Abstract

In this study, we present a radiative transfer model, so-called OSOAA, that is able to predict the radiance and degree of polarization within the coupled atmosphere-ocean system in the presence of a rough sea surface. The OSOAA model solves the radiative transfer equation using the successive orders of scattering method. Comparisons with another operational radiative transfer model showed a satisfactory agreement within 0.8%. The OSOAA model has been designed with a graphical user interface to make it user friendly for the community. The radiance and degree of polarization are provided at any level, from the top of atmosphere to the ocean bottom. An application of the OSOAA model is carried out to quantify the directional variations of the water leaving reflectance and degree of polarization for phytoplankton and mineral-like dominated waters. The difference between the water leaving reflectance at a given geometry and that obtained for the nadir direction could reach 40%, thus questioning the Lambertian assumption of the sea surface that is used by inverse satellite algorithms dedicated to multi-angular sensors. It is shown as well that the directional features of the water leaving reflectance are weakly dependent on wind speed. The quantification of the directional variations of the water leaving reflectance obtained in this study should help to correctly exploit the satellite data that will be acquired by the current or forthcoming multi-angular satellite sensors.

© 2015 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
A vector radiative transfer model for coupled atmosphere and ocean systems based on successive order of scattering method

Peng-Wang Zhai, Yongxiang Hu, Charles R. Trepte, and Patricia L. Lucker
Opt. Express 17(4) 2057-2079 (2009)

Investigation of the variations in the water leaving polarized reflectance from the POLDER satellite data over two biogeochemical contrasted oceanic areas.

Hubert Loisel, Lucile Duforet, David Dessailly, Malik Chami, and Philippe Dubuisson
Opt. Express 16(17) 12905-12918 (2008)

References

  • View by:
  • |
  • |
  • |

  1. G. N. Plass, T. J. Humphreys, and G. W. Kattawar, “Ocean-atmosphere interface: its influence on radiation,” Appl. Opt. 20(6), 917–931 (1981).
    [Crossref] [PubMed]
  2. 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(8), 1453–1472 (1989).
    [Crossref]
  3. C. N. Adams and G. W. Kattawar, “Effect of volume-scattering function on the errors induced when polarization is neglected in radiance calculations in an atmosphere-ocean system,” Appl. Opt. 32(24), 4610–4617 (1993).
    [Crossref] [PubMed]
  4. M. I. Mishchenko, A. A. Lacis, and L. D. Travis, “Errors induced by the neglect of polarization in radiance calculations for Rayleigh-scattering atmospheres,” J. Quant. Spectrosc. Radiat. Transf. 51(3), 491–510 (1994).
    [Crossref]
  5. A. Lacis, J. Chowdhary, M. I. Mishenko, and B. Cairns, “Modeling errors in diffuse-sky radiation: vector vs scalar treatment,” Geophys. Res. Lett. 25(2), 135–138 (1998).
    [Crossref]
  6. M. Chami and M. D. Platel, “Sensitivity of the retrieval of the inherent optical properties of marine particles in coastal waters to the directional variations and the polarization of the reflectance,” J. Geophys. Res. 112(C5), C05037 (2007).
    [Crossref]
  7. M. Chami, “Importance of the polarization in the retrieval of oceanic constituents from the remote sensing reflectance,” J. Geophys. Res.- Oceans 112(C5), C05026 (2007).
    [Crossref]
  8. H. R. Gordon, J. W. Brown, and R. H. Evans, “Exact Rayleigh scattering calculations for use with the Nimbus-7 coastal zone color scanner,” Appl. Opt. 27(5), 862–871 (1988).
    [Crossref] [PubMed]
  9. J. Cariou, B. L. Jeune, J. Lotrian, and Y. Guern, “Polarization effects of seawater and underwater targets,” Appl. Opt. 29(11), 1689–1695 (1990).
    [Crossref] [PubMed]
  10. T. H. Waterman, “Polarization patterns in submarine illumination,” Science 120(3127), 927–932 (1954).
    [Crossref] [PubMed]
  11. M. Chami, R. Santer, and E. Dilligeard, “Radiative transfer model for the computation of radiance and polarization in an ocean-atmosphere system: polarization properties of suspended matter for remote sensing,” Appl. Opt. 40(15), 2398–2416 (2001).
    [Crossref] [PubMed]
  12. P. W. Zhai, Y. Hu, C. R. Trepte, and P. L. Lucker, “A vector radiative transfer model for coupled atmosphere and ocean systems based on successive order of scattering method,” Opt. Express 17(4), 2057–2079 (2009).
    [Crossref] [PubMed]
  13. P. Zhai, Y. Hu, J. Chowdhary, R. C. Trepte, P. L. Lucker, and D. B. Josset, “A vector radiative transfer model for coupled atmosphere and ocean systems with a rough interface,” J. Quant. Spect. Radiative Transfer (2010).
  14. Z. Jin, T. P. Charlock, K. Rutledge, K. Stamnes, and Y. Wang, “Analytical solution of radiative transfer in the coupled atmosphere-ocean system with a rough surface,” Appl. Opt. 45(28), 7443–7455 (2006).
    [Crossref] [PubMed]
  15. E. R. Sommersten, J. K. Lotsberg, K. Stamnes, and J. J. Stamnes, “Discrete ordinate and Monte Carlo simulations for polarized radiative transfer in a coupled system consisting of two media with different refractive indices,” J. Quant. Spectrosc. Radiat. Transf. 111(4), 616–633 (2010).
    [Crossref]
  16. Y. You, P. W. Zhai, G. W. Kattawar, and P. Yang, “Polarized radiance fields under a dynamic ocean surface: a three-dimensional radiative transfer solution,” Appl. Opt. 48(16), 3019–3029 (2009).
    [Crossref] [PubMed]
  17. J. Chowdhary, B. Cairns, and L. D. Travis, “Contribution of water-leaving radiances to multiangle, multispectral polarimetric observations over the open ocean: bio-optical model results for case 1 waters,” Appl. Opt. 45(22), 5542–5567 (2006).
    [Crossref] [PubMed]
  18. X. He, Y. Bai, Q. Zhu, and F. Gong, “A vector radiative transfer model of coupled ocean–atmosphere system using matrix-operator method for rough sea-surface,” J. Quant. Spectrosc. Radiat. Transf. 111(10), 1426–1448 (2010).
    [Crossref]
  19. Y. Ota, A. Higurashi, T. Nakajima, and T. Yokota, “Matrix formulations of radiative transfer including the polarization effect in a coupled atmosphere–ocean system,” J. Quant. Spectrosc. Radiat. Transf. 111(6), 878–894 (2010).
    [Crossref]
  20. A. Hollstein and J. Fischer, “Radiative transfer solutions for coupled atmosphere ocean systems using the matrix operator technique,” J. Quant. Spectrosc. Radiat. Transf. 113(7), 536–548 (2012).
    [Crossref]
  21. K. Voss and A. Chapin, “Upwelling radiance distribution camera system, NURADS,” Opt. Express 13(11), 4250–4262 (2005).
    [Crossref] [PubMed]
  22. K. J. Voss and N. Souaidia, “POLRADS: polarization radiance distribution measurement system,” Opt. Express 18(19), 19672–19680 (2010).
    [Crossref] [PubMed]
  23. D. Antoine, A. Morel, E. Leymarie, A. Houyou, B. Gentili, S. Victori, J. P. Buis, S. Meunier, M. Canini, D. Crozel, B. Fougnie, and P. Henry, “Underwater radiance distributions measured with miniaturized multispectral radiance cameras,” J. Atmos. Ocean. Technol. 30(1), 74–95 (2013).
    [Crossref]
  24. S. Kay, J. Hedley, S. Lavender, and A. Nimmo-Smith, “Light transfer at the ocean surface modeled using high resolution sea surface realizations,” Opt. Express 19(7), 6493–6504 (2011).
    [Crossref] [PubMed]
  25. 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(D14), 16989–17013 (1997).
    [Crossref]
  26. C. D. Mobley, “Polarized reflectance and transmittance properties of windblown sea surfaces,” Appl. Opt. 54(15), 4828–4849 (2015).
    [Crossref] [PubMed]
  27. Z. Jin, NASA Langley Research Center, One Enterprise Parkway, Suite 300, Hampton, Virginia 23666 (personal communication, 2015).
  28. M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Multiple Scattering of Light by Particles (New York, Cambridge University, 2006, pp.508,).
  29. J. Lenoble, M. Herman, J. L. Deuze, B. Lafrance, R. Santer, and D. Tanre, “A successive order of scattering code for solving the vector equation of transfer in the earth’s atmosphere with aerosols,” J. Quant. Spectrosc. Radiat. Transf. 107(3), 479–507 (2007).
    [Crossref]
  30. C. Cox and W. H. Munk, “Measurements of the roughness of the sea surface from photographs of the Sun’s glitter,” J. Opt. Soc. Am. 44(11), 838–850 (1954).
    [Crossref]
  31. J. F. De Haan, P. B. Bosma, and J. W. Hovenier, “The adding method for multiple scattering calculations of polarized light,” J. Astron. Astrophys. 183, 371–391 (1987).
  32. J. Chowdhary, Multiple Scattering of Polarized Light in Atmosphere-ocean Systems: Application to Sensitivity Analyses of Aerosol Polarimetry. (Ph.D thesis, Columbia University, 1999).
  33. M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge University, 2002).
  34. J. T. Adams and G. W. Kattawar, “Neutral points in an atmosphere-ocean system. 1: Upwelling light field,” Appl. Opt. 36(9), 1976–1986 (1997).
    [Crossref] [PubMed]
  35. E. P. Shettle and R. W. Fenn, ”Models for the aerosols of the lower atmosphere and the effects of humidity variations on their optical properties,”,Air Force Geophysics Laboratory. September 1979, AFGL-TR-79–0214, Environnemental Research papers, No. 676. (1979).
  36. World Climate Research Programme, “A preliminary cloudless standard atmosphere for radiation computation,” WCP-112, WMO/TD Report No 24, Geneva, Switzerland, March (1986).
  37. M. Chami, A. Thirouard, and T. Harmel, “POLVSM (Polarized Volume Scattering Meter) instrument: an innovative device to measure the directional and polarized scattering properties of hydrosols,” Opt. Express 22(21), 26403–26428 (2014).
    [Crossref] [PubMed]
  38. H. Slade, Y. C. Agrawal, and O. A. Mikkelsen, “Comparison of measured and theoretical scattering and polarization properties of narrow size range irregular sediment particles,” presented at Oceans, San Diego, 23–27 (2013).
  39. H. Tan, R. Doerffer, T. Oishi, and A. Tanaka, “A new approach to measure the volume scattering function,” Opt. Express 21(16), 18697–18711 (2013).
    [Crossref] [PubMed]
  40. M. E. Zugger, A. Messmer, T. J. Kane, J. Prentice, B. Concannon, A. Laux, and L. Mullen, “Optical scattering properties of phytoplankton: Measurements and comparison of various species at scattering angles between 1°and 170°,” Limnol. Oceanogr. 53(1), 381–386 (2008).
    [Crossref]
  41. J. K. Lotsberg, E. Marken, J. J. Stamnes, S. R. Erga, K. Aursland, and C. Olseng, “Laboratory measurements of light scattering from marine particles,” Limnol. Oceanogr. Methods 5, 34–40 (2007).
    [Crossref]
  42. B. Shao, J. S. Jaffe, M. Chachisvilis, and S. C. Esener, “Angular resolved light scattering for discriminating among marine picoplankton: modeling and experimental measurements,” Opt. Express 14(25), 12473–12484 (2006).
    [Crossref] [PubMed]
  43. P. Y. Deschamps, F. M. Breon, M. Leroy, A. Podaire, A. Bricaud, J. C. Buriez, and G. Seze, “The Polder mission - instrument characteristics and scientific objectives,” IEEE Trans. Geosci. Rem. Sens. 32(3), 598–615 (1994).
    [Crossref]
  44. J. Chowdhary, B. Cairns, F. Waquet, K. Knobelspiesse, M. Ottaviani, J. Redemann, L. Travis, and M. Mishchenko, “Sensitivity of multiangle, multispectral polarimetric remote sensing over open oceans to water-leaving radiance: analyses of RSP data acquired during the MILAGRO campaign,” Remote Sens. Environ. 118, 284–308 (2012), doi:.
    [Crossref]
  45. F. Waquet, F. Peers, P. Goloub, F. Ducos, F. Thieuleux, Y. Derimian, J. Riedi, M. Chami, and D. Tanré, “Retrieval of the Eyjafjallajökull volcanic aerosol optical and microphysical properties from POLDER/PARASOL measurements,” Atmos. Chem. Phys. 14(4), 1755–1768 (2014).
    [Crossref]
  46. J. A. Limbacher and R. A. Kahn, “MISR research-aerosol-algorithm refinements for dark water retrievals,” Atmos. Meas. Tech. 7(11), 3989–4007 (2014).
    [Crossref]
  47. J. V. Martonchik, D. J. Diner, R. Kahn, M. Verstraete, B. Pinty, H. R. Gordon, and T. P. Ackerman, “Techniques for the retrieval of aerosol properties over land and ocean using multiangle imaging,” IEEE Trans. Geosci. Rem. Sens. 36(4), 1212–1227 (1998).
    [Crossref]
  48. J. L. Deuze, P. Goloub, M. Herman, A. Marchand, G. Perry, S. Susana, and D. Tanre, “Estimate of the aerosol properties over the ocean with POLDER,” J. Geophys. Res. Atmos. 105(D12), 15329–15346 (2000).
    [Crossref]
  49. R. A. Kahn, W. H. Li, J. V. Martonchik, C. J. Bruegge, D. J. Diner, B. J. Gaitley, W. Abdou, O. Dubovik, B. Holben, A. Smirnov, Z. Jin, and D. Clark, “MISR calibration and implications for low-light-level aerosol retrieval over dark water,” J. Atmos. Sci. 62(4), 1032–1052 (2005).
    [Crossref]
  50. A. M. Sayer, G. E. Thomas, and R. G. Grainger, “A sea surface reflectance model for (A)ATSR, and application to aerosol retrievals,” Atmos. Meas. Tech. 3(4), 813–838 (2010).
    [Crossref]
  51. A. Morel and B. Gentili, “Diffuse reflectance of oceanic waters: its dependence on Sun angle as influenced by the molecular scattering contribution,” Appl. Opt. 30(30), 4427–4438 (1991).
    [Crossref] [PubMed]
  52. A. Morel and B. Gentili, “Diffuse reflectance of oceanic waters. III. Implication of bidirectionality for the remote-sensing problem,” Appl. Opt. 35(24), 4850–4862 (1996).
    [Crossref] [PubMed]
  53. 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(30), 6289–6306 (2002).
    [Crossref] [PubMed]
  54. P. Zhai, Y. Hu, R. C. Trepte, D. Winker, P. Lucker, Z. Lee, and D. Josset, “Uncertainty in the bidirectional reflectance model for oceanic waters,” Appl. Opt. 54(13), 4061–4069 (2015).
    [Crossref]
  55. A. Morel and L. Prieur, “Analysis of variations in ocean color,” Limnol. Oceanogr. 22(4), 709–722 (1977).
    [Crossref]
  56. T. Harmel and M. Chami, “Influence of polarimetric satellite data measured in the visible region on aerosol detection and on the performance of atmospheric correction procedure over open ocean waters,” Opt. Express 19(21), 20960–20983 (2011).
    [Crossref] [PubMed]

