Abstract

We compare Monte Carlo (MC) and discrete-ordinate radiative-transfer (DISORT) simulations of irradiances in a one-dimensional coupled atmosphere-ocean (CAO) system consisting of horizontal plane-parallel layers. The two models have precisely the same physical basis, including coupling between the atmosphere and the ocean, and we use precisely the same atmospheric and oceanic input parameters for both codes. For a plane atmosphere-ocean interface we find agreement between irradiances obtained with the two codes to within 1%, both in the atmosphere and the ocean. Our tests cover case 1 water, scattering by density fluctuations both in the atmosphere and in the ocean, and scattering by particulate matter represented by a one-parameter Henyey-Greenstein (HG) scattering phase function. The CAO-MC code has an advantage over the CAO-DISORT code in that it can handle surface waves on the atmosphere-ocean interface, but the CAO-DISORT code is computationally much faster. Therefore we use CAO-MC simulations to study the influence of ocean surface waves and propose a way to correct the results of the CAO-DISORT code so as to obtain fast and accurate underwater irradiances in the presence of surface waves.

© 2003 Optical Society of America

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  3. K. Stamnes, W. Li, B. Yan, A. Barnard, W. S. Pegau, J. J. Stamnes, “Accurate and self-consistent ocean color algorithm: simultaneous retrieval of aerosol optical properties and chlorophyll concentrations,” Appl. Opt. 49, 939–951 (2003).
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    [CrossRef]
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    [CrossRef] [PubMed]
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  15. G. Kattawar, C. Adams, “Stokes vector calculations of the submarine light field in an atmosphere-ocean with scattering according to the Rayleigh phase matrix: effect of interface refractive index on radiance and polarization,” Limnol. Oceanogr. 34, 1453–1472 (1989).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2003 (2)

K. Stamnes, W. Li, B. Yan, A. Barnard, W. S. Pegau, J. J. Stamnes, “Accurate and self-consistent ocean color algorithm: simultaneous retrieval of aerosol optical properties and chlorophyll concentrations,” Appl. Opt. 49, 939–951 (2003).
[CrossRef]

B. Yan, K. Stamnes, “Fast yet accurate computation of the complete radiance distribution in the coupled atmosphere-ocean system,” J. Quant. Spectrosc. Radiat. Transfer 76, 207–223 (2003).
[CrossRef]

2001 (2)

1999 (1)

Z. Jin, J. J. Simpson, “Bidirectional anisotropic reflectance of snow and sea ice in AVHRR channel 1 and 2 spectral regions—Part I: theoretical analysis,” IEEE Trans. Geosci. Remote Sensing 37, 543–554 (1999).
[CrossRef]

1998 (1)

1994 (2)

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

Z. Jin, K. Stamnes, W. F. Weeks, S. C. Tsay, “The effect of sea ice on the solar energy budget in the atmosphere-sea ice-ocean system: a model study,” Geophys. Res. 99, 25281–25294 (1994).
[CrossRef]

1993 (1)

1991 (2)

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

A. Morel, “Light and marine photosynthesis: a model with geochemical and climatological implications,” Prog. Oceanogr. 26, 263–306 (1991).
[CrossRef]

1989 (2)

C. Mobley, “A numerical model for the computation of radiance distributions in natural waters with wind-roughened surfaces,” Limnol. Oceanogr. 34, 1473–1483 (1989).
[CrossRef]

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

1988 (2)

1983 (1)

1975 (2)

1974 (1)

1973 (1)

G. Kattawar, G. N. Plass, J. A. Quinn, “Monte Carlo calculation of polarization of radiation in the earth’s atmosphere-ocean system,” J. Phys. Oceanogr. 3, 353–372 (1973).
[CrossRef]

1972 (2)

G. Plass, G. Kattawar, “Monte Carlo calculations of radiative transfer in the Earth’s atmosphere ocean system: I. Flux in the atmosphere and ocean,” Phys. Oceanogr. 2, 139–145 (1972).
[CrossRef]

