Abstract

A three-dimensional Monte Carlo code is used to compute the ultraviolet zenith sky radiance; the code is validated by comparison with a successive-orders-of-scattering code. The amplifications of global irradiance, diffuse irradiance, and zenith radiance that are due to multiple reflectances between a snow-covered ground surface and the atmosphere are compared. For an inhomogeneous Lambertian surface, the contribution of the site environment is analyzed; it depends slightly on the atmospheric turbidity and on the surface reflectance distribution. However, in most cases one can expect approximately 12–15% of the reflected photon contribution to come from within 1 km about the observation site, 25–30% come from areas from 1 to 5 km from the site, 43–47% from 5 to 30 km, and still 10–15% reflected at larger distances. An average contribution function is proposed and used to compute an effective reflectance, which permits retrieval of the sky radiance within 2–4% with a one-dimensional model.

© 2000 Optical Society of America

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References

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  1. S. Chandrasekhar, Radiative Transfer (Dover, New York, 1949).
  2. E. Shettle, A. E. S. Green, “Multiple scattering calculation of the middle ultraviolet reaching the ground,” Appl. Opt. 13, 1567–1581 (1974).
    [CrossRef] [PubMed]
  3. J. Lenoble, “Modeling of the influence of snow reflectance on ultraviolet irradiance for cloudless sky,” Appl. Opt. 37, 2441–2447 (1998).
    [CrossRef]
  4. T. F. Eck, P. K. Bhartia, P. H. Hwang, L. L. Stowe, “Reflectivity of Earth’s surface and clouds in ultraviolet from satellite observations,” J. Geophys. Res. 92, 4287–4296 (1987).
    [CrossRef]
  5. M. Blumthaler, W. Ambach, “Solar UV albedo of various surfaces,” Photochem. Photobiol. 48, 85–88 (1988).
    [CrossRef] [PubMed]
  6. U. Feister, R. Grewe, “Spectral albedo measurements in the UV and visible region over different types of surfaces,” Photochem. Photobiol. 62, 736–744 (1995).
    [CrossRef]
  7. C. Sergent, E. Pougatch, M. Sudul, B. Bourdelles, “Experimental investigation of optical snow properties,” Ann. Glaciol. 17, 281–287 (1993).
  8. R. L. McKenzie, K. J. Paulin, S. Madronich, “Effects of snow cover on UV irradiance and surface albedo: a case study,” J. Geophys. Res. 103, 28,785–28,792 (1998).
    [CrossRef]
  9. E. Pachart, J. Lenoble, C. Brogniez, D. Masserot, J. L. Bocquet, “Ultraviolet spectral irradiance in the French Alps: results of two campaigns,” J. Geophys. Res. 104, 16,777–16,784 (1999).
    [CrossRef]
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    [CrossRef]
  11. M. Degünther, R. Meerkötter, A. Albold, G. Seckmeyer, “Case study of inhomogeneous surface albedo on UV irradiance,” Geophys. Res. Lett. 25, 3587–3590 (1998).
    [CrossRef]
  12. P. Ricchiazzi, C. Gautier, “Investigation of the effect of surface heterogeneity and topography on the radiation environment of Palmer Station, Antarctica, with an hybrid 3-D radiative transfer model,” J. Geophys. Res. 103, 6161–6176 (1998).
    [CrossRef]
  13. I. Smolskaia, M. Numez, K. Michael, “Measurements of erythemal irradiance near Davis Station, Antarctica: effect of inhomogeneous surface albedo,” Geophys. Res. Lett. 26, 1381–1384 (1999).
    [CrossRef]
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    [CrossRef]
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2000 (1)

M. van Weele, T. J. Martin, M. Blumthaler, C. Brogniez, P. N. den Outer, O. Engelsen, J. Lenoble, B. Mayer, G. Pfister, A. Ruggaber, B. Walravens, P. Weihs, B. G. Gardiner, D. Gillotay, D. Haferl, A. Kylling, G. Seckmeyer, W. M. F. Wauben, “From model intercomparison towards benchmark UV spectra for six real atmospheric cases,” J. Geophys. Res. 105, 4915–4925 (2000).
[CrossRef]