2015 (2)

2014 (3)

M. Chami, A. Thirouard, and T. Harmel, “POLVSM (Polarized Volume Scattering Meter) instrument: an innovative device to measure the directional and polarized scattering properties of hydrosols,” Opt. Express 22(21), 26403–26428 (2014).
[Crossref] [PubMed]

F. Waquet, F. Peers, P. Goloub, F. Ducos, F. Thieuleux, Y. Derimian, J. Riedi, M. Chami, and D. Tanré, “Retrieval of the Eyjafjallajökull volcanic aerosol optical and microphysical properties from POLDER/PARASOL measurements,” Atmos. Chem. Phys. 14(4), 1755–1768 (2014).
[Crossref]

J. A. Limbacher and R. A. Kahn, “MISR research-aerosol-algorithm refinements for dark water retrievals,” Atmos. Meas. Tech. 7(11), 3989–4007 (2014).
[Crossref]

2013 (2)

H. Tan, R. Doerffer, T. Oishi, and A. Tanaka, “A new approach to measure the volume scattering function,” Opt. Express 21(16), 18697–18711 (2013).
[Crossref] [PubMed]

D. Antoine, A. Morel, E. Leymarie, A. Houyou, B. Gentili, S. Victori, J. P. Buis, S. Meunier, M. Canini, D. Crozel, B. Fougnie, and P. Henry, “Underwater radiance distributions measured with miniaturized multispectral radiance cameras,” J. Atmos. Ocean. Technol. 30(1), 74–95 (2013).
[Crossref]

2012 (2)

A. Hollstein and J. Fischer, “Radiative transfer solutions for coupled atmosphere ocean systems using the matrix operator technique,” J. Quant. Spectrosc. Radiat. Transf. 113(7), 536–548 (2012).
[Crossref]

J. Chowdhary, B. Cairns, F. Waquet, K. Knobelspiesse, M. Ottaviani, J. Redemann, L. Travis, and M. Mishchenko, “Sensitivity of multiangle, multispectral polarimetric remote sensing over open oceans to water-leaving radiance: analyses of RSP data acquired during the MILAGRO campaign,” Remote Sens. Environ. 118, 284–308 (2012), doi:.
[Crossref]

2011 (2)

2010 (5)

A. M. Sayer, G. E. Thomas, and R. G. Grainger, “A sea surface reflectance model for (A)ATSR, and application to aerosol retrievals,” Atmos. Meas. Tech. 3(4), 813–838 (2010).
[Crossref]

K. J. Voss and N. Souaidia, “POLRADS: polarization radiance distribution measurement system,” Opt. Express 18(19), 19672–19680 (2010).
[Crossref] [PubMed]

E. R. Sommersten, J. K. Lotsberg, K. Stamnes, and J. J. Stamnes, “Discrete ordinate and Monte Carlo simulations for polarized radiative transfer in a coupled system consisting of two media with different refractive indices,” J. Quant. Spectrosc. Radiat. Transf. 111(4), 616–633 (2010).
[Crossref]

X. He, Y. Bai, Q. Zhu, and F. Gong, “A vector radiative transfer model of coupled ocean–atmosphere system using matrix-operator method for rough sea-surface,” J. Quant. Spectrosc. Radiat. Transf. 111(10), 1426–1448 (2010).
[Crossref]

Y. Ota, A. Higurashi, T. Nakajima, and T. Yokota, “Matrix formulations of radiative transfer including the polarization effect in a coupled atmosphere–ocean system,” J. Quant. Spectrosc. Radiat. Transf. 111(6), 878–894 (2010).
[Crossref]

2009 (2)

2008 (1)

M. E. Zugger, A. Messmer, T. J. Kane, J. Prentice, B. Concannon, A. Laux, and L. Mullen, “Optical scattering properties of phytoplankton: Measurements and comparison of various species at scattering angles between 1°and 170°,” Limnol. Oceanogr. 53(1), 381–386 (2008).
[Crossref]

2007 (4)

J. K. Lotsberg, E. Marken, J. J. Stamnes, S. R. Erga, K. Aursland, and C. Olseng, “Laboratory measurements of light scattering from marine particles,” Limnol. Oceanogr. Methods 5, 34–40 (2007).
[Crossref]

J. Lenoble, M. Herman, J. L. Deuze, B. Lafrance, R. Santer, and D. Tanre, “A successive order of scattering code for solving the vector equation of transfer in the earth’s atmosphere with aerosols,” J. Quant. Spectrosc. Radiat. Transf. 107(3), 479–507 (2007).
[Crossref]

M. Chami and M. D. Platel, “Sensitivity of the retrieval of the inherent optical properties of marine particles in coastal waters to the directional variations and the polarization of the reflectance,” J. Geophys. Res. 112(C5), C05037 (2007).
[Crossref]

M. Chami, “Importance of the polarization in the retrieval of oceanic constituents from the remote sensing reflectance,” J. Geophys. Res.- Oceans 112(C5), C05026 (2007).
[Crossref]

2006 (3)

2005 (2)

K. Voss and A. Chapin, “Upwelling radiance distribution camera system, NURADS,” Opt. Express 13(11), 4250–4262 (2005).
[Crossref] [PubMed]

R. A. Kahn, W. H. Li, J. V. Martonchik, C. J. Bruegge, D. J. Diner, B. J. Gaitley, W. Abdou, O. Dubovik, B. Holben, A. Smirnov, Z. Jin, and D. Clark, “MISR calibration and implications for low-light-level aerosol retrieval over dark water,” J. Atmos. Sci. 62(4), 1032–1052 (2005).
[Crossref]

2002 (1)

2001 (1)

2000 (1)

J. L. Deuze, P. Goloub, M. Herman, A. Marchand, G. Perry, S. Susana, and D. Tanre, “Estimate of the aerosol properties over the ocean with POLDER,” J. Geophys. Res. Atmos. 105(D12), 15329–15346 (2000).
[Crossref]

1998 (2)

A. Lacis, J. Chowdhary, M. I. Mishenko, and B. Cairns, “Modeling errors in diffuse-sky radiation: vector vs scalar treatment,” Geophys. Res. Lett. 25(2), 135–138 (1998).
[Crossref]

J. V. Martonchik, D. J. Diner, R. Kahn, M. Verstraete, B. Pinty, H. R. Gordon, and T. P. Ackerman, “Techniques for the retrieval of aerosol properties over land and ocean using multiangle imaging,” IEEE Trans. Geosci. Rem. Sens. 36(4), 1212–1227 (1998).
[Crossref]

1997 (2)

J. T. Adams and G. W. Kattawar, “Neutral points in an atmosphere-ocean system. 1: Upwelling light field,” Appl. Opt. 36(9), 1976–1986 (1997).
[Crossref] [PubMed]

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(D14), 16989–17013 (1997).
[Crossref]

1996 (1)

1994 (2)

P. Y. Deschamps, F. M. Breon, M. Leroy, A. Podaire, A. Bricaud, J. C. Buriez, and G. Seze, “The Polder mission - instrument characteristics and scientific objectives,” IEEE Trans. Geosci. Rem. Sens. 32(3), 598–615 (1994).
[Crossref]

M. I. Mishchenko, A. A. Lacis, and L. D. Travis, “Errors induced by the neglect of polarization in radiance calculations for Rayleigh-scattering atmospheres,” J. Quant. Spectrosc. Radiat. Transf. 51(3), 491–510 (1994).
[Crossref]

1993 (1)

1991 (1)

1990 (1)

1989 (1)

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(8), 1453–1472 (1989).
[Crossref]

1988 (1)

1987 (1)

J. F. De Haan, P. B. Bosma, and J. W. Hovenier, “The adding method for multiple scattering calculations of polarized light,” J. Astron. Astrophys. 183, 371–391 (1987).

