and W. Munk, "Statistics of the sea-surface derived from sun-glitter," J. Mar. Res. 13, 198-227 (1954).

Aas, E.

Adams, C. N.

G. W. Kattawar, and C. N. Adams, "Stokes vector calculations of the submarine light field in an atmosphere-ocean with scattering according to a Rayleigh phase matrix: effect of interface refractive index on radiance and polarization," Limnol. Oceanogr. 34, 1453-1472 (1989).
[CrossRef]

Adams, J. T.

Allali, K.

A. Bricaud, A. Morel, M. Babin, K. Allali, H. Claustre, Erratum: "Variations of light absorption by suspended particles with chlorophyll a concentration in oceanic (case 1) waters: analysis and implications for bio-optical models," J. Geophys. Res. 104, 8025 (1999).
[CrossRef]

A. Bricaud, A. Morel, M. Babin, K. Allali, and H. Claustre, "Variations of light absorption by suspended particles with chlorophyll a concentration in oceanic (case 1) waters: analysis and implications for bio-optical models," J. Geophys. Res. 103, 31033-31044 (1998).
[CrossRef]

Antoine, D.

Babin, M.

H. Loisel, D. Stramski, B. G. Mitchel, F. Fell, V. Fournier-Sicre, B. Lemasle, and M. Babin, "Comparison of the ocean inherent properties obtained from measurements and inverse modeling," Appl. Opt. 40, 2384-2397 (2001).
[CrossRef]

A. Bricaud, A. Morel, M. Babin, K. Allali, H. Claustre, Erratum: "Variations of light absorption by suspended particles with chlorophyll a concentration in oceanic (case 1) waters: analysis and implications for bio-optical models," J. Geophys. Res. 104, 8025 (1999).
[CrossRef]

A. Bricaud, A. Morel, M. Babin, K. Allali, and H. Claustre, "Variations of light absorption by suspended particles with chlorophyll a concentration in oceanic (case 1) waters: analysis and implications for bio-optical models," J. Geophys. Res. 103, 31033-31044 (1998).
[CrossRef]

Baker, K. S.

H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, and D. K. Clark, "A semianalytical radiance model of ocean color," J. Geophys. Res. 93, 10909-10924 (1988).
[CrossRef]

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

Benard, S.

A. Quirantes and S. Benard, "Light scattering by marine algae: two-layer spherical and nonspherical models," J. Quant. Spectrosc. Radiat. Transfer 89, 311-321 (2004).
[CrossRef]

Bernard, A. H.

M. S. Twardowski, E. Boss, J. B. Macdonald, W. S. Pegau, A. H. Bernard, and J. R. V. Zaneveld, "A model for estimating bulk refractive index from the optical backscattering efficiency ratio and the implications for understanding particle composition in case I and II waters," J. Geophys. Res. 106, 14129-14142 (2001).
[CrossRef]

Bogucki, D.

D. Stramski, E. Boss, D. Bogucki, and K. J. Voss, "The role of seawater constituents in light backscattering in the ocean," Prog. Oceanog. 61, 27-56 (2004).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1980).

Bosma, P. B.

J. F. de Haan, P. B. Bosma, and J. W. Hovenier, "The adding method for multiple scattering computations of polarized light," Astron. Astrophys. 183, 371-391 (1987).

Boss, E.

D. Stramski, E. Boss, D. Bogucki, and K. J. Voss, "The role of seawater constituents in light backscattering in the ocean," Prog. Oceanog. 61, 27-56 (2004).
[CrossRef]

C. D. Mobley, L. K. Sundman, and E. Boss, "Phase function effects on oceanic light fields," Appl. Opt. 41, 1035-1050 (2002).
[CrossRef] [PubMed]

M. S. Twardowski, E. Boss, J. B. Macdonald, W. S. Pegau, A. H. Bernard, and J. R. V. Zaneveld, "A model for estimating bulk refractive index from the optical backscattering efficiency ratio and the implications for understanding particle composition in case I and II waters," J. Geophys. Res. 106, 14129-14142 (2001).
[CrossRef]

Boynton, G. C.

Brennan, M. J.

Bricaud, A.