1999 (3)

I. Smolskaia, M. Numez, K. Michael, “Measurements of erythemal irradiance near Davis Station, Antarctica: effect of inhomogeneous surface albedo,” Geophys. Res. Lett. 26, 1381–1384 (1999).
[CrossRef]

E. Pachart, J. Lenoble, C. Brogniez, D. Masserot, J. L. Bocquet, “Ultraviolet spectral irradiance in the French Alps: results of two campaigns,” J. Geophys. Res. 104, 16,777–16,784 (1999).
[CrossRef]

H. Schwander, B. Mayer, A. Ruggaber, A. Albold, G. Seckmeyer, P. Koepke, “Method to determine snow albedo values in the UV for radiative transfer modeling,” Appl. Opt. 38, 3869–3875 (1999).
[CrossRef]

1998 (4)

M. Degünther, R. Meerkötter, A. Albold, G. Seckmeyer, “Case study of inhomogeneous surface albedo on UV irradiance,” Geophys. Res. Lett. 25, 3587–3590 (1998).
[CrossRef]

P. Ricchiazzi, C. Gautier, “Investigation of the effect of surface heterogeneity and topography on the radiation environment of Palmer Station, Antarctica, with an hybrid 3-D radiative transfer model,” J. Geophys. Res. 103, 6161–6176 (1998).
[CrossRef]

J. Lenoble, “Modeling of the influence of snow reflectance on ultraviolet irradiance for cloudless sky,” Appl. Opt. 37, 2441–2447 (1998).
[CrossRef]

R. L. McKenzie, K. J. Paulin, S. Madronich, “Effects of snow cover on UV irradiance and surface albedo: a case study,” J. Geophys. Res. 103, 28,785–28,792 (1998).
[CrossRef]

1995 (1)

U. Feister, R. Grewe, “Spectral albedo measurements in the UV and visible region over different types of surfaces,” Photochem. Photobiol. 62, 736–744 (1995).
[CrossRef]

1993 (1)

C. Sergent, E. Pougatch, M. Sudul, B. Bourdelles, “Experimental investigation of optical snow properties,” Ann. Glaciol. 17, 281–287 (1993).

1988 (1)

M. Blumthaler, W. Ambach, “Solar UV albedo of various surfaces,” Photochem. Photobiol. 48, 85–88 (1988).
[CrossRef] [PubMed]

1987 (1)

T. F. Eck, P. K. Bhartia, P. H. Hwang, L. L. Stowe, “Reflectivity of Earth’s surface and clouds in ultraviolet from satellite observations,” J. Geophys. Res. 92, 4287–4296 (1987).
[CrossRef]

1981 (1)

1974 (1)

Albold, A.

H. Schwander, B. Mayer, A. Ruggaber, A. Albold, G. Seckmeyer, P. Koepke, “Method to determine snow albedo values in the UV for radiative transfer modeling,” Appl. Opt. 38, 3869–3875 (1999).
[CrossRef]

M. Degünther, R. Meerkötter, A. Albold, G. Seckmeyer, “Case study of inhomogeneous surface albedo on UV irradiance,” Geophys. Res. Lett. 25, 3587–3590 (1998).
[CrossRef]

Ambach, W.

M. Blumthaler, W. Ambach, “Solar UV albedo of various surfaces,” Photochem. Photobiol. 48, 85–88 (1988).
[CrossRef] [PubMed]

Bhartia, P. K.

T. F. Eck, P. K. Bhartia, P. H. Hwang, L. L. Stowe, “Reflectivity of Earth’s surface and clouds in ultraviolet from satellite observations,” J. Geophys. Res. 92, 4287–4296 (1987).
[CrossRef]

Blumthaler, M.