1981 (1)

1977 (1)

A. Morel and L. Prieur, “Analysis of variations in ocean color,” Limnol. Oceanogr. 22(4), 709–722 (1977).
[Crossref]

1954 (2)

Abdou, W.

R. A. Kahn, W. H. Li, J. V. Martonchik, C. J. Bruegge, D. J. Diner, B. J. Gaitley, W. Abdou, O. Dubovik, B. Holben, A. Smirnov, Z. Jin, and D. Clark, “MISR calibration and implications for low-light-level aerosol retrieval over dark water,” J. Atmos. Sci. 62(4), 1032–1052 (2005).
[Crossref]

Ackerman, T. P.

J. V. Martonchik, D. J. Diner, R. Kahn, M. Verstraete, B. Pinty, H. R. Gordon, and T. P. Ackerman, “Techniques for the retrieval of aerosol properties over land and ocean using multiangle imaging,” IEEE Trans. Geosci. Rem. Sens. 36(4), 1212–1227 (1998).
[Crossref]

Adams, C. N.

C. N. Adams and G. W. Kattawar, “Effect of volume-scattering function on the errors induced when polarization is neglected in radiance calculations in an atmosphere-ocean system,” Appl. Opt. 32(24), 4610–4617 (1993).
[Crossref] [PubMed]

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(8), 1453–1472 (1989).
[Crossref]

Adams, J. T.

Antoine, D.

D. Antoine, A. Morel, E. Leymarie, A. Houyou, B. Gentili, S. Victori, J. P. Buis, S. Meunier, M. Canini, D. Crozel, B. Fougnie, and P. Henry, “Underwater radiance distributions measured with miniaturized multispectral radiance cameras,” J. Atmos. Ocean. Technol. 30(1), 74–95 (2013).
[Crossref]

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(30), 6289–6306 (2002).
[Crossref] [PubMed]

Aursland, K.

J. K. Lotsberg, E. Marken, J. J. Stamnes, S. R. Erga, K. Aursland, and C. Olseng, “Laboratory measurements of light scattering from marine particles,” Limnol. Oceanogr. Methods 5, 34–40 (2007).
[Crossref]

Bai, Y.

X. He, Y. Bai, Q. Zhu, and F. Gong, “A vector radiative transfer model of coupled ocean–atmosphere system using matrix-operator method for rough sea-surface,” J. Quant. Spectrosc. Radiat. Transf. 111(10), 1426–1448 (2010).
[Crossref]

Bosma, P. B.

J. F. De Haan, P. B. Bosma, and J. W. Hovenier, “The adding method for multiple scattering calculations of polarized light,” J. Astron. Astrophys. 183, 371–391 (1987).

Breon, F. M.

P. Y. Deschamps, F. M. Breon, M. Leroy, A. Podaire, A. Bricaud, J. C. Buriez, and G. Seze, “The Polder mission - instrument characteristics and scientific objectives,” IEEE Trans. Geosci. Rem. Sens. 32(3), 598–615 (1994).
[Crossref]

Bricaud, A.

P. Y. Deschamps, F. M. Breon, M. Leroy, A. Podaire, A. Bricaud, J. C. Buriez, and G. Seze, “The Polder mission - instrument characteristics and scientific objectives,” IEEE Trans. Geosci. Rem. Sens. 32(3), 598–615 (1994).
[Crossref]

Brown, J. W.

Bruegge, C. J.

R. A. Kahn, W. H. Li, J. V. Martonchik, C. J. Bruegge, D. J. Diner, B. J. Gaitley, W. Abdou, O. Dubovik, B. Holben, A. Smirnov, Z. Jin, and D. Clark, “MISR calibration and implications for low-light-level aerosol retrieval over dark water,” J. Atmos. Sci. 62(4), 1032–1052 (2005).
[Crossref]

Buis, J. P.

D. Antoine, A. Morel, E. Leymarie, A. Houyou, B. Gentili, S. Victori, J. P. Buis, S. Meunier, M. Canini, D. Crozel, B. Fougnie, and P. Henry, “Underwater radiance distributions measured with miniaturized multispectral radiance cameras,” J. Atmos. Ocean. Technol. 30(1), 74–95 (2013).
[Crossref]

Buriez, J. C.

P. Y. Deschamps, F. M. Breon, M. Leroy, A. Podaire, A. Bricaud, J. C. Buriez, and G. Seze, “The Polder mission - instrument characteristics and scientific objectives,” IEEE Trans. Geosci. Rem. Sens. 32(3), 598–615 (1994).
[Crossref]

Cairns, B.

J. Chowdhary, B. Cairns, F. Waquet, K. Knobelspiesse, M. Ottaviani, J. Redemann, L. Travis, and M. Mishchenko, “Sensitivity of multiangle, multispectral polarimetric remote sensing over open oceans to water-leaving radiance: analyses of RSP data acquired during the MILAGRO campaign,” Remote Sens. Environ. 118, 284–308 (2012), doi:.
[Crossref]

J. Chowdhary, B. Cairns, and L. D. Travis, “Contribution of water-leaving radiances to multiangle, multispectral polarimetric observations over the open ocean: bio-optical model results for case 1 waters,” Appl. Opt. 45(22), 5542–5567 (2006).
[Crossref] [PubMed]

A. Lacis, J. Chowdhary, M. I. Mishenko, and B. Cairns, “Modeling errors in diffuse-sky radiation: vector vs scalar treatment,” Geophys. Res. Lett. 25(2), 135–138 (1998).
[Crossref]

Canini, M.

D. Antoine, A. Morel, E. Leymarie, A. Houyou, B. Gentili, S. Victori, J. P. Buis, S. Meunier, M. Canini, D. Crozel, B. Fougnie, and P. Henry, “Underwater radiance distributions measured with miniaturized multispectral radiance cameras,” J. Atmos. Ocean. Technol. 30(1), 74–95 (2013).
[Crossref]

Cariou, J.

Chachisvilis, M.

Chami, M.

M. Chami, A. Thirouard, and T. Harmel, “POLVSM (Polarized Volume Scattering Meter) instrument: an innovative device to measure the directional and polarized scattering properties of hydrosols,” Opt. Express 22(21), 26403–26428 (2014).
[Crossref] [PubMed]

F. Waquet, F. Peers, P. Goloub, F. Ducos, F. Thieuleux, Y. Derimian, J. Riedi, M. Chami, and D. Tanré, “Retrieval of the Eyjafjallajökull volcanic aerosol optical and microphysical properties from POLDER/PARASOL measurements,” Atmos. Chem. Phys. 14(4), 1755–1768 (2014).
[Crossref]

T. Harmel and M. Chami, “Influence of polarimetric satellite data measured in the visible region on aerosol detection and on the performance of atmospheric correction procedure over open ocean waters,” Opt. Express 19(21), 20960–20983 (2011).
[Crossref] [PubMed]

M. Chami and M. D. Platel, “Sensitivity of the retrieval of the inherent optical properties of marine particles in coastal waters to the directional variations and the polarization of the reflectance,” J. Geophys. Res. 112(C5), C05037 (2007).
[Crossref]

M. Chami, “Importance of the polarization in the retrieval of oceanic constituents from the remote sensing reflectance,” J. Geophys. Res.- Oceans 112(C5), C05026 (2007).
[Crossref]

M. Chami, R. Santer, and E. Dilligeard, “Radiative transfer model for the computation of radiance and polarization in an ocean-atmosphere system: polarization properties of suspended matter for remote sensing,” Appl. Opt. 40(15), 2398–2416 (2001).
[Crossref] [PubMed]

Chapin, A.

Charlock, T. P.

Chowdhary, J.

J. Chowdhary, B. Cairns, F. Waquet, K. Knobelspiesse, M. Ottaviani, J. Redemann, L. Travis, and M. Mishchenko, “Sensitivity of multiangle, multispectral polarimetric remote sensing over open oceans to water-leaving radiance: analyses of RSP data acquired during the MILAGRO campaign,” Remote Sens. Environ. 118, 284–308 (2012), doi:.
[Crossref]

J. Chowdhary, B. Cairns, and L. D. Travis, “Contribution of water-leaving radiances to multiangle, multispectral polarimetric observations over the open ocean: bio-optical model results for case 1 waters,” Appl. Opt. 45(22), 5542–5567 (2006).
[Crossref] [PubMed]

A. Lacis, J. Chowdhary, M. I. Mishenko, and B. Cairns, “Modeling errors in diffuse-sky radiation: vector vs scalar treatment,” Geophys. Res. Lett. 25(2), 135–138 (1998).
[Crossref]

Clark, D.

R. A. Kahn, W. H. Li, J. V. Martonchik, C. J. Bruegge, D. J. Diner, B. J. Gaitley, W. Abdou, O. Dubovik, B. Holben, A. Smirnov, Z. Jin, and D. Clark, “MISR calibration and implications for low-light-level aerosol retrieval over dark water,” J. Atmos. Sci. 62(4), 1032–1052 (2005).
[Crossref]

Concannon, B.

M. E. Zugger, A. Messmer, T. J. Kane, J. Prentice, B. Concannon, A. Laux, and L. Mullen, “Optical scattering properties of phytoplankton: Measurements and comparison of various species at scattering angles between 1°and 170°,” Limnol. Oceanogr. 53(1), 381–386 (2008).
[Crossref]

Cox, C.

Crozel, D.

D. Antoine, A. Morel, E. Leymarie, A. Houyou, B. Gentili, S. Victori, J. P. Buis, S. Meunier, M. Canini, D. Crozel, B. Fougnie, and P. Henry, “Underwater radiance distributions measured with miniaturized multispectral radiance cameras,” J. Atmos. Ocean. Technol. 30(1), 74–95 (2013).
[Crossref]

De Haan, J. F.

J. F. De Haan, P. B. Bosma, and J. W. Hovenier, “The adding method for multiple scattering calculations of polarized light,” J. Astron. Astrophys. 183, 371–391 (1987).

Derimian, Y.

F. Waquet, F. Peers, P. Goloub, F. Ducos, F. Thieuleux, Y. Derimian, J. Riedi, M. Chami, and D. Tanré, “Retrieval of the Eyjafjallajökull volcanic aerosol optical and microphysical properties from POLDER/PARASOL measurements,” Atmos. Chem. Phys. 14(4), 1755–1768 (2014).
[Crossref]

Deschamps, P. Y.

P. Y. Deschamps, F. M. Breon, M. Leroy, A. Podaire, A. Bricaud, J. C. Buriez, and G. Seze, “The Polder mission - instrument characteristics and scientific objectives,” IEEE Trans. Geosci. Rem. Sens. 32(3), 598–615 (1994).
[Crossref]

Deuze, J. L.

J. Lenoble, M. Herman, J. L. Deuze, B. Lafrance, R. Santer, and D. Tanre, “A successive order of scattering code for solving the vector equation of transfer in the earth’s atmosphere with aerosols,” J. Quant. Spectrosc. Radiat. Transf. 107(3), 479–507 (2007).
[Crossref]

J. L. Deuze, P. Goloub, M. Herman, A. Marchand, G. Perry, S. Susana, and D. Tanre, “Estimate of the aerosol properties over the ocean with POLDER,” J. Geophys. Res. Atmos. 105(D12), 15329–15346 (2000).
[Crossref]

Dilligeard, E.

Diner, D. J.