D. Stramski, A. Bricaud, and A. Morel, "Modeling the inherent optical properties of the ocean based on the detailed composition of the planktonic community," Appl. Opt. 40, 2929-2945 (2001).
[CrossRef]

A. Bricaud, A. Morel, M. Babin, K. Allali, H. Claustre, Erratum: "Variations of light absorption by suspended particles with chlorophyll a concentration in oceanic (case 1) waters: analysis and implications for bio-optical models," J. Geophys. Res. 104, 8025 (1999).
[CrossRef]

A. Bricaud, A. Morel, M. Babin, K. Allali, and H. Claustre, "Variations of light absorption by suspended particles with chlorophyll a concentration in oceanic (case 1) waters: analysis and implications for bio-optical models," J. Geophys. Res. 103, 31033-31044 (1998).
[CrossRef]

Brown, J. F.

Brown, J. W.

H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, and D. K. Clark, "A semianalytical radiance model of ocean color," J. Geophys. Res. 93, 10909-10924 (1988).
[CrossRef]

Brown, O. B.

H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, and D. K. Clark, "A semianalytical radiance model of ocean color," J. Geophys. Res. 93, 10909-10924 (1988).
[CrossRef]

O. B. Brown and H. R. Gordon, "Two component Mie scattering models of Sargasso Sea particles," Appl. Opt. 12, 2461-2465 (1973).
[CrossRef] [PubMed]

Burg, R.

M. I. Mishchenko, B. Cairns, J. E. Hansen, L. D. Travis, R. Burg, Y. J. Kaufman, J. V. Martins, and E. P. Shettle, "Monitoring of aerosol forcing of climate from space: analysis of measurement requirements," J. Quant. Spectrosc. Radiat. Transfer 88, 149-161 (2004).
[CrossRef]

Cairns, B.

J. Chowdhary, B. Cairns, M. I. Mishchenko, P. V. Hobbs, G. F. Cota, J. Redemann, K. Rutledge, B. N. Holben, and E. Russel, "Retrievals of aerosol scattering and absorption properties from photo-polarimetric observations over the ocean during the CLAMS experiment," J. Atmos. Sci. 62, 1093-1117 (2005).
[CrossRef]

M. I. Mishchenko, B. Cairns, J. E. Hansen, L. D. Travis, R. Burg, Y. J. Kaufman, J. V. Martins, and E. P. Shettle, "Monitoring of aerosol forcing of climate from space: analysis of measurement requirements," J. Quant. Spectrosc. Radiat. Transfer 88, 149-161 (2004).
[CrossRef]

J. Chowdhary, B. Cairns, and L. D. Travis, "Case studies of aerosol retrievals over the ocean from multiangle, multispectral photopolarimetric remote sensing data," J. Atmos. Sci. 59, 383-397 (2002).
[CrossRef]

J. Chowdhary, B. Cairns, M. I. Mishchenko, and L. D. Travis, "Retrieval of aerosol properties over the ocean using multispectral and multiangle photopolarimetric measurements from the Research Scanning Polarimeter," Geophys. Res. Lett. 28, 243-246 (2001).
[CrossRef]

B. Cairns, L. D. Travis, and E. E. Russel, "The Research Scanning Polarimeter: calibration and ground-based measurements," in Polarization: Measurements, Analysis, and Remote Sensing II, D. H. Goldstein and D. H. Chenault, eds., Proc. SPIE 3754, 186-196 (1999).
[CrossRef]

Chami, M.

Charlock, T. P.

Z. Jin, T. P. Charlock, and K. Rutledge, "Analysis of broadband solar radiation and albedo over the ocean surface at COVE," J. Atmos. Ocean. Technol. 19, 1585-1601 (2002).
[CrossRef]

Charlton, F.

H. Volten, J. F. de Haan, J. W. Hovenier, R. Schreurs, W. Vassen, A. G. Dekker, H. J. Hoogenboom, and F. Charlton, "Laboratory measurements of angular distributions of light scattering by phytoplankton and silt," Limnol. Oceanogr. 43, 1180-1197 (1998).
[CrossRef]

Chowdhary, J.

J. Chowdhary, B. Cairns, M. I. Mishchenko, P. V. Hobbs, G. F. Cota, J. Redemann, K. Rutledge, B. N. Holben, and E. Russel, "Retrievals of aerosol scattering and absorption properties from photo-polarimetric observations over the ocean during the CLAMS experiment," J. Atmos. Sci. 62, 1093-1117 (2005).
[CrossRef]

J. Chowdhary, B. Cairns, and L. D. Travis, "Case studies of aerosol retrievals over the ocean from multiangle, multispectral photopolarimetric remote sensing data," J. Atmos. Sci. 59, 383-397 (2002).
[CrossRef]

J. Chowdhary, B. Cairns, M. I. Mishchenko, and L. D. Travis, "Retrieval of aerosol properties over the ocean using multispectral and multiangle photopolarimetric measurements from the Research Scanning Polarimeter," Geophys. Res. Lett. 28, 243-246 (2001).
[CrossRef]

J. Chowdhary, "Multiple scattering of polarized light in atmosphere-ocean systems", Ph.D. thesis (Columbia University, New York, 1999).