M. van Weele, T. J. Martin, M. Blumthaler, C. Brogniez, P. N. den Outer, O. Engelsen, J. Lenoble, B. Mayer, G. Pfister, A. Ruggaber, B. Walravens, P. Weihs, B. G. Gardiner, D. Gillotay, D. Haferl, A. Kylling, G. Seckmeyer, W. M. F. Wauben, “From model intercomparison towards benchmark UV spectra for six real atmospheric cases,” J. Geophys. Res. 105, 4915–4925 (2000).
[CrossRef]

M. Blumthaler, W. Ambach, “Solar UV albedo of various surfaces,” Photochem. Photobiol. 48, 85–88 (1988).
[CrossRef] [PubMed]

Bocquet, J. L.

E. Pachart, J. Lenoble, C. Brogniez, D. Masserot, J. L. Bocquet, “Ultraviolet spectral irradiance in the French Alps: results of two campaigns,” J. Geophys. Res. 104, 16,777–16,784 (1999).
[CrossRef]

Bourdelles, B.

C. Sergent, E. Pougatch, M. Sudul, B. Bourdelles, “Experimental investigation of optical snow properties,” Ann. Glaciol. 17, 281–287 (1993).

Brogniez, C.

M. van Weele, T. J. Martin, M. Blumthaler, C. Brogniez, P. N. den Outer, O. Engelsen, J. Lenoble, B. Mayer, G. Pfister, A. Ruggaber, B. Walravens, P. Weihs, B. G. Gardiner, D. Gillotay, D. Haferl, A. Kylling, G. Seckmeyer, W. M. F. Wauben, “From model intercomparison towards benchmark UV spectra for six real atmospheric cases,” J. Geophys. Res. 105, 4915–4925 (2000).
[CrossRef]

E. Pachart, J. Lenoble, C. Brogniez, D. Masserot, J. L. Bocquet, “Ultraviolet spectral irradiance in the French Alps: results of two campaigns,” J. Geophys. Res. 104, 16,777–16,784 (1999).
[CrossRef]

Chandrasekhar, S.

S. Chandrasekhar, Radiative Transfer (Dover, New York, 1949).

Degünther, M.

M. Degünther, R. Meerkötter, A. Albold, G. Seckmeyer, “Case study of inhomogeneous surface albedo on UV irradiance,” Geophys. Res. Lett. 25, 3587–3590 (1998).
[CrossRef]

den Outer, P. N.

M. van Weele, T. J. Martin, M. Blumthaler, C. Brogniez, P. N. den Outer, O. Engelsen, J. Lenoble, B. Mayer, G. Pfister, A. Ruggaber, B. Walravens, P. Weihs, B. G. Gardiner, D. Gillotay, D. Haferl, A. Kylling, G. Seckmeyer, W. M. F. Wauben, “From model intercomparison towards benchmark UV spectra for six real atmospheric cases,” J. Geophys. Res. 105, 4915–4925 (2000).
[CrossRef]

Deschamps, P. Y.

Eck, T. F.

T. F. Eck, P. K. Bhartia, P. H. Hwang, L. L. Stowe, “Reflectivity of Earth’s surface and clouds in ultraviolet from satellite observations,” J. Geophys. Res. 92, 4287–4296 (1987).
[CrossRef]

Engelsen, O.

M. van Weele, T. J. Martin, M. Blumthaler, C. Brogniez, P. N. den Outer, O. Engelsen, J. Lenoble, B. Mayer, G. Pfister, A. Ruggaber, B. Walravens, P. Weihs, B. G. Gardiner, D. Gillotay, D. Haferl, A. Kylling, G. Seckmeyer, W. M. F. Wauben, “From model intercomparison towards benchmark UV spectra for six real atmospheric cases,” J. Geophys. Res. 105, 4915–4925 (2000).
[CrossRef]

Feister, U.

U. Feister, R. Grewe, “Spectral albedo measurements in the UV and visible region over different types of surfaces,” Photochem. Photobiol. 62, 736–744 (1995).
[CrossRef]

Gardiner, B. G.