R. A. Kahn, W. H. Li, J. V. Martonchik, C. J. Bruegge, D. J. Diner, B. J. Gaitley, W. Abdou, O. Dubovik, B. Holben, A. Smirnov, Z. Jin, and D. Clark, “MISR calibration and implications for low-light-level aerosol retrieval over dark water,” J. Atmos. Sci. 62(4), 1032–1052 (2005).
[Crossref]

J. V. Martonchik, D. J. Diner, R. Kahn, M. Verstraete, B. Pinty, H. R. Gordon, and T. P. Ackerman, “Techniques for the retrieval of aerosol properties over land and ocean using multiangle imaging,” IEEE Trans. Geosci. Rem. Sens. 36(4), 1212–1227 (1998).
[Crossref]

Doerffer, R.

Dubovik, O.

R. A. Kahn, W. H. Li, J. V. Martonchik, C. J. Bruegge, D. J. Diner, B. J. Gaitley, W. Abdou, O. Dubovik, B. Holben, A. Smirnov, Z. Jin, and D. Clark, “MISR calibration and implications for low-light-level aerosol retrieval over dark water,” J. Atmos. Sci. 62(4), 1032–1052 (2005).
[Crossref]

Ducos, F.

F. Waquet, F. Peers, P. Goloub, F. Ducos, F. Thieuleux, Y. Derimian, J. Riedi, M. Chami, and D. Tanré, “Retrieval of the Eyjafjallajökull volcanic aerosol optical and microphysical properties from POLDER/PARASOL measurements,” Atmos. Chem. Phys. 14(4), 1755–1768 (2014).
[Crossref]

Erga, S. R.

J. K. Lotsberg, E. Marken, J. J. Stamnes, S. R. Erga, K. Aursland, and C. Olseng, “Laboratory measurements of light scattering from marine particles,” Limnol. Oceanogr. Methods 5, 34–40 (2007).
[Crossref]

Esener, S. C.

Evans, R. H.

Fischer, J.

A. Hollstein and J. Fischer, “Radiative transfer solutions for coupled atmosphere ocean systems using the matrix operator technique,” J. Quant. Spectrosc. Radiat. Transf. 113(7), 536–548 (2012).
[Crossref]

Fougnie, B.

D. Antoine, A. Morel, E. Leymarie, A. Houyou, B. Gentili, S. Victori, J. P. Buis, S. Meunier, M. Canini, D. Crozel, B. Fougnie, and P. Henry, “Underwater radiance distributions measured with miniaturized multispectral radiance cameras,” J. Atmos. Ocean. Technol. 30(1), 74–95 (2013).
[Crossref]

Gaitley, B. J.

R. A. Kahn, W. H. Li, J. V. Martonchik, C. J. Bruegge, D. J. Diner, B. J. Gaitley, W. Abdou, O. Dubovik, B. Holben, A. Smirnov, Z. Jin, and D. Clark, “MISR calibration and implications for low-light-level aerosol retrieval over dark water,” J. Atmos. Sci. 62(4), 1032–1052 (2005).
[Crossref]

Gentili, B.

Goloub, P.

F. Waquet, F. Peers, P. Goloub, F. Ducos, F. Thieuleux, Y. Derimian, J. Riedi, M. Chami, and D. Tanré, “Retrieval of the Eyjafjallajökull volcanic aerosol optical and microphysical properties from POLDER/PARASOL measurements,” Atmos. Chem. Phys. 14(4), 1755–1768 (2014).
[Crossref]

J. L. Deuze, P. Goloub, M. Herman, A. Marchand, G. Perry, S. Susana, and D. Tanre, “Estimate of the aerosol properties over the ocean with POLDER,” J. Geophys. Res. Atmos. 105(D12), 15329–15346 (2000).
[Crossref]

Gong, F.

X. He, Y. Bai, Q. Zhu, and F. Gong, “A vector radiative transfer model of coupled ocean–atmosphere system using matrix-operator method for rough sea-surface,” J. Quant. Spectrosc. Radiat. Transf. 111(10), 1426–1448 (2010).
[Crossref]

Gordon, H. R.

J. V. Martonchik, D. J. Diner, R. Kahn, M. Verstraete, B. Pinty, H. R. Gordon, and T. P. Ackerman, “Techniques for the retrieval of aerosol properties over land and ocean using multiangle imaging,” IEEE Trans. Geosci. Rem. Sens. 36(4), 1212–1227 (1998).
[Crossref]

H. R. Gordon, J. W. Brown, and R. H. Evans, “Exact Rayleigh scattering calculations for use with the Nimbus-7 coastal zone color scanner,” Appl. Opt. 27(5), 862–871 (1988).
[Crossref] [PubMed]

Grainger, R. G.

A. M. Sayer, G. E. Thomas, and R. G. Grainger, “A sea surface reflectance model for (A)ATSR, and application to aerosol retrievals,” Atmos. Meas. Tech. 3(4), 813–838 (2010).
[Crossref]

Guern, Y.

Harmel, T.

He, X.

X. He, Y. Bai, Q. Zhu, and F. Gong, “A vector radiative transfer model of coupled ocean–atmosphere system using matrix-operator method for rough sea-surface,” J. Quant. Spectrosc. Radiat. Transf. 111(10), 1426–1448 (2010).
[Crossref]

Hedley, J.

Henry, P.

D. Antoine, A. Morel, E. Leymarie, A. Houyou, B. Gentili, S. Victori, J. P. Buis, S. Meunier, M. Canini, D. Crozel, B. Fougnie, and P. Henry, “Underwater radiance distributions measured with miniaturized multispectral radiance cameras,” J. Atmos. Ocean. Technol. 30(1), 74–95 (2013).
[Crossref]

Herman, M.

J. Lenoble, M. Herman, J. L. Deuze, B. Lafrance, R. Santer, and D. Tanre, “A successive order of scattering code for solving the vector equation of transfer in the earth’s atmosphere with aerosols,” J. Quant. Spectrosc. Radiat. Transf. 107(3), 479–507 (2007).
[Crossref]

J. L. Deuze, P. Goloub, M. Herman, A. Marchand, G. Perry, S. Susana, and D. Tanre, “Estimate of the aerosol properties over the ocean with POLDER,” J. Geophys. Res. Atmos. 105(D12), 15329–15346 (2000).
[Crossref]

Higurashi, A.

Y. Ota, A. Higurashi, T. Nakajima, and T. Yokota, “Matrix formulations of radiative transfer including the polarization effect in a coupled atmosphere–ocean system,” J. Quant. Spectrosc. Radiat. Transf. 111(6), 878–894 (2010).
[Crossref]

Holben, B.

R. A. Kahn, W. H. Li, J. V. Martonchik, C. J. Bruegge, D. J. Diner, B. J. Gaitley, W. Abdou, O. Dubovik, B. Holben, A. Smirnov, Z. Jin, and D. Clark, “MISR calibration and implications for low-light-level aerosol retrieval over dark water,” J. Atmos. Sci. 62(4), 1032–1052 (2005).
[Crossref]

Hollstein, A.

A. Hollstein and J. Fischer, “Radiative transfer solutions for coupled atmosphere ocean systems using the matrix operator technique,” J. Quant. Spectrosc. Radiat. Transf. 113(7), 536–548 (2012).
[Crossref]

Houyou, A.

D. Antoine, A. Morel, E. Leymarie, A. Houyou, B. Gentili, S. Victori, J. P. Buis, S. Meunier, M. Canini, D. Crozel, B. Fougnie, and P. Henry, “Underwater radiance distributions measured with miniaturized multispectral radiance cameras,” J. Atmos. Ocean. Technol. 30(1), 74–95 (2013).
[Crossref]

Hovenier, J. W.

J. F. De Haan, P. B. Bosma, and J. W. Hovenier, “The adding method for multiple scattering calculations of polarized light,” J. Astron. Astrophys. 183, 371–391 (1987).

Hu, Y.

Humphreys, T. J.

Jaffe, J. S.

Jeune, B. L.

Jin, Z.

Z. Jin, T. P. Charlock, K. Rutledge, K. Stamnes, and Y. Wang, “Analytical solution of radiative transfer in the coupled atmosphere-ocean system with a rough surface,” Appl. Opt. 45(28), 7443–7455 (2006).
[Crossref] [PubMed]

R. A. Kahn, W. H. Li, J. V. Martonchik, C. J. Bruegge, D. J. Diner, B. J. Gaitley, W. Abdou, O. Dubovik, B. Holben, A. Smirnov, Z. Jin, and D. Clark, “MISR calibration and implications for low-light-level aerosol retrieval over dark water,” J. Atmos. Sci. 62(4), 1032–1052 (2005).
[Crossref]

Josset, D.

Kahn, R.

J. V. Martonchik, D. J. Diner, R. Kahn, M. Verstraete, B. Pinty, H. R. Gordon, and T. P. Ackerman, “Techniques for the retrieval of aerosol properties over land and ocean using multiangle imaging,” IEEE Trans. Geosci. Rem. Sens. 36(4), 1212–1227 (1998).
[Crossref]

Kahn, R. A.

J. A. Limbacher and R. A. Kahn, “MISR research-aerosol-algorithm refinements for dark water retrievals,” Atmos. Meas. Tech. 7(11), 3989–4007 (2014).
[Crossref]

R. A. Kahn, W. H. Li, J. V. Martonchik, C. J. Bruegge, D. J. Diner, B. J. Gaitley, W. Abdou, O. Dubovik, B. Holben, A. Smirnov, Z. Jin, and D. Clark, “MISR calibration and implications for low-light-level aerosol retrieval over dark water,” J. Atmos. Sci. 62(4), 1032–1052 (2005).
[Crossref]

Kane, T. J.

M. E. Zugger, A. Messmer, T. J. Kane, J. Prentice, B. Concannon, A. Laux, and L. Mullen, “Optical scattering properties of phytoplankton: Measurements and comparison of various species at scattering angles between 1°and 170°,” Limnol. Oceanogr. 53(1), 381–386 (2008).
[Crossref]

Kattawar, G. W.

Kay, S.

Knobelspiesse, K.

J. Chowdhary, B. Cairns, F. Waquet, K. Knobelspiesse, M. Ottaviani, J. Redemann, L. Travis, and M. Mishchenko, “Sensitivity of multiangle, multispectral polarimetric remote sensing over open oceans to water-leaving radiance: analyses of RSP data acquired during the MILAGRO campaign,” Remote Sens. Environ. 118, 284–308 (2012), doi:.
[Crossref]

Lacis, A.

A. Lacis, J. Chowdhary, M. I. Mishenko, and B. Cairns, “Modeling errors in diffuse-sky radiation: vector vs scalar treatment,” Geophys. Res. Lett. 25(2), 135–138 (1998).
[Crossref]

Lacis, A. A.

M. I. Mishchenko, A. A. Lacis, and L. D. Travis, “Errors induced by the neglect of polarization in radiance calculations for Rayleigh-scattering atmospheres,” J. Quant. Spectrosc. Radiat. Transf. 51(3), 491–510 (1994).
[Crossref]

Lafrance, B.

J. Lenoble, M. Herman, J. L. Deuze, B. Lafrance, R. Santer, and D. Tanre, “A successive order of scattering code for solving the vector equation of transfer in the earth’s atmosphere with aerosols,” J. Quant. Spectrosc. Radiat. Transf. 107(3), 479–507 (2007).
[Crossref]

Laux, A.

M. E. Zugger, A. Messmer, T. J. Kane, J. Prentice, B. Concannon, A. Laux, and L. Mullen, “Optical scattering properties of phytoplankton: Measurements and comparison of various species at scattering angles between 1°and 170°,” Limnol. Oceanogr. 53(1), 381–386 (2008).
[Crossref]

Lavender, S.