Clark, D. K.

H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, and D. K. Clark, "A semianalytical radiance model of ocean color," J. Geophys. Res. 93, 10909-10924 (1988).
[CrossRef]

Claustre, H.

A. Bricaud, A. Morel, M. Babin, K. Allali, H. Claustre, Erratum: "Variations of light absorption by suspended particles with chlorophyll a concentration in oceanic (case 1) waters: analysis and implications for bio-optical models," J. Geophys. Res. 104, 8025 (1999).
[CrossRef]

A. Bricaud, A. Morel, M. Babin, K. Allali, and H. Claustre, "Variations of light absorption by suspended particles with chlorophyll a concentration in oceanic (case 1) waters: analysis and implications for bio-optical models," J. Geophys. Res. 103, 31033-31044 (1998).
[CrossRef]

Cota, G. F.

J. Chowdhary, B. Cairns, M. I. Mishchenko, P. V. Hobbs, G. F. Cota, J. Redemann, K. Rutledge, B. N. Holben, and E. Russel, "Retrievals of aerosol scattering and absorption properties from photo-polarimetric observations over the ocean during the CLAMS experiment," J. Atmos. Sci. 62, 1093-1117 (2005).
[CrossRef]

Cox, C.

C. Cox and W. Munk, "Statistics of the sea-surface derived from sun-glitter," J. Mar. Res. 13, 198-227 (1954).

de Haan, J. F.

H. Volten, J. F. de Haan, J. W. Hovenier, R. Schreurs, W. Vassen, A. G. Dekker, H. J. Hoogenboom, and F. Charlton, "Laboratory measurements of angular distributions of light scattering by phytoplankton and silt," Limnol. Oceanogr. 43, 1180-1197 (1998).
[CrossRef]

P. Stamnes, J. F. de Haan, and J. W. Hovenier, "The polarized internal radiation field of a planetary atmosphere," Astron. Astrophys. 225, 239-259 (1989).

J. F. de Haan, P. B. Bosma, and J. W. Hovenier, "The adding method for multiple scattering computations of polarized light," Astron. Astrophys. 183, 371-391 (1987).

J. W. Hovenier and J. F. de Haan, "Polarized light in planetary atmospheres for perpendicular directions," Astron. Astrophys. 146, 185-191 (1985).

de Rooij, W. A.

W. A. de Rooij and C. C. A. H. van der Stap, "Expansion of Mie scattering matrices in generalized spherical functions," Astron. Astrophys. 131, 237-248 (1984).

Dekker, A. G.

H. Volten, J. F. de Haan, J. W. Hovenier, R. Schreurs, W. Vassen, A. G. Dekker, H. J. Hoogenboom, and F. Charlton, "Laboratory measurements of angular distributions of light scattering by phytoplankton and silt," Limnol. Oceanogr. 43, 1180-1197 (1998).
[CrossRef]

Deschamps, P.-Y.

R. Frouin, M. Schindling, and P.-Y. Deschamps, "Spectral reflectance of sea-foam in the visible and near-infrared: In-situ measurements and remote sensing applications," J. Geophys. Res. 101, 14361-14371 (1996).
[CrossRef]

Deuzé, J.-L.

B. Gérard, J.-L. Deuzé, M. Herman, Y. J. Kaufman, P. Lallart, C. Oudard, L. A. Remer, B. Roger, B. Six, and D. Tanré, "Comparisons between POLDER 2 and MODIS/Terra aerosol retrievals over ocean," J. Geophys. Res. 110, D24211, doi: (2005).
[CrossRef]

Dillegeard, E.

Dirk, R. W. J.

Evans, R. H.

H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, and D. K. Clark, "A semianalytical radiance model of ocean color," J. Geophys. Res. 93, 10909-10924 (1988).
[CrossRef]

Fell, F.

Fischer, J.

J. Fischer and H. Grassl, "Radiative transfer in an atmosphere-ocean system: an azimuthal dependent matrix-operator approach," Appl. Opt. 23, 1023-1039 (1984).
[CrossRef]

Fournier-Sicre, V.