M. van Weele, T. J. Martin, M. Blumthaler, C. Brogniez, P. N. den Outer, O. Engelsen, J. Lenoble, B. Mayer, G. Pfister, A. Ruggaber, B. Walravens, P. Weihs, B. G. Gardiner, D. Gillotay, D. Haferl, A. Kylling, G. Seckmeyer, W. M. F. Wauben, “From model intercomparison towards benchmark UV spectra for six real atmospheric cases,” J. Geophys. Res. 105, 4915–4925 (2000).
[CrossRef]

Gautier, C.

P. Ricchiazzi, C. Gautier, “Investigation of the effect of surface heterogeneity and topography on the radiation environment of Palmer Station, Antarctica, with an hybrid 3-D radiative transfer model,” J. Geophys. Res. 103, 6161–6176 (1998).
[CrossRef]

Gillotay, D.

M. van Weele, T. J. Martin, M. Blumthaler, C. Brogniez, P. N. den Outer, O. Engelsen, J. Lenoble, B. Mayer, G. Pfister, A. Ruggaber, B. Walravens, P. Weihs, B. G. Gardiner, D. Gillotay, D. Haferl, A. Kylling, G. Seckmeyer, W. M. F. Wauben, “From model intercomparison towards benchmark UV spectra for six real atmospheric cases,” J. Geophys. Res. 105, 4915–4925 (2000).
[CrossRef]

Green, A. E. S.

Grewe, R.

U. Feister, R. Grewe, “Spectral albedo measurements in the UV and visible region over different types of surfaces,” Photochem. Photobiol. 62, 736–744 (1995).
[CrossRef]

Haferl, D.

M. van Weele, T. J. Martin, M. Blumthaler, C. Brogniez, P. N. den Outer, O. Engelsen, J. Lenoble, B. Mayer, G. Pfister, A. Ruggaber, B. Walravens, P. Weihs, B. G. Gardiner, D. Gillotay, D. Haferl, A. Kylling, G. Seckmeyer, W. M. F. Wauben, “From model intercomparison towards benchmark UV spectra for six real atmospheric cases,” J. Geophys. Res. 105, 4915–4925 (2000).
[CrossRef]

Herman, M.

Hwang, P. H.

T. F. Eck, P. K. Bhartia, P. H. Hwang, L. L. Stowe, “Reflectivity of Earth’s surface and clouds in ultraviolet from satellite observations,” J. Geophys. Res. 92, 4287–4296 (1987).
[CrossRef]

Koepke, P.

Kylling, A.

M. van Weele, T. J. Martin, M. Blumthaler, C. Brogniez, P. N. den Outer, O. Engelsen, J. Lenoble, B. Mayer, G. Pfister, A. Ruggaber, B. Walravens, P. Weihs, B. G. Gardiner, D. Gillotay, D. Haferl, A. Kylling, G. Seckmeyer, W. M. F. Wauben, “From model intercomparison towards benchmark UV spectra for six real atmospheric cases,” J. Geophys. Res. 105, 4915–4925 (2000).
[CrossRef]

Lenoble, J.

M. van Weele, T. J. Martin, M. Blumthaler, C. Brogniez, P. N. den Outer, O. Engelsen, J. Lenoble, B. Mayer, G. Pfister, A. Ruggaber, B. Walravens, P. Weihs, B. G. Gardiner, D. Gillotay, D. Haferl, A. Kylling, G. Seckmeyer, W. M. F. Wauben, “From model intercomparison towards benchmark UV spectra for six real atmospheric cases,” J. Geophys. Res. 105, 4915–4925 (2000).
[CrossRef]

E. Pachart, J. Lenoble, C. Brogniez, D. Masserot, J. L. Bocquet, “Ultraviolet spectral irradiance in the French Alps: results of two campaigns,” J. Geophys. Res. 104, 16,777–16,784 (1999).
[CrossRef]

J. Lenoble, “Modeling of the influence of snow reflectance on ultraviolet irradiance for cloudless sky,” Appl. Opt. 37, 2441–2447 (1998).
[CrossRef]

Madronich, S.