Lee, Z.

Lenoble, J.

J. Lenoble, M. Herman, J. L. Deuze, B. Lafrance, R. Santer, and D. Tanre, “A successive order of scattering code for solving the vector equation of transfer in the earth’s atmosphere with aerosols,” J. Quant. Spectrosc. Radiat. Transf. 107(3), 479–507 (2007).
[Crossref]

Leroy, M.

P. Y. Deschamps, F. M. Breon, M. Leroy, A. Podaire, A. Bricaud, J. C. Buriez, and G. Seze, “The Polder mission - instrument characteristics and scientific objectives,” IEEE Trans. Geosci. Rem. Sens. 32(3), 598–615 (1994).
[Crossref]

Leymarie, E.

D. Antoine, A. Morel, E. Leymarie, A. Houyou, B. Gentili, S. Victori, J. P. Buis, S. Meunier, M. Canini, D. Crozel, B. Fougnie, and P. Henry, “Underwater radiance distributions measured with miniaturized multispectral radiance cameras,” J. Atmos. Ocean. Technol. 30(1), 74–95 (2013).
[Crossref]

Li, W. H.

R. A. Kahn, W. H. Li, J. V. Martonchik, C. J. Bruegge, D. J. Diner, B. J. Gaitley, W. Abdou, O. Dubovik, B. Holben, A. Smirnov, Z. Jin, and D. Clark, “MISR calibration and implications for low-light-level aerosol retrieval over dark water,” J. Atmos. Sci. 62(4), 1032–1052 (2005).
[Crossref]

Limbacher, J. A.

J. A. Limbacher and R. A. Kahn, “MISR research-aerosol-algorithm refinements for dark water retrievals,” Atmos. Meas. Tech. 7(11), 3989–4007 (2014).
[Crossref]

Lotrian, J.

Lotsberg, J. K.

E. R. Sommersten, J. K. Lotsberg, K. Stamnes, and J. J. Stamnes, “Discrete ordinate and Monte Carlo simulations for polarized radiative transfer in a coupled system consisting of two media with different refractive indices,” J. Quant. Spectrosc. Radiat. Transf. 111(4), 616–633 (2010).
[Crossref]

J. K. Lotsberg, E. Marken, J. J. Stamnes, S. R. Erga, K. Aursland, and C. Olseng, “Laboratory measurements of light scattering from marine particles,” Limnol. Oceanogr. Methods 5, 34–40 (2007).
[Crossref]

Lucker, P.

Lucker, P. L.

Marchand, A.

J. L. Deuze, P. Goloub, M. Herman, A. Marchand, G. Perry, S. Susana, and D. Tanre, “Estimate of the aerosol properties over the ocean with POLDER,” J. Geophys. Res. Atmos. 105(D12), 15329–15346 (2000).
[Crossref]

Marken, E.

J. K. Lotsberg, E. Marken, J. J. Stamnes, S. R. Erga, K. Aursland, and C. Olseng, “Laboratory measurements of light scattering from marine particles,” Limnol. Oceanogr. Methods 5, 34–40 (2007).
[Crossref]

Martonchik, J. V.

R. A. Kahn, W. H. Li, J. V. Martonchik, C. J. Bruegge, D. J. Diner, B. J. Gaitley, W. Abdou, O. Dubovik, B. Holben, A. Smirnov, Z. Jin, and D. Clark, “MISR calibration and implications for low-light-level aerosol retrieval over dark water,” J. Atmos. Sci. 62(4), 1032–1052 (2005).
[Crossref]

J. V. Martonchik, D. J. Diner, R. Kahn, M. Verstraete, B. Pinty, H. R. Gordon, and T. P. Ackerman, “Techniques for the retrieval of aerosol properties over land and ocean using multiangle imaging,” IEEE Trans. Geosci. Rem. Sens. 36(4), 1212–1227 (1998).
[Crossref]

Messmer, A.

M. E. Zugger, A. Messmer, T. J. Kane, J. Prentice, B. Concannon, A. Laux, and L. Mullen, “Optical scattering properties of phytoplankton: Measurements and comparison of various species at scattering angles between 1°and 170°,” Limnol. Oceanogr. 53(1), 381–386 (2008).
[Crossref]

Meunier, S.

D. Antoine, A. Morel, E. Leymarie, A. Houyou, B. Gentili, S. Victori, J. P. Buis, S. Meunier, M. Canini, D. Crozel, B. Fougnie, and P. Henry, “Underwater radiance distributions measured with miniaturized multispectral radiance cameras,” J. Atmos. Ocean. Technol. 30(1), 74–95 (2013).
[Crossref]

Mishchenko, M.

J. Chowdhary, B. Cairns, F. Waquet, K. Knobelspiesse, M. Ottaviani, J. Redemann, L. Travis, and M. Mishchenko, “Sensitivity of multiangle, multispectral polarimetric remote sensing over open oceans to water-leaving radiance: analyses of RSP data acquired during the MILAGRO campaign,” Remote Sens. Environ. 118, 284–308 (2012), doi:.
[Crossref]

Mishchenko, M. I.

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(D14), 16989–17013 (1997).
[Crossref]

M. I. Mishchenko, A. A. Lacis, and L. D. Travis, “Errors induced by the neglect of polarization in radiance calculations for Rayleigh-scattering atmospheres,” J. Quant. Spectrosc. Radiat. Transf. 51(3), 491–510 (1994).
[Crossref]

Mishenko, M. I.

A. Lacis, J. Chowdhary, M. I. Mishenko, and B. Cairns, “Modeling errors in diffuse-sky radiation: vector vs scalar treatment,” Geophys. Res. Lett. 25(2), 135–138 (1998).
[Crossref]

Mobley, C. D.

Morel, A.

Mullen, L.

M. E. Zugger, A. Messmer, T. J. Kane, J. Prentice, B. Concannon, A. Laux, and L. Mullen, “Optical scattering properties of phytoplankton: Measurements and comparison of various species at scattering angles between 1°and 170°,” Limnol. Oceanogr. 53(1), 381–386 (2008).
[Crossref]

Munk, W. H.

Nakajima, T.

Y. Ota, A. Higurashi, T. Nakajima, and T. Yokota, “Matrix formulations of radiative transfer including the polarization effect in a coupled atmosphere–ocean system,” J. Quant. Spectrosc. Radiat. Transf. 111(6), 878–894 (2010).
[Crossref]

Nimmo-Smith, A.

Oishi, T.

Olseng, C.

J. K. Lotsberg, E. Marken, J. J. Stamnes, S. R. Erga, K. Aursland, and C. Olseng, “Laboratory measurements of light scattering from marine particles,” Limnol. Oceanogr. Methods 5, 34–40 (2007).
[Crossref]

Ota, Y.

Y. Ota, A. Higurashi, T. Nakajima, and T. Yokota, “Matrix formulations of radiative transfer including the polarization effect in a coupled atmosphere–ocean system,” J. Quant. Spectrosc. Radiat. Transf. 111(6), 878–894 (2010).
[Crossref]

Ottaviani, M.

J. Chowdhary, B. Cairns, F. Waquet, K. Knobelspiesse, M. Ottaviani, J. Redemann, L. Travis, and M. Mishchenko, “Sensitivity of multiangle, multispectral polarimetric remote sensing over open oceans to water-leaving radiance: analyses of RSP data acquired during the MILAGRO campaign,” Remote Sens. Environ. 118, 284–308 (2012), doi:.
[Crossref]

Peers, F.

F. Waquet, F. Peers, P. Goloub, F. Ducos, F. Thieuleux, Y. Derimian, J. Riedi, M. Chami, and D. Tanré, “Retrieval of the Eyjafjallajökull volcanic aerosol optical and microphysical properties from POLDER/PARASOL measurements,” Atmos. Chem. Phys. 14(4), 1755–1768 (2014).
[Crossref]

Perry, G.

J. L. Deuze, P. Goloub, M. Herman, A. Marchand, G. Perry, S. Susana, and D. Tanre, “Estimate of the aerosol properties over the ocean with POLDER,” J. Geophys. Res. Atmos. 105(D12), 15329–15346 (2000).
[Crossref]

Pinty, B.

J. V. Martonchik, D. J. Diner, R. Kahn, M. Verstraete, B. Pinty, H. R. Gordon, and T. P. Ackerman, “Techniques for the retrieval of aerosol properties over land and ocean using multiangle imaging,” IEEE Trans. Geosci. Rem. Sens. 36(4), 1212–1227 (1998).
[Crossref]

Plass, G. N.

Platel, M. D.

M. Chami and M. D. Platel, “Sensitivity of the retrieval of the inherent optical properties of marine particles in coastal waters to the directional variations and the polarization of the reflectance,” J. Geophys. Res. 112(C5), C05037 (2007).
[Crossref]

Podaire, A.

P. Y. Deschamps, F. M. Breon, M. Leroy, A. Podaire, A. Bricaud, J. C. Buriez, and G. Seze, “The Polder mission - instrument characteristics and scientific objectives,” IEEE Trans. Geosci. Rem. Sens. 32(3), 598–615 (1994).
[Crossref]

Prentice, J.

M. E. Zugger, A. Messmer, T. J. Kane, J. Prentice, B. Concannon, A. Laux, and L. Mullen, “Optical scattering properties of phytoplankton: Measurements and comparison of various species at scattering angles between 1°and 170°,” Limnol. Oceanogr. 53(1), 381–386 (2008).
[Crossref]

Prieur, L.

A. Morel and L. Prieur, “Analysis of variations in ocean color,” Limnol. Oceanogr. 22(4), 709–722 (1977).
[Crossref]

Redemann, J.

J. Chowdhary, B. Cairns, F. Waquet, K. Knobelspiesse, M. Ottaviani, J. Redemann, L. Travis, and M. Mishchenko, “Sensitivity of multiangle, multispectral polarimetric remote sensing over open oceans to water-leaving radiance: analyses of RSP data acquired during the MILAGRO campaign,” Remote Sens. Environ. 118, 284–308 (2012), doi:.
[Crossref]

Riedi, J.

F. Waquet, F. Peers, P. Goloub, F. Ducos, F. Thieuleux, Y. Derimian, J. Riedi, M. Chami, and D. Tanré, “Retrieval of the Eyjafjallajökull volcanic aerosol optical and microphysical properties from POLDER/PARASOL measurements,” Atmos. Chem. Phys. 14(4), 1755–1768 (2014).
[Crossref]

Rutledge, K.

Santer, R.

J. Lenoble, M. Herman, J. L. Deuze, B. Lafrance, R. Santer, and D. Tanre, “A successive order of scattering code for solving the vector equation of transfer in the earth’s atmosphere with aerosols,” J. Quant. Spectrosc. Radiat. Transf. 107(3), 479–507 (2007).
[Crossref]

M. Chami, R. Santer, and E. Dilligeard, “Radiative transfer model for the computation of radiance and polarization in an ocean-atmosphere system: polarization properties of suspended matter for remote sensing,” Appl. Opt. 40(15), 2398–2416 (2001).
[Crossref] [PubMed]

Sayer, A. M.

A. M. Sayer, G. E. Thomas, and R. G. Grainger, “A sea surface reflectance model for (A)ATSR, and application to aerosol retrievals,” Atmos. Meas. Tech. 3(4), 813–838 (2010).
[Crossref]

Seze, G.

P. Y. Deschamps, F. M. Breon, M. Leroy, A. Podaire, A. Bricaud, J. C. Buriez, and G. Seze, “The Polder mission - instrument characteristics and scientific objectives,” IEEE Trans. Geosci. Rem. Sens. 32(3), 598–615 (1994).
[Crossref]

Shao, B.