Frouin, R.

R. Frouin, M. Schindling, and P.-Y. Deschamps, "Spectral reflectance of sea-foam in the visible and near-infrared: In-situ measurements and remote sensing applications," J. Geophys. Res. 101, 14361-14371 (1996).
[CrossRef]

Fry, E. S.

Gentili, B.

Gentilli, B.

Gérard, B.

B. Gérard, J.-L. Deuzé, M. Herman, Y. J. Kaufman, P. Lallart, C. Oudard, L. A. Remer, B. Roger, B. Six, and D. Tanré, "Comparisons between POLDER 2 and MODIS/Terra aerosol retrievals over ocean," J. Geophys. Res. 110, D24211, doi: (2005).
[CrossRef]

Gordon, H. R.

H. R. Gordon, "Normalized water-leaving radiance: revisiting the influence of surface roughness," Appl. Opt. 44, 241-248 (2005).
[CrossRef] [PubMed]

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B. Cairns, L. D. Travis, and E. E. Russel, "The Research Scanning Polarimeter: calibration and ground-based measurements," in Polarization: Measurements, Analysis, and Remote Sensing II, D. H. Goldstein and D. H. Chenault, eds., Proc. SPIE 3754, 186-196 (1999).
[CrossRef]

Prog. Oceanog. (2)

D. Stramski and D. A. Kiefer, "Light scattering by microorganisms in the open ocean," Prog. Oceanog. 28, 343-381 (1991).
[CrossRef]

D. Stramski, E. Boss, D. Bogucki, and K. J. Voss, "The role of seawater constituents in light backscattering in the ocean," Prog. Oceanog. 61, 27-56 (2004).
[CrossRef]

Space Sci. Rev. (1)

J. E. Hansen and L. D. Travis, "Light scattering in planetary atmospheres," Space Sci. Rev. 16, 527-610 (1974).
[CrossRef]

Tellus (2)

M. Jonasz and H. Prandke, "Comparison of measured and computed light scattering in the Baltic," Tellus , Ser. B 38B, 144-157 (1986).
[CrossRef]

M. Jonasz, "Particle-size distributions in the Baltic," Tellus , Ser. B 35, 346-35 (1983).

Other (10)

J. Chowdhary, "Multiple scattering of polarized light in atmosphere-ocean systems", Ph.D. thesis (Columbia University, New York, 1999).

M. Born and E. Wolf, Principles of Optics (Pergamon, 1980).

R. E. Walker, Marine Light Field Statistics (Wiley, 1994).

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission by Small Particles (Cambridge U. Press, 2002).

T. J. Petzold, "Volume scattering functions for selected ocean waters," in Light in Sea, J.E.Tyler, ed. (Dowden, Hutchinson, and Ross, 1977), pp. 152-157.

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, 1957).

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

H. R. Gordon and A. Morel, Remote Assessment of Ocean Color for Interpretation of Satellite Visible Imagery: A Review (Springer-Verlag, 1983).

M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, Light Scattering by Non-Spherical Particles (Academic Press, 2000).

A. Morel, "Optical properties of pure water and pure sea water," in Optical Aspects of Oceanography, N.G.Jerlov and E.SteemanNielsen, eds. (Academic Press, 1974), pp. 1-24.

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Figures (11)

Fig. 1
Fig. 1

Local geometry of light traveling through O in the direction of k, where k is a unit vector specified by the polar angles (θ, φ).

Fig. 2
Fig. 2

(Color online) On the relation between the Junge exponent γ hyd and refractive index m hyd of hydrosol particles. Circles, results obtained from minimizing Eq. (25). Error bars, range for which d d min + 1 % in Eq. (25). Solid line, line given by Eq. (26) to fit circles. Hydro I and II, results obtained from other considerations (see text).

Fig. 3
Fig. 3

(a) Degree of linear polarization for single scattering of unpolarized light. The dashed red line corresponds to scattering by pure seawater ( p w ) . The lines for m plk are for scattering by hydrosol particles with m hyd = m plk and γ hyd given by Eq. (26). (b) Same as (a) except for m hyd = m det . Also shown are cases for the hydro I and II particles defined in Fig. 2.