D. G. Collins, W. G. Blattner, M. B. Wells, H. G. Horak, “Backward Monte Carlo calculations of the polarization characteristics of the radiation field emerging from spherical shell atmospheres,” Appl. Opt. 11, 2684–2705 (1972).
[CrossRef] [PubMed]

1969 (1)

1968 (1)

G. N. Plass, G. W. Kattawar, “Monte Carlo calculations of light scattering from clouds,” Appl. Opt. 7, 669–704 (1968).
[CrossRef]

1954 (1)

1941 (1)

L. C. Henyey, J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).
[CrossRef]

Adams, C.

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

Barnard, A.

K. Stamnes, W. Li, B. Yan, A. Barnard, W. S. Pegau, J. J. Stamnes, “Accurate and self-consistent ocean color algorithm: simultaneous retrieval of aerosol optical properties and chlorophyll concentrations,” Appl. Opt. 49, 939–951 (2003).
[CrossRef]

Blattner, W.

Blattner, W. G.

Born, M.

M. Born, E. Wolf, Principles of Optics (Cambridge University, Cambridge, UK, 1980).

Bosch, J. J. T.

Brown, O.

Chen, B.

Collins, D.

Collins, D. G.

Cox, C.

Elterman, L.

L. Elterman, “UV, visible, and IR attenuation for altitude to 50 km,” AFCRL-68-0153 (Air Force Cambridge Research Laboratory, Bedford, Mass., 1968).

Erga, S. R.

Fenn, R. W.

E. P. Shettle, 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, Hanscomb AFB, Mass. 01731, 1979).

Ferwerda, H. A.

Frette, Ø.

Gentili, B.

Gordon, H.

Gordon, H. R.

Greenstein, J. L.

L. C. Henyey, J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).
[CrossRef]

Groenhuis, R. A. J.

Guinn, J.

Henyey, L. C.

L. C. Henyey, J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).
[CrossRef]

Horak, H.

Horak, H. G.

Jacobs, M.

Jayaweera, K.

Jiang, S.

S. Jiang, K. Stamnes, “Enhancement of the downward solar irradiance across the atmosphere-sea ice interface,” J. Geophys. Res., submitted for publication.

Jin, Z.

Z. Jin, J. J. Simpson, “Bidirectional anisotropic reflectance of snow and sea ice in AVHRR channel 1 and 2 spectral regions—Part I: theoretical analysis,” IEEE Trans. Geosci. Remote Sensing 37, 543–554 (1999).
[CrossRef]

Z. Jin, K. Stamnes, W. F. Weeks, S. C. Tsay, “The effect of sea ice on the solar energy budget in the atmosphere-sea ice-ocean system: a model study,” Geophys. Res. 99, 25281–25294 (1994).
[CrossRef]

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

C. D. Mobley, B. Gentili, H. R. Gordon, Z. Jin, G. W. Kattawar, A. Morel, P. Reinersman, K. Stamnes, R. H. Stavn, “Comparison of numerical models for computing underwater light fields,” Appl. Opt. 32, 7484–7504 (1993).
[CrossRef] [PubMed]

Kattawar, G.

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

G. Plass, G. Kattawar, J. Guinn, “Radiative transfer in the Earth’s atmosphere and ocean: influence of ocean waves,” Appl. Opt. 14, 1924–1936 (1975).
[CrossRef] [PubMed]

G. Kattawar, G. N. Plass, J. A. Quinn, “Monte Carlo calculation of polarization of radiation in the earth’s atmosphere-ocean system,” J. Phys. Oceanogr. 3, 353–372 (1973).
[CrossRef]

G. Plass, G. Kattawar, “Monte Carlo calculations of radiative transfer in the Earth’s atmosphere ocean system: I. Flux in the atmosphere and ocean,” Phys. Oceanogr. 2, 139–145 (1972).
[CrossRef]

G. Plass, G. Kattawar, “Radiative transfer in an atmosphere-ocean system,” Appl. Opt. 8, 455–466 (1969).
[CrossRef]

Kattawar, G. W.