Smirnov, A.

R. A. Kahn, W. H. Li, J. V. Martonchik, C. J. Bruegge, D. J. Diner, B. J. Gaitley, W. Abdou, O. Dubovik, B. Holben, A. Smirnov, Z. Jin, and D. Clark, “MISR calibration and implications for low-light-level aerosol retrieval over dark water,” J. Atmos. Sci. 62(4), 1032–1052 (2005).
[Crossref]

Sommersten, E. R.

E. R. Sommersten, J. K. Lotsberg, K. Stamnes, and J. J. Stamnes, “Discrete ordinate and Monte Carlo simulations for polarized radiative transfer in a coupled system consisting of two media with different refractive indices,” J. Quant. Spectrosc. Radiat. Transf. 111(4), 616–633 (2010).
[Crossref]

Souaidia, N.

Stamnes, J. J.

E. R. Sommersten, J. K. Lotsberg, K. Stamnes, and J. J. Stamnes, “Discrete ordinate and Monte Carlo simulations for polarized radiative transfer in a coupled system consisting of two media with different refractive indices,” J. Quant. Spectrosc. Radiat. Transf. 111(4), 616–633 (2010).
[Crossref]

J. K. Lotsberg, E. Marken, J. J. Stamnes, S. R. Erga, K. Aursland, and C. Olseng, “Laboratory measurements of light scattering from marine particles,” Limnol. Oceanogr. Methods 5, 34–40 (2007).
[Crossref]

Stamnes, K.

E. R. Sommersten, J. K. Lotsberg, K. Stamnes, and J. J. Stamnes, “Discrete ordinate and Monte Carlo simulations for polarized radiative transfer in a coupled system consisting of two media with different refractive indices,” J. Quant. Spectrosc. Radiat. Transf. 111(4), 616–633 (2010).
[Crossref]

Z. Jin, T. P. Charlock, K. Rutledge, K. Stamnes, and Y. Wang, “Analytical solution of radiative transfer in the coupled atmosphere-ocean system with a rough surface,” Appl. Opt. 45(28), 7443–7455 (2006).
[Crossref] [PubMed]

Susana, S.

J. L. Deuze, P. Goloub, M. Herman, A. Marchand, G. Perry, S. Susana, and D. Tanre, “Estimate of the aerosol properties over the ocean with POLDER,” J. Geophys. Res. Atmos. 105(D12), 15329–15346 (2000).
[Crossref]

Tan, H.

Tanaka, A.

Tanre, D.

J. Lenoble, M. Herman, J. L. Deuze, B. Lafrance, R. Santer, and D. Tanre, “A successive order of scattering code for solving the vector equation of transfer in the earth’s atmosphere with aerosols,” J. Quant. Spectrosc. Radiat. Transf. 107(3), 479–507 (2007).
[Crossref]

J. L. Deuze, P. Goloub, M. Herman, A. Marchand, G. Perry, S. Susana, and D. Tanre, “Estimate of the aerosol properties over the ocean with POLDER,” J. Geophys. Res. Atmos. 105(D12), 15329–15346 (2000).
[Crossref]

Tanré, D.

F. Waquet, F. Peers, P. Goloub, F. Ducos, F. Thieuleux, Y. Derimian, J. Riedi, M. Chami, and D. Tanré, “Retrieval of the Eyjafjallajökull volcanic aerosol optical and microphysical properties from POLDER/PARASOL measurements,” Atmos. Chem. Phys. 14(4), 1755–1768 (2014).
[Crossref]

Thieuleux, F.

F. Waquet, F. Peers, P. Goloub, F. Ducos, F. Thieuleux, Y. Derimian, J. Riedi, M. Chami, and D. Tanré, “Retrieval of the Eyjafjallajökull volcanic aerosol optical and microphysical properties from POLDER/PARASOL measurements,” Atmos. Chem. Phys. 14(4), 1755–1768 (2014).
[Crossref]

Thirouard, A.

Thomas, G. E.

A. M. Sayer, G. E. Thomas, and R. G. Grainger, “A sea surface reflectance model for (A)ATSR, and application to aerosol retrievals,” Atmos. Meas. Tech. 3(4), 813–838 (2010).
[Crossref]

Travis, L.

J. Chowdhary, B. Cairns, F. Waquet, K. Knobelspiesse, M. Ottaviani, J. Redemann, L. Travis, and M. Mishchenko, “Sensitivity of multiangle, multispectral polarimetric remote sensing over open oceans to water-leaving radiance: analyses of RSP data acquired during the MILAGRO campaign,” Remote Sens. Environ. 118, 284–308 (2012), doi:.
[Crossref]

Travis, L. D.

J. Chowdhary, B. Cairns, and L. D. Travis, “Contribution of water-leaving radiances to multiangle, multispectral polarimetric observations over the open ocean: bio-optical model results for case 1 waters,” Appl. Opt. 45(22), 5542–5567 (2006).
[Crossref] [PubMed]

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(D14), 16989–17013 (1997).
[Crossref]

M. I. Mishchenko, A. A. Lacis, and L. D. Travis, “Errors induced by the neglect of polarization in radiance calculations for Rayleigh-scattering atmospheres,” J. Quant. Spectrosc. Radiat. Transf. 51(3), 491–510 (1994).
[Crossref]

Trepte, C. R.

Trepte, R. C.

Verstraete, M.

J. V. Martonchik, D. J. Diner, R. Kahn, M. Verstraete, B. Pinty, H. R. Gordon, and T. P. Ackerman, “Techniques for the retrieval of aerosol properties over land and ocean using multiangle imaging,” IEEE Trans. Geosci. Rem. Sens. 36(4), 1212–1227 (1998).
[Crossref]

Victori, S.

D. Antoine, A. Morel, E. Leymarie, A. Houyou, B. Gentili, S. Victori, J. P. Buis, S. Meunier, M. Canini, D. Crozel, B. Fougnie, and P. Henry, “Underwater radiance distributions measured with miniaturized multispectral radiance cameras,” J. Atmos. Ocean. Technol. 30(1), 74–95 (2013).
[Crossref]

Voss, K.

Voss, K. J.

Wang, Y.

Waquet, F.

F. Waquet, F. Peers, P. Goloub, F. Ducos, F. Thieuleux, Y. Derimian, J. Riedi, M. Chami, and D. Tanré, “Retrieval of the Eyjafjallajökull volcanic aerosol optical and microphysical properties from POLDER/PARASOL measurements,” Atmos. Chem. Phys. 14(4), 1755–1768 (2014).
[Crossref]

J. Chowdhary, B. Cairns, F. Waquet, K. Knobelspiesse, M. Ottaviani, J. Redemann, L. Travis, and M. Mishchenko, “Sensitivity of multiangle, multispectral polarimetric remote sensing over open oceans to water-leaving radiance: analyses of RSP data acquired during the MILAGRO campaign,” Remote Sens. Environ. 118, 284–308 (2012), doi:.
[Crossref]

Waterman, T. H.

T. H. Waterman, “Polarization patterns in submarine illumination,” Science 120(3127), 927–932 (1954).
[Crossref] [PubMed]

Winker, D.

Yang, P.

Yokota, T.

Y. Ota, A. Higurashi, T. Nakajima, and T. Yokota, “Matrix formulations of radiative transfer including the polarization effect in a coupled atmosphere–ocean system,” J. Quant. Spectrosc. Radiat. Transf. 111(6), 878–894 (2010).
[Crossref]

You, Y.

Zhai, P.

Zhai, P. W.

Zhu, Q.

X. He, Y. Bai, Q. Zhu, and F. Gong, “A vector radiative transfer model of coupled ocean–atmosphere system using matrix-operator method for rough sea-surface,” J. Quant. Spectrosc. Radiat. Transf. 111(10), 1426–1448 (2010).
[Crossref]

Zugger, M. E.

M. E. Zugger, A. Messmer, T. J. Kane, J. Prentice, B. Concannon, A. Laux, and L. Mullen, “Optical scattering properties of phytoplankton: Measurements and comparison of various species at scattering angles between 1°and 170°,” Limnol. Oceanogr. 53(1), 381–386 (2008).
[Crossref]

Appl. Opt. (14)

G. N. Plass, T. J. Humphreys, and G. W. Kattawar, “Ocean-atmosphere interface: its influence on radiation,” Appl. Opt. 20(6), 917–931 (1981).
[Crossref] [PubMed]

C. N. Adams and G. W. Kattawar, “Effect of volume-scattering function on the errors induced when polarization is neglected in radiance calculations in an atmosphere-ocean system,” Appl. Opt. 32(24), 4610–4617 (1993).
[Crossref] [PubMed]

H. R. Gordon, J. W. Brown, and R. H. Evans, “Exact Rayleigh scattering calculations for use with the Nimbus-7 coastal zone color scanner,” Appl. Opt. 27(5), 862–871 (1988).
[Crossref] [PubMed]

J. Cariou, B. L. Jeune, J. Lotrian, and Y. Guern, “Polarization effects of seawater and underwater targets,” Appl. Opt. 29(11), 1689–1695 (1990).
[Crossref] [PubMed]

M. Chami, R. Santer, and E. Dilligeard, “Radiative transfer model for the computation of radiance and polarization in an ocean-atmosphere system: polarization properties of suspended matter for remote sensing,” Appl. Opt. 40(15), 2398–2416 (2001).
[Crossref] [PubMed]

Z. Jin, T. P. Charlock, K. Rutledge, K. Stamnes, and Y. Wang, “Analytical solution of radiative transfer in the coupled atmosphere-ocean system with a rough surface,” Appl. Opt. 45(28), 7443–7455 (2006).
[Crossref] [PubMed]

Y. You, P. W. Zhai, G. W. Kattawar, and P. Yang, “Polarized radiance fields under a dynamic ocean surface: a three-dimensional radiative transfer solution,” Appl. Opt. 48(16), 3019–3029 (2009).
[Crossref] [PubMed]

J. Chowdhary, B. Cairns, and L. D. Travis, “Contribution of water-leaving radiances to multiangle, multispectral polarimetric observations over the open ocean: bio-optical model results for case 1 waters,” Appl. Opt. 45(22), 5542–5567 (2006).
[Crossref] [PubMed]

C. D. Mobley, “Polarized reflectance and transmittance properties of windblown sea surfaces,” Appl. Opt. 54(15), 4828–4849 (2015).
[Crossref] [PubMed]

J. T. Adams and G. W. Kattawar, “Neutral points in an atmosphere-ocean system. 1: Upwelling light field,” Appl. Opt. 36(9), 1976–1986 (1997).
[Crossref] [PubMed]

A. Morel and B. Gentili, “Diffuse reflectance of oceanic waters: its dependence on Sun angle as influenced by the molecular scattering contribution,” Appl. Opt. 30(30), 4427–4438 (1991).
[Crossref] [PubMed]

A. Morel and B. Gentili, “Diffuse reflectance of oceanic waters. III. Implication of bidirectionality for the remote-sensing problem,” Appl. Opt. 35(24), 4850–4862 (1996).
[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(30), 6289–6306 (2002).
[Crossref] [PubMed]

P. Zhai, Y. Hu, R. C. Trepte, D. Winker, P. Lucker, Z. Lee, and D. Josset, “Uncertainty in the bidirectional reflectance model for oceanic waters,” Appl. Opt. 54(13), 4061–4069 (2015).
[Crossref]

Atmos. Chem. Phys. (1)