Fig. 4
Fig. 4

(a) Scattering functions (normalized by 4π) for hydrosol particles with m hyd and γ hyd provided by the legend and Eq. (26), respectively. (b) Same as (a) except for the plankton, detritus, and mineral particles specified in Table 1. Also shown are cases for the mixture of detritus and plankton particles (D–P Mix), for the mixture of mineral and detritus particles (M–P Mix), for the TTHG used by Walker (Ref. 89) to fit Petzold's (Ref. 13) measurements, and for scattering by pure seawater. The cases for the D–P mixture correspond to f det = 0.1 , 0.2 , . . . , 0.8 , 0.9 .

Fig. 5
Fig. 5

(Color online) On the relation between the backscattering efficiency q hyd and hydrosol refractive index m hyd . Circles, results obtained from the Mie theory with γ hyd given by Eq. (26). Error bars, range in q hyd corresponding to the range in γ hyd shown in Fig. 2 by the error bars. Minimum q p , smallest backscattering efficiency for [ Chl ] = 3.0 mg / m 3 and 410 λ 600   nm according to Eq. (12). Maximum q p , largest backscattering efficiency for [ Chl ] = 0.03 mg / m 3 and 410 λ 600   nm according to Eq. (12).

Fig. 6
Fig. 6

(a) On the relation between the backscattering efficiency q hyd and the chlorophyll a concentration [Chl]. q p : backscattering efficiency provided by Eq. (12) as a function of λ and [Chl]. Circles, backscattering efficiency for the D–P mixture specified in Table 1 and f det given by Table 2. Pluses, backscattering efficiency for a one-term Henyey–Greenstein function with varying asymmetry parameter g p (see Fig. 9). (b) The change in particle fraction f det with chlorophyll a concentration [Chl]. Circles, f det values given in Table 2. Dotted line, line given by Eq. (28) to fit circles.

Fig. 7
Fig. 7

(Color online) (a) Degree of linear polarization for single scattering of unpolarized light by the plankton, detritus, and mineral particles specified in Table 1. Also shown are cases for the mixture of detritus and plankton particles (D–P Mix), and for the mixture of mineral and detritus particles (M–P Mix). The cases for the D–P mixture correspond to [ Chl ] = 0.3 and 30.0 mg / m 3 , while those for the M–P mixture to [Chl] = 0.03, 0.1, 0.3, 1.0, and 3.0 mg / m 3 . (b) Same as (a) except for including scattering by seawater for the D–P mixture (D–P Bulk) and for the M–P mixture (M–P Bulk). The chlorophyll a concentration [Chl] is 0.3 mg / m 3 for the D–P bulk mixture, and 0.03 and 1.0 mg / m 3 for the M–P bulk mixture.

Fig. 8
Fig. 8

(Color online) (a) The ocean body irradiance ratio A blk just below the ocean surface as a function of λ and [Chl]. Curves, statistical predictions by the bio-optical model discussed in Subsection 2.B. Circles, radiative transfer (RT) results for the TTHG hydrosol scattering function of Fig. 4(b). Pluses, RT results for the mixture of plankton and detritus particles specified in Table 1 with f det fixed at 0.68. Crosses, RT results for the mixture of plankton and detritus particles specified in Table 1 with f det fixed at 0.32. (b) Same as (a) except for the following. Circles, RT results for the mixture of plankton and detritus particles specified in Table 1 with f det varied according to Table 2. Crosses, RT results for the mixture of plankton and mineral particles specified in Table 1 with f mnr varied according to Table 2. Pluses, RT results for a one-term Henyey–Greenstein function with varying asymmetry parameter g p (see Fig. 9).

Fig. 9
Fig. 9

On the relation between the asymmetry parameter of hydrosol particles and chlorophyll a concentration [Chl]. Circles results for the mixture of plankton and detritus particles specified in Table 1 with f det varied according to Table 2. Pluses, values used for the one-term Henyey–Greenstein functions in Figs. 6(a) and 8(b). Crosses, results for the mixture of plankton and mineral particles specified in Table 1 with f mnr varied according to Table 2. Dotted line, line given by Eq. (29) to fit crosses.

Fig. 10
Fig. 10

Polar diagrams of the spaceborne total (first two columns) and polarized (last two columns) reflectance for water-leaving radiances normalized by I max and P max , respectively. Results are for an atmosphere–ocean system consisting of a molecular atmosphere that is bounded from below by an ocean system with W = 7 m / s and [ Chl ] = 0.1 mg / m 3 . The solar zenith angle corresponds to μ 0 = 0.9 (first row), 0.7 (second row), and 0.5 (third row), and is depicted by a yellow star in the antisolar point. The left- and right-hand-side hemispheres are for the D–P and M–P mixture, respectively, defined by Tables 1 and 2. The wavelength λ is 410   nm for diagrams (a)–(c) and (g)–(i), and 550   nm for diagrams (d)–(f) and (j)–(l).