Li, W.

K. Stamnes, W. Li, B. Yan, A. Barnard, W. S. Pegau, J. J. Stamnes, “Accurate and self-consistent ocean color algorithm: simultaneous retrieval of aerosol optical properties and chlorophyll concentrations,” Appl. Opt. 49, 939–951 (2003).
[CrossRef]

Mobley, C.

C. Mobley, “A numerical model for the computation of radiance distributions in natural waters with wind-roughened surfaces,” Limnol. Oceanogr. 34, 1473–1483 (1989).
[CrossRef]

Mobley, C. D.

Morel, A.

C. D. Mobley, B. Gentili, H. R. Gordon, Z. Jin, G. W. Kattawar, A. Morel, P. Reinersman, K. Stamnes, R. H. Stavn, “Comparison of numerical models for computing underwater light fields,” Appl. Opt. 32, 7484–7504 (1993).
[CrossRef] [PubMed]

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

A. Morel, “Light and marine photosynthesis: a model with geochemical and climatological implications,” Prog. Oceanogr. 26, 263–306 (1991).
[CrossRef]

A. Morel, “Optical properties of pure water and pure sea water,” in Optical Aspects of Oceanography, N. G. Jerlov, E. S. Nielsen, eds. (Academic, New York, 1974), pp. 1–24.

Munk, W.

Pegau, W. S.

K. Stamnes, W. Li, B. Yan, A. Barnard, W. S. Pegau, J. J. Stamnes, “Accurate and self-consistent ocean color algorithm: simultaneous retrieval of aerosol optical properties and chlorophyll concentrations,” Appl. Opt. 49, 939–951 (2003).
[CrossRef]

Plass, G.

Plass, G. N.

G. Kattawar, G. N. Plass, J. A. Quinn, “Monte Carlo calculation of polarization of radiation in the earth’s atmosphere-ocean system,” J. Phys. Oceanogr. 3, 353–372 (1973).
[CrossRef]

G. N. Plass, G. W. Kattawar, “Monte Carlo calculations of light scattering from clouds,” Appl. Opt. 7, 669–704 (1968).
[CrossRef]

Quinn, J. A.

G. Kattawar, G. N. Plass, J. A. Quinn, “Monte Carlo calculation of polarization of radiation in the earth’s atmosphere-ocean system,” J. Phys. Oceanogr. 3, 353–372 (1973).
[CrossRef]

Reinersman, P.

Shettle, E. P.

E. P. Shettle, 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, Hanscomb AFB, Mass. 01731, 1979).

Simpson, J. J.

Z. Jin, J. J. Simpson, “Bidirectional anisotropic reflectance of snow and sea ice in AVHRR channel 1 and 2 spectral regions—Part I: theoretical analysis,” IEEE Trans. Geosci. Remote Sensing 37, 543–554 (1999).
[CrossRef]

Stamnes, J. J.

Stamnes, K.

K. Stamnes, W. Li, B. Yan, A. Barnard, W. S. Pegau, J. J. Stamnes, “Accurate and self-consistent ocean color algorithm: simultaneous retrieval of aerosol optical properties and chlorophyll concentrations,” Appl. Opt. 49, 939–951 (2003).
[CrossRef]

B. Yan, K. Stamnes, “Fast yet accurate computation of the complete radiance distribution in the coupled atmosphere-ocean system,” J. Quant. Spectrosc. Radiat. Transfer 76, 207–223 (2003).
[CrossRef]

Ø. Frette, S. R. Erga, J. J. Stamnes, K. Stamnes, “Optical remote sensing of waters with vertical structure,” Appl. Opt. 40, 1478–1487 (2001).
[CrossRef]

B. Chen, K. Stamnes, J. J. Stamnes, “Validity of diffusion approximation in bio-optical imaging,” Appl. Opt. 40, 6356–6366 (2001).
[CrossRef]