F. Waquet, F. Peers, P. Goloub, F. Ducos, F. Thieuleux, Y. Derimian, J. Riedi, M. Chami, and D. Tanré, “Retrieval of the Eyjafjallajökull volcanic aerosol optical and microphysical properties from POLDER/PARASOL measurements,” Atmos. Chem. Phys. 14(4), 1755–1768 (2014).
[Crossref]

Atmos. Meas. Tech. (2)

J. A. Limbacher and R. A. Kahn, “MISR research-aerosol-algorithm refinements for dark water retrievals,” Atmos. Meas. Tech. 7(11), 3989–4007 (2014).
[Crossref]

A. M. Sayer, G. E. Thomas, and R. G. Grainger, “A sea surface reflectance model for (A)ATSR, and application to aerosol retrievals,” Atmos. Meas. Tech. 3(4), 813–838 (2010).
[Crossref]

Geophys. Res. Lett. (1)

A. Lacis, J. Chowdhary, M. I. Mishenko, and B. Cairns, “Modeling errors in diffuse-sky radiation: vector vs scalar treatment,” Geophys. Res. Lett. 25(2), 135–138 (1998).
[Crossref]

IEEE Trans. Geosci. Rem. Sens. (2)

P. Y. Deschamps, F. M. Breon, M. Leroy, A. Podaire, A. Bricaud, J. C. Buriez, and G. Seze, “The Polder mission - instrument characteristics and scientific objectives,” IEEE Trans. Geosci. Rem. Sens. 32(3), 598–615 (1994).
[Crossref]

J. V. Martonchik, D. J. Diner, R. Kahn, M. Verstraete, B. Pinty, H. R. Gordon, and T. P. Ackerman, “Techniques for the retrieval of aerosol properties over land and ocean using multiangle imaging,” IEEE Trans. Geosci. Rem. Sens. 36(4), 1212–1227 (1998).
[Crossref]

J. Astron. Astrophys. (1)

J. F. De Haan, P. B. Bosma, and J. W. Hovenier, “The adding method for multiple scattering calculations of polarized light,” J. Astron. Astrophys. 183, 371–391 (1987).

J. Atmos. Ocean. Technol. (1)

D. Antoine, A. Morel, E. Leymarie, A. Houyou, B. Gentili, S. Victori, J. P. Buis, S. Meunier, M. Canini, D. Crozel, B. Fougnie, and P. Henry, “Underwater radiance distributions measured with miniaturized multispectral radiance cameras,” J. Atmos. Ocean. Technol. 30(1), 74–95 (2013).
[Crossref]

J. Atmos. Sci. (1)

R. A. Kahn, W. H. Li, J. V. Martonchik, C. J. Bruegge, D. J. Diner, B. J. Gaitley, W. Abdou, O. Dubovik, B. Holben, A. Smirnov, Z. Jin, and D. Clark, “MISR calibration and implications for low-light-level aerosol retrieval over dark water,” J. Atmos. Sci. 62(4), 1032–1052 (2005).
[Crossref]

J. Geophys. Res. (2)

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(D14), 16989–17013 (1997).
[Crossref]

M. Chami and M. D. Platel, “Sensitivity of the retrieval of the inherent optical properties of marine particles in coastal waters to the directional variations and the polarization of the reflectance,” J. Geophys. Res. 112(C5), C05037 (2007).
[Crossref]

J. Geophys. Res. Atmos. (1)

J. L. Deuze, P. Goloub, M. Herman, A. Marchand, G. Perry, S. Susana, and D. Tanre, “Estimate of the aerosol properties over the ocean with POLDER,” J. Geophys. Res. Atmos. 105(D12), 15329–15346 (2000).
[Crossref]

J. Geophys. Res.- Oceans (1)

M. Chami, “Importance of the polarization in the retrieval of oceanic constituents from the remote sensing reflectance,” J. Geophys. Res.- Oceans 112(C5), C05026 (2007).
[Crossref]

J. Opt. Soc. Am. (1)

J. Quant. Spectrosc. Radiat. Transf. (6)

J. Lenoble, M. Herman, J. L. Deuze, B. Lafrance, R. Santer, and D. Tanre, “A successive order of scattering code for solving the vector equation of transfer in the earth’s atmosphere with aerosols,” J. Quant. Spectrosc. Radiat. Transf. 107(3), 479–507 (2007).
[Crossref]

M. I. Mishchenko, A. A. Lacis, and L. D. Travis, “Errors induced by the neglect of polarization in radiance calculations for Rayleigh-scattering atmospheres,” J. Quant. Spectrosc. Radiat. Transf. 51(3), 491–510 (1994).
[Crossref]

X. He, Y. Bai, Q. Zhu, and F. Gong, “A vector radiative transfer model of coupled ocean–atmosphere system using matrix-operator method for rough sea-surface,” J. Quant. Spectrosc. Radiat. Transf. 111(10), 1426–1448 (2010).
[Crossref]

Y. Ota, A. Higurashi, T. Nakajima, and T. Yokota, “Matrix formulations of radiative transfer including the polarization effect in a coupled atmosphere–ocean system,” J. Quant. Spectrosc. Radiat. Transf. 111(6), 878–894 (2010).
[Crossref]

A. Hollstein and J. Fischer, “Radiative transfer solutions for coupled atmosphere ocean systems using the matrix operator technique,” J. Quant. Spectrosc. Radiat. Transf. 113(7), 536–548 (2012).
[Crossref]

E. R. Sommersten, J. K. Lotsberg, K. Stamnes, and J. J. Stamnes, “Discrete ordinate and Monte Carlo simulations for polarized radiative transfer in a coupled system consisting of two media with different refractive indices,” J. Quant. Spectrosc. Radiat. Transf. 111(4), 616–633 (2010).
[Crossref]

Limnol. Oceanogr. (3)

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(8), 1453–1472 (1989).
[Crossref]

M. E. Zugger, A. Messmer, T. J. Kane, J. Prentice, B. Concannon, A. Laux, and L. Mullen, “Optical scattering properties of phytoplankton: Measurements and comparison of various species at scattering angles between 1°and 170°,” Limnol. Oceanogr. 53(1), 381–386 (2008).
[Crossref]

A. Morel and L. Prieur, “Analysis of variations in ocean color,” Limnol. Oceanogr. 22(4), 709–722 (1977).
[Crossref]

Limnol. Oceanogr. Methods (1)

J. K. Lotsberg, E. Marken, J. J. Stamnes, S. R. Erga, K. Aursland, and C. Olseng, “Laboratory measurements of light scattering from marine particles,” Limnol. Oceanogr. Methods 5, 34–40 (2007).
[Crossref]

Opt. Express (8)

B. Shao, J. S. Jaffe, M. Chachisvilis, and S. C. Esener, “Angular resolved light scattering for discriminating among marine picoplankton: modeling and experimental measurements,” Opt. Express 14(25), 12473–12484 (2006).
[Crossref] [PubMed]

H. Tan, R. Doerffer, T. Oishi, and A. Tanaka, “A new approach to measure the volume scattering function,” Opt. Express 21(16), 18697–18711 (2013).
[Crossref] [PubMed]

M. Chami, A. Thirouard, and T. Harmel, “POLVSM (Polarized Volume Scattering Meter) instrument: an innovative device to measure the directional and polarized scattering properties of hydrosols,” Opt. Express 22(21), 26403–26428 (2014).
[Crossref] [PubMed]

S. Kay, J. Hedley, S. Lavender, and A. Nimmo-Smith, “Light transfer at the ocean surface modeled using high resolution sea surface realizations,” Opt. Express 19(7), 6493–6504 (2011).
[Crossref] [PubMed]

P. W. Zhai, Y. Hu, C. R. Trepte, and P. L. Lucker, “A vector radiative transfer model for coupled atmosphere and ocean systems based on successive order of scattering method,” Opt. Express 17(4), 2057–2079 (2009).
[Crossref] [PubMed]

K. Voss and A. Chapin, “Upwelling radiance distribution camera system, NURADS,” Opt. Express 13(11), 4250–4262 (2005).
[Crossref] [PubMed]

K. J. Voss and N. Souaidia, “POLRADS: polarization radiance distribution measurement system,” Opt. Express 18(19), 19672–19680 (2010).
[Crossref] [PubMed]

T. Harmel and M. Chami, “Influence of polarimetric satellite data measured in the visible region on aerosol detection and on the performance of atmospheric correction procedure over open ocean waters,” Opt. Express 19(21), 20960–20983 (2011).
[Crossref] [PubMed]

Remote Sens. Environ. (1)

J. Chowdhary, B. Cairns, F. Waquet, K. Knobelspiesse, M. Ottaviani, J. Redemann, L. Travis, and M. Mishchenko, “Sensitivity of multiangle, multispectral polarimetric remote sensing over open oceans to water-leaving radiance: analyses of RSP data acquired during the MILAGRO campaign,” Remote Sens. Environ. 118, 284–308 (2012), doi:.
[Crossref]

Science (1)

T. H. Waterman, “Polarization patterns in submarine illumination,” Science 120(3127), 927–932 (1954).
[Crossref] [PubMed]

Other (8)

P. Zhai, Y. Hu, J. Chowdhary, R. C. Trepte, P. L. Lucker, and D. B. Josset, “A vector radiative transfer model for coupled atmosphere and ocean systems with a rough interface,” J. Quant. Spect. Radiative Transfer (2010).

Z. Jin, NASA Langley Research Center, One Enterprise Parkway, Suite 300, Hampton, Virginia 23666 (personal communication, 2015).

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Multiple Scattering of Light by Particles (New York, Cambridge University, 2006, pp.508,).

J. Chowdhary, Multiple Scattering of Polarized Light in Atmosphere-ocean Systems: Application to Sensitivity Analyses of Aerosol Polarimetry. (Ph.D thesis, Columbia University, 1999).

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

H. Slade, Y. C. Agrawal, and O. A. Mikkelsen, “Comparison of measured and theoretical scattering and polarization properties of narrow size range irregular sediment particles,” presented at Oceans, San Diego, 23–27 (2013).

E. P. Shettle and R. W. Fenn, ”Models for the aerosols of the lower atmosphere and the effects of humidity variations on their optical properties,”,Air Force Geophysics Laboratory. September 1979, AFGL-TR-79–0214, Environnemental Research papers, No. 676. (1979).

World Climate Research Programme, “A preliminary cloudless standard atmosphere for radiation computation,” WCP-112, WMO/TD Report No 24, Geneva, Switzerland, March (1986).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1
Fig. 1

Geometry of the propagation of the light across a rough sea surface for the case of a downward incident beam coming from the atmosphere and entering into the ocean (air to sea). The directions of the incident beam, the reflection and the transmission of light are shown. In Fig. 1, the notations are as follows: θia is the incidence angle (i.e. half angle between the incident and the reflection directions), θtw is the angle of refraction relative to the direction perpendicular to the facet of the wave n , θn is the zenith angle that corresponds to the direction perpendicular to the facet of wave, θt is the zenith angle of the transmission direction, ϕ is the azimuth, s , v , and t are the vectors describing the coordinates of the incident, reflected and transmitted light respectively. m is the refractive index of the water.

Fig. 2
Fig. 2

Geometry of the propagation of the light across a rough sea surface for the case of an upward radiation exiting the ocean (sea to air). The directions of the incident beam, the reflection and the transmission of light are shown. The incident direction is given by the vector s . In Fig. 2, the notations are as follows: θiw and θta are respectively the incidence angle and the angle of refraction relative to the direction perpendicular to the facet of wave n . θn is the zenith angle that corresponds to the direction perpendicular to the facet of wave. θ’ and ϕ' are respectively the zenith and azimuth angle of the incident beam relative to the vertical axis z. θ’ and ϕ' are the zenith and azimuth angle of the reflected beam. s , v , and t are the vectors describing the coordinates of the incident, reflected and transmitted light respectively. m is the refractive index of the water.