Fig. 11
Fig. 11

Same as Fig. 10 except for [ Chl ] = 1.0 mg / m 3 .

Tables (2)

Tables Icon

Table 1 Reference D–P and M–P Mixtures

Tables Icon

Table 2 Mixing Ratios of the D–P and M–P Mixtures Referenced in Table 1

Equations (34)

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I = [ I Q U V ] ,
P = Q 2 + U 2 .
u d I ˜ ( τ , u , φ ) = I ˜ ( τ , u , φ ) d τ + ω 4 π 1 1 u d u × 0 2 π d φ Z ( u , φ ; u , φ ) × I ˜ ( τ , u , φ ) d τ ,
Z ( u , φ ; u , φ ) = L ( π i 2 ) F ( Θ ) L ( i 1 ) .
F ( Θ ) = [ a 1 ( Θ ) b 1 ( Θ ) 0 0 b 1 ( Θ ) a 2 ( Θ ) 0 0 0 0 a 3 ( Θ ) 0 0 0 0 a 4 ( Θ ) ] ,
4 π F ( Θ ) d Ω 4 π = 1 ,
A blk ( λ ) = E u ( λ ) E d ( λ ) ,
A blk ( λ ) = α s blk ( λ ) a blk ( λ ) ,
s blk ( λ ) = 0.5 b w ( λ ) + q p ( λ ) b p ( λ = 550 ) ,
q p ( λ ) = 2 π π / 2 π F p ( Θ , λ ) 4 π sin ( Θ ) d Θ ,
b p ( λ ) = b p 0 [ Chl ] 0.766 ( 550 / λ ) , b p 0 = 0.416 ,
q p ( λ ) = 0.002 + 0.01 { 0.50 0.25 log 10 [ Chl ] } × ( λ / 550 ) k ,
k = { 0.5 ( log 10 [ Chl ] 0.3 ) , 0.02 [ Chl ] 2   mg   m 3 0, otherwise .
a blk ( λ ) = K blk ( λ ) { 1 A blk ( λ ) } μ d μ u μ d A blk ( λ ) + μ u ,
K blk ( λ ) = K w ( λ ) + K bio ( λ )
K w ( λ ) = a w ( λ ) + 0.5 b w ( λ )
K bio ( λ ) = χ ( λ ) [ Chl ] e ( λ ) .
F blk ( Θ , λ ) = b w ( λ ) F w ( Θ , λ ) + b p ( λ ) F p ( Θ , λ ) b w ( λ ) + b p ( λ ) ,
ω blk ( λ ) = b w ( λ ) + b p ( λ ) b w ( λ ) + b p ( λ ) + a blk ( λ ) ,
n hyd ( r ) = Cr - γ hyd ,
0 n hyd ( r ) d r = 1 .
F p ( Θ , λ )
= ( 1 f det ) σ plk ( λ ) F plk ( Θ , λ ) + f det σ det ( λ ) F det ( Θ , λ ) ( 1 f det ) σ plk ( λ ) + f det σ det ( λ ) ,
q p ( λ ) = ( 1 f det ) σ plk ( λ ) q plk ( λ ) + f det σ det ( λ ) q det ( λ ) ( 1 f det ) σ plk ( λ ) + f det σ det ( λ ) ,
π I ˜ ( μ , φ ) = μ 0 R ( μ , φ ; μ 0 , φ 0 ) I ˜ 0 ( μ 0 , φ 0 ) .
d = 1 N i = 1 N h [ p hyd ( Θ i ) p w ( Θ i ) ] 2
γ hyd = 6.63 m hyd 3.25 ( ± 0.05 )
a p ( λ ) = 0.06 A ( λ ) [ Chl ] 0.65 ,
f det ( Chl ) = 0.91 [ Chl ] 0.08 0.49 ( ± 0.015 ) ,
g p ( Chl ) = 0.991 0.024 [ Chl ] 0.23 ( ± 0.001 ) .
I ^ rs = π I ˜ rs μ 0 S 0 ,
P ^ rs = π P ˜ rs μ 0 S 0 = π Q ˜ rs 2 + U ˜ rs 2 μ 0 S 0 .
I ¯ rs = I ^ rs max ( I ^ rs ) I ^ rs I max ,
P ¯ rs = P ^ rs max ( P ^ rs ) P ^ rs P max ,

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