Ø. Frette, J. J. Stamnes, K. Stamnes, “Optical remote sensing of marine constituents in coastal waters: a feasibility study,” Appl. Opt. 37, 8318–8326 (1998).
[CrossRef]

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

Z. Jin, K. Stamnes, W. F. Weeks, S. C. Tsay, “The effect of sea ice on the solar energy budget in the atmosphere-sea ice-ocean system: a model study,” Geophys. Res. 99, 25281–25294 (1994).
[CrossRef]

C. D. Mobley, B. Gentili, H. R. Gordon, Z. Jin, G. W. Kattawar, A. Morel, P. Reinersman, K. Stamnes, R. H. Stavn, “Comparison of numerical models for computing underwater light fields,” Appl. Opt. 32, 7484–7504 (1993).
[CrossRef] [PubMed]

K. Stamnes, S. C. Tsay, W. J. Wiscombe, K. Jayaweera, “Numerically stable algorithm for discrete-ordinate-method radiative transfer in multiple scattering and emitting layered media,” Appl. Opt. 27, 2502–2509 (1988).
[CrossRef] [PubMed]

S. Jiang, K. Stamnes, “Enhancement of the downward solar irradiance across the atmosphere-sea ice interface,” J. Geophys. Res., submitted for publication.

G. E. Thomas, K. Stamnes, Radiative Transfer in the Atmosphere and Ocean (Cambridge University, Cambridge, UK, 1999).

Stavn, R.

Stavn, R. H.

Thomas, G. E.

G. E. Thomas, K. Stamnes, Radiative Transfer in the Atmosphere and Ocean (Cambridge University, Cambridge, UK, 1999).

Tsay, S. C.

Z. Jin, K. Stamnes, W. F. Weeks, S. C. Tsay, “The effect of sea ice on the solar energy budget in the atmosphere-sea ice-ocean system: a model study,” Geophys. Res. 99, 25281–25294 (1994).
[CrossRef]

K. Stamnes, S. C. Tsay, W. J. Wiscombe, K. Jayaweera, “Numerically stable algorithm for discrete-ordinate-method radiative transfer in multiple scattering and emitting layered media,” Appl. Opt. 27, 2502–2509 (1988).
[CrossRef] [PubMed]

van de Hulst, H. C.

H. C. van de Hulst, Multiple Light Scattering—Tables, Formulas and Applications (Academic, New York, 1980).

Weeks, W. F.

Z. Jin, K. Stamnes, W. F. Weeks, S. C. Tsay, “The effect of sea ice on the solar energy budget in the atmosphere-sea ice-ocean system: a model study,” Geophys. Res. 99, 25281–25294 (1994).
[CrossRef]

Weidemann, A.

Wells, M.

Wells, M. B.

Wiscombe, W. J.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Cambridge University, Cambridge, UK, 1980).

Yan, B.

K. Stamnes, W. Li, B. Yan, A. Barnard, W. S. Pegau, J. J. Stamnes, “Accurate and self-consistent ocean color algorithm: simultaneous retrieval of aerosol optical properties and chlorophyll concentrations,” Appl. Opt. 49, 939–951 (2003).
[CrossRef]

B. Yan, K. Stamnes, “Fast yet accurate computation of the complete radiance distribution in the coupled atmosphere-ocean system,” J. Quant. Spectrosc. Radiat. Transfer 76, 207–223 (2003).
[CrossRef]

Appl. Opt. (16)

Ø. Frette, J. J. Stamnes, K. Stamnes, “Optical remote sensing of marine constituents in coastal waters: a feasibility study,” Appl. Opt. 37, 8318–8326 (1998).
[CrossRef]

Ø. Frette, S. R. Erga, J. J. Stamnes, K. Stamnes, “Optical remote sensing of waters with vertical structure,” Appl. Opt. 40, 1478–1487 (2001).
[CrossRef]

K. Stamnes, W. Li, B. Yan, A. Barnard, W. S. Pegau, J. J. Stamnes, “Accurate and self-consistent ocean color algorithm: simultaneous retrieval of aerosol optical properties and chlorophyll concentrations,” Appl. Opt. 49, 939–951 (2003).
[CrossRef]