Fig. 3
Fig. 3

Comparisons of the Stokes parameters I, Q and U normalized to an extraterrestrial irradiance value of π as a function of the viewing angle between the eGAP and OSOAA models at the sea surface level (level 0 + ): (a) at 412 (top panel) and (b) at 660 nm (lower panel) for the conditions of simulations outlined in section 3.1 (solar zenith angle SZA value of 30°, wind speed value of 7 m s−1 (W07)). In the left column, eGAP calculations are shown as solid lines; OSOAA outputs are shown as dotted lines. The absolute differences (middle column) between the eGAP and OSOAA Stokes parameters are noted ΔI = IeGAP-IOSOAA, ΔQ = QeGAP-QOSOAA and ΔU = UeGAP-UOSOAA. The relative differences (right column), which are defined as ΔI/IeGAP, ΔQ/QeGAP, ΔU/UeGAP, are expressed in percents.

Fig. 4
Fig. 4

Polar diagram of the ratio between the water leaving reflectance (Stokes parameter I) calculated at level 0 + at all geometries of observations and the water leaving reflectance calculated at nadir direction (i.e. the viewing angle is zero) (Stokes parameter Inadir) when the wind speed is 7 m s−1, for a solar zenith angle of 30°: (a) for the phytoplankton case of simulation (the chlorophyll a concentration is 1 mg m−3), (b) for the mineral-like particles case of simulations (the mineral-like particles concentration is 5 mg ��−1). Note that the sole contribution of the ocean layer is represented here (see text in section 4.1). The circles correspond to the viewing angle by step of 10° where the viewing angle of 0° is in the center of the diagram. The detailed conditions of simulation are reported in section 4.1. The convention used here for the definition of the azimuth is as follows: an azimuth value of 180° corresponds to the half-plane that contains the sun (solar plane) (i.e. backscattering directions) while the azimuth value of 0° corresponds to the half-plane that contains the specular reflection (anti-solar half–plane) (i.e. forward scattering directions).

Fig. 5
Fig. 5

Influence of the wind speed on the directional variations of the water leaving reflectance at the level 0 + . The ratio I/Inadir is calculated here as a function of wind speed for a viewing zenith angle value of 60° in the anti-solar half-plane (azimuth value of 0°). The solar zenith angle value is 30°. The results are shown for the cases where phytoplankton and mineral-like hydrosols are present in the water column. The conditions of simulations are similar as those used in Fig. 4 (see also text in section 4.1).

Fig. 6
Fig. 6

Polar diagrams of the degree of polarization calculated at level 0 + at all geometries of observations when the wind speed is 7 m s−1, for a solar zenith angle of 30°: (a) for the phytoplankton case of simulation (the chlorophyll a concentration is 1 mg m−3), (b) for the mineral-like particles case of simulations (the mineral-like particles concentration is 5 mg ��−1). Note that the sole contribution of the ocean layer is represented here (see text in section 4.1). The circles correspond to the viewing angle by step of 10° where the viewing angle of 0° is in the center of the diagram. The detailed conditions of simulation are reported in section 4.1. The convention used here for the definition of the azimuth is as follows: an azimuth value of 180° corresponds to the half-plane that contains the sun (solar plane) (i.e. backscattering directions) while the azimuth value of 0° corresponds to the half-plane that contains the specular reflection (anti-solar half–plane) (i.e. forward scattering directions).

Tables (2)

Tables Icon

Table 1 Values of the optical properties of the air and seawater molecules used for the validation of OSOAA model. The absorption and scattering coefficients of pure seawater, noted aw and bw respectively, are also reported (in m−1).

Tables Icon

Table 2 Results showing the conservation of energy within OSOAA model based on Eq. (31). Ed(0 + ) is the downwelling plane irradiance just above the sea surface; Ed(0-) is the downwelling irradiance just beneath the surface, Eu(0 + ) is the upwelling irradiance just above the sea surface. The simulations are carried out using OSOAA model with a transparent atmosphere, a transparent ocean, and a solar zenith angle of 30 degrees (see section 3.2 for details). Since the extraterrestrial solar irradiance value is π, the irradiances values are dimensionless. The relative difference between Ed(0 + ) and the sum (Ed(0-) + Eu(0 + )) is also reported (in %).

Equations (32)

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

p( θ n , φ n )= 1 π σ 2 . cos 3 θ n ×exp( tan 2 θ n σ 2 ),
σ 2 = 0.003 + 0.00512 ×W.
{ Order 1 : L ¯ R 1 ( τ, μ r , φ r ) = 1 4π. μ r × RAA ¯ ¯ ( μ r , φ r , μ 0 , φ 0 )× E ¯ .exp( τ/ μ 0 ), Order n : L ¯ R n ( τ, μ r , φ r ) = 1 4π. μ r × φ'=0 2π μ'=1 0 RAA ¯ ¯ ( μ r , φ r ,μ',φ' )× L ¯ n1 ( τ,μ',φ' ).dμ'.dφ',
RAA ¯ ¯ ( μ r , φ r ,μ',φ' )= g R ( μ r , φ r ,μ',φ' ) × ¯ ¯ ( χ ). RF ¯ ¯ AA ( θ i a ). ¯ ¯ ( χ' ),
g R ( μ r , φ r ,μ',φ' )= 1 σ 2 . cos 4 θ n ×exp( tan 2 θ n σ 2 ),
¯ ¯ ( χ' )=( 1 0 0 0 cos2χ' sin2χ' 0 sin2χ' cos2χ' ).
RF ¯ ¯ AA ( θ i a )=( R 11 ( θ i a ) R 12 ( θ i a ) 0 R 12 ( θ i a ) R 11 ( θ i a ) 0 0 0 R 33 ( θ i a ) ),
{ R 11 ( θ i a )=0.5×[ ( r ( θ i a ) ) 2 + ( r r ( θ i a ) ) 2 ], R 12 ( θ i a )=0.5×[ ( r ( θ i a ) ) 2 ( r r ( θ i a ) ) 2 ] , R 33 ( θ i a )= r ( θ i a )× r r ( θ i a ),
r ( θ i a )= m 2 .cos θ i a - m 2 - sin 2 ( θ i a ) m 2 .cos θ i a + m 2 - sin 2 ( θ i a ) ,
r r ( θ i a )= cos θ i a - m 2 - sin 2 ( θ i a ) cos θ i a + m 2 - sin 2 ( θ i a ) ,
{ Order 1 : L ¯ T 1 0 ( τ, μ t , φ t ) = 1 π. μ t × TAW ¯ ¯ ( μ t , φ t , μ 0 , φ 0 ). E ¯ .exp( τ/ μ 0 ), Order n : L ¯ T n 0 ( τ, μ t , φ t ) = 1 π. μ t × φ'=0 2π μ'=1 0 TAW ¯ ¯ ( μ t , φ t ,μ',φ' ). L ¯ n1 0+ ( τ,μ',φ' ).dμ'.dφ',
TAW ¯ ¯ ( μ t , φ t ,μ',φ' )= g T ( μ t , φ t ,μ',φ' )× ¯ ¯ ( χ t ). TF ¯ ¯ AW FLUX ( θ i a ). ¯ ¯ ( χ t ' ) × m 2 .cos θ t w .cos θ i a ( m.cos θ t w cos θ i a ) 2 ,
g T ( μ t , φ t ,μ',φ' )= g R ( μ r , φ r ,μ',φ' ).
TF ¯ ¯ AW FLUX ( θ i a )= m.cos θ t w cos θ i a ×( t 11 ( θ i a ) t 12 ( θ i a ) 0 t 12 ( θ i a ) t 11 ( θ i a ) 0 0 0 t 33 ( θ i a ) ),
{ t 11 ( θ i a )=0.5×[ ( t ( θ i a ) ) 2 + ( t r ( θ i a ) ) 2 ], t 12 ( θ i a )=0.5×[ ( t ( θ i a ) ) 2 ( t r ( θ i a ) ) 2 ] t 33 ( θ i a )= t ( θ i a )× t r ( θ i a ), ,
t ( θ i a )= 1 m ×( 1+ r ( θ i a ) ),
t r ( θ i a )=1+ r r ( θ i a ).
L ¯ R n sea ( 0-, μ r , φ r )= 1 4π.( μ r ) × φ'=0 2π μ'=0 1 RWW ¯ ¯ ( μ r , φ r ,μ',φ' ). L ¯ n1 sea ( 0-,μ',φ' ).dμ'.dφ' ,
RWW ¯ ¯ ( μ,φ,μ',φ' )= g R ( μ r , φ r ,μ',φ' ) × ¯ ¯ ( χ w ). RF ¯ ¯ WW ( θ i w ). ¯ ¯ ( χ w ' ),
RF ¯ ¯ WW ( θ i w )=( R 11 ( θ i w ) R 12 ( θ i w ) 0 R 12 ( θ i w ) R 11 ( θ i w ) 0 0 0 R 33 ( θ i w ) ),
{ R 11 ( θ i w )=0.5×[ ( r ( θ i w ) ) 2 + ( r r ( θ i w ) ) 2 ], R 12 ( θ i w )=0.5×[ ( r ( θ i w ) ) 2 ( r r ( θ i w ) ) 2 ], R 33 ( θ i w )= r ( θ i w )× r r ( θ i w ),
r ( θ i w )= cos θ i w m× 1-m 2 . sin 2 ( θ i w ) cos θ i w +m× 1-m 2 . sin 2 ( θ i w ) ,
r r ( θ i w )= m.cos θ i w 1-m 2 . sin 2 ( θ i w ) m.cos θ i w + 1-m 2 . sin 2 ( θ i w ) .
{ R 11 ( θ i w > θ lim w )=1, R 12 ( θ i w > θ lim w )=0, R 33 ( θ i w > θ lim w )=1.
L ¯ T n sea ( 0+, μ t , φ t )= 1 π. μ t × φ'=0 2π μ'=0 1 TWA ¯ ¯ ( μ t , φ t ,μ',φ' ). L ¯ n1 sea ( 0-,μ',φ' ).dμ'.dφ' ,
TWA ¯ ¯ ( μ t , φ t ,μ',φ' )= g T ( μ t , φ t ,μ',φ' )× ¯ ¯ ( χ wt ). TF ¯ ¯ WA FLUX ( θ i w ). ¯ ¯ ( χ wt ' ) × cos θ t a .cos θ i w ( m.cos θ i w cos θ t a ) 2 ,
TF ¯ ¯ WA FLUX ( θ i w )= cos θ t a m.cos θ i w ×( t 11 ( θ i w ) t 12 ( θ i w ) 0 t 12 ( θ i w ) t 11 ( θ i w ) 0 0 0 t 33 ( θ i w ) ),
{ t 11 ( θ i w )=0.5×[ ( t ( θ i w ) ) 2 + ( t r ( θ i w ) ) 2 ], t 12 ( θ i w )=0.5×[ ( t ( θ i w ) ) 2 ( t r ( θ i w ) ) 2 ], t 33 ( θ i w )= t ( θ i w )× t r ( θ i w ),
t ( θ i w )=m×( 1+ r ( θ i w ) ),
t r ( θ i w )=1+ r r ( θ i w ).
E d (0+)= E d (0)+ E u (0+)+ E u (0),
DOP= Q 2 + U 2 I .

Metrics