R. L. McKenzie, K. J. Paulin, S. Madronich, “Effects of snow cover on UV irradiance and surface albedo: a case study,” J. Geophys. Res. 103, 28,785–28,792 (1998).
[CrossRef]

Martin, T. J.

M. van Weele, T. J. Martin, M. Blumthaler, C. Brogniez, P. N. den Outer, O. Engelsen, J. Lenoble, B. Mayer, G. Pfister, A. Ruggaber, B. Walravens, P. Weihs, B. G. Gardiner, D. Gillotay, D. Haferl, A. Kylling, G. Seckmeyer, W. M. F. Wauben, “From model intercomparison towards benchmark UV spectra for six real atmospheric cases,” J. Geophys. Res. 105, 4915–4925 (2000).
[CrossRef]

Masserot, D.

E. Pachart, J. Lenoble, C. Brogniez, D. Masserot, J. L. Bocquet, “Ultraviolet spectral irradiance in the French Alps: results of two campaigns,” J. Geophys. Res. 104, 16,777–16,784 (1999).
[CrossRef]

Mayer, B.

M. van Weele, T. J. Martin, M. Blumthaler, C. Brogniez, P. N. den Outer, O. Engelsen, J. Lenoble, B. Mayer, G. Pfister, A. Ruggaber, B. Walravens, P. Weihs, B. G. Gardiner, D. Gillotay, D. Haferl, A. Kylling, G. Seckmeyer, W. M. F. Wauben, “From model intercomparison towards benchmark UV spectra for six real atmospheric cases,” J. Geophys. Res. 105, 4915–4925 (2000).
[CrossRef]

H. Schwander, B. Mayer, A. Ruggaber, A. Albold, G. Seckmeyer, P. Koepke, “Method to determine snow albedo values in the UV for radiative transfer modeling,” Appl. Opt. 38, 3869–3875 (1999).
[CrossRef]

McKenzie, R. L.

R. L. McKenzie, K. J. Paulin, S. Madronich, “Effects of snow cover on UV irradiance and surface albedo: a case study,” J. Geophys. Res. 103, 28,785–28,792 (1998).
[CrossRef]

Meerkötter, R.

M. Degünther, R. Meerkötter, A. Albold, G. Seckmeyer, “Case study of inhomogeneous surface albedo on UV irradiance,” Geophys. Res. Lett. 25, 3587–3590 (1998).
[CrossRef]

Michael, K.

I. Smolskaia, M. Numez, K. Michael, “Measurements of erythemal irradiance near Davis Station, Antarctica: effect of inhomogeneous surface albedo,” Geophys. Res. Lett. 26, 1381–1384 (1999).
[CrossRef]

Numez, M.

I. Smolskaia, M. Numez, K. Michael, “Measurements of erythemal irradiance near Davis Station, Antarctica: effect of inhomogeneous surface albedo,” Geophys. Res. Lett. 26, 1381–1384 (1999).
[CrossRef]

Pachart, E.

E. Pachart, J. Lenoble, C. Brogniez, D. Masserot, J. L. Bocquet, “Ultraviolet spectral irradiance in the French Alps: results of two campaigns,” J. Geophys. Res. 104, 16,777–16,784 (1999).
[CrossRef]

Paulin, K. J.

R. L. McKenzie, K. J. Paulin, S. Madronich, “Effects of snow cover on UV irradiance and surface albedo: a case study,” J. Geophys. Res. 103, 28,785–28,792 (1998).
[CrossRef]

Pfister, G.

M. van Weele, T. J. Martin, M. Blumthaler, C. Brogniez, P. N. den Outer, O. Engelsen, J. Lenoble, B. Mayer, G. Pfister, A. Ruggaber, B. Walravens, P. Weihs, B. G. Gardiner, D. Gillotay, D. Haferl, A. Kylling, G. Seckmeyer, W. M. F. Wauben, “From model intercomparison towards benchmark UV spectra for six real atmospheric cases,” J. Geophys. Res. 105, 4915–4925 (2000).
[CrossRef]

Pougatch, E.