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

B. Chen, K. Stamnes, J. J. Stamnes, “Validity of diffusion approximation in bio-optical imaging,” Appl. Opt. 40, 6356–6366 (2001).
[CrossRef]

K. Stamnes, S. C. Tsay, W. J. Wiscombe, K. Jayaweera, “Numerically stable algorithm for discrete-ordinate-method radiative transfer in multiple scattering and emitting layered media,” Appl. Opt. 27, 2502–2509 (1988).
[CrossRef] [PubMed]

D. G. Collins, W. G. Blattner, M. B. Wells, H. G. Horak, “Backward Monte Carlo calculations of the polarization characteristics of the radiation field emerging from spherical shell atmospheres,” Appl. Opt. 11, 2684–2705 (1972).
[CrossRef] [PubMed]

G. N. Plass, G. W. Kattawar, “Monte Carlo calculations of light scattering from clouds,” Appl. Opt. 7, 669–704 (1968).
[CrossRef]

C. D. Mobley, B. Gentili, H. R. Gordon, Z. Jin, G. W. Kattawar, A. Morel, P. Reinersman, K. Stamnes, R. H. Stavn, “Comparison of numerical models for computing underwater light fields,” Appl. Opt. 32, 7484–7504 (1993).
[CrossRef] [PubMed]

H. Gordon, O. Brown, M. Jacobs, “Computed relationships between the inherent and apparent optical properties of a flat homogeneous ocean,” Appl. Opt. 14, 417–427 (1975).
[CrossRef] [PubMed]

G. Plass, G. Kattawar, J. Guinn, “Radiative transfer in the Earth’s atmosphere and ocean: influence of ocean waves,” Appl. Opt. 14, 1924–1936 (1975).
[CrossRef] [PubMed]

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

W. Blattner, H. Horak, D. Collins, M. Wells, “Monte Carlo studies of the sky radiation at twilight,” Appl. Opt. 13, 534–547 (1974).
[CrossRef] [PubMed]

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

G. Plass, G. Kattawar, “Radiative transfer in an atmosphere-ocean system,” Appl. Opt. 8, 455–466 (1969).
[CrossRef]

R. A. J. Groenhuis, H. A. Ferwerda, J. J. T. Bosch, “Scattering and absorption of turbid materials determined from reflected measurements,” Appl. Opt. 22, 2456–2462 (1983).
[CrossRef] [PubMed]

Astrophys. J. (1)

L. C. Henyey, J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).
[CrossRef]

Geophys. Res. (1)

Z. Jin, K. Stamnes, W. F. Weeks, S. C. Tsay, “The effect of sea ice on the solar energy budget in the atmosphere-sea ice-ocean system: a model study,” Geophys. Res. 99, 25281–25294 (1994).
[CrossRef]

IEEE Trans. Geosci. Remote Sensing (1)

Z. Jin, J. J. Simpson, “Bidirectional anisotropic reflectance of snow and sea ice in AVHRR channel 1 and 2 spectral regions—Part I: theoretical analysis,” IEEE Trans. Geosci. Remote Sensing 37, 543–554 (1999).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Phys. Oceanogr. (1)

G. Kattawar, G. N. Plass, J. A. Quinn, “Monte Carlo calculation of polarization of radiation in the earth’s atmosphere-ocean system,” J. Phys. Oceanogr. 3, 353–372 (1973).
[CrossRef]

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

B. Yan, K. Stamnes, “Fast yet accurate computation of the complete radiance distribution in the coupled atmosphere-ocean system,” J. Quant. Spectrosc. Radiat. Transfer 76, 207–223 (2003).
[CrossRef]

Limnol. Oceanogr. (2)

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

C. Mobley, “A numerical model for the computation of radiance distributions in natural waters with wind-roughened surfaces,” Limnol. Oceanogr. 34, 1473–1483 (1989).
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