C. Sergent, E. Pougatch, M. Sudul, B. Bourdelles, “Experimental investigation of optical snow properties,” Ann. Glaciol. 17, 281–287 (1993).

Ricchiazzi, P.

P. Ricchiazzi, C. Gautier, “Investigation of the effect of surface heterogeneity and topography on the radiation environment of Palmer Station, Antarctica, with an hybrid 3-D radiative transfer model,” J. Geophys. Res. 103, 6161–6176 (1998).
[CrossRef]

Ruggaber, A.

M. van Weele, T. J. Martin, M. Blumthaler, C. Brogniez, P. N. den Outer, O. Engelsen, J. Lenoble, B. Mayer, G. Pfister, A. Ruggaber, B. Walravens, P. Weihs, B. G. Gardiner, D. Gillotay, D. Haferl, A. Kylling, G. Seckmeyer, W. M. F. Wauben, “From model intercomparison towards benchmark UV spectra for six real atmospheric cases,” J. Geophys. Res. 105, 4915–4925 (2000).
[CrossRef]

H. Schwander, B. Mayer, A. Ruggaber, A. Albold, G. Seckmeyer, P. Koepke, “Method to determine snow albedo values in the UV for radiative transfer modeling,” Appl. Opt. 38, 3869–3875 (1999).
[CrossRef]

Schwander, H.

Seckmeyer, G.

M. van Weele, T. J. Martin, M. Blumthaler, C. Brogniez, P. N. den Outer, O. Engelsen, J. Lenoble, B. Mayer, G. Pfister, A. Ruggaber, B. Walravens, P. Weihs, B. G. Gardiner, D. Gillotay, D. Haferl, A. Kylling, G. Seckmeyer, W. M. F. Wauben, “From model intercomparison towards benchmark UV spectra for six real atmospheric cases,” J. Geophys. Res. 105, 4915–4925 (2000).
[CrossRef]

H. Schwander, B. Mayer, A. Ruggaber, A. Albold, G. Seckmeyer, P. Koepke, “Method to determine snow albedo values in the UV for radiative transfer modeling,” Appl. Opt. 38, 3869–3875 (1999).
[CrossRef]

M. Degünther, R. Meerkötter, A. Albold, G. Seckmeyer, “Case study of inhomogeneous surface albedo on UV irradiance,” Geophys. Res. Lett. 25, 3587–3590 (1998).
[CrossRef]

Sergent, C.

C. Sergent, E. Pougatch, M. Sudul, B. Bourdelles, “Experimental investigation of optical snow properties,” Ann. Glaciol. 17, 281–287 (1993).

Shettle, E.

Smolskaia, I.

I. Smolskaia, M. Numez, K. Michael, “Measurements of erythemal irradiance near Davis Station, Antarctica: effect of inhomogeneous surface albedo,” Geophys. Res. Lett. 26, 1381–1384 (1999).
[CrossRef]

Stowe, L. L.

T. F. Eck, P. K. Bhartia, P. H. Hwang, L. L. Stowe, “Reflectivity of Earth’s surface and clouds in ultraviolet from satellite observations,” J. Geophys. Res. 92, 4287–4296 (1987).
[CrossRef]

Sudul, M.

C. Sergent, E. Pougatch, M. Sudul, B. Bourdelles, “Experimental investigation of optical snow properties,” Ann. Glaciol. 17, 281–287 (1993).

Tanré, D.

van Weele, M.

M. van Weele, T. J. Martin, M. Blumthaler, C. Brogniez, P. N. den Outer, O. Engelsen, J. Lenoble, B. Mayer, G. Pfister, A. Ruggaber, B. Walravens, P. Weihs, B. G. Gardiner, D. Gillotay, D. Haferl, A. Kylling, G. Seckmeyer, W. M. F. Wauben, “From model intercomparison towards benchmark UV spectra for six real atmospheric cases,” J. Geophys. Res. 105, 4915–4925 (2000).
[CrossRef]

Walravens, B.

M. van Weele, T. J. Martin, M. Blumthaler, C. Brogniez, P. N. den Outer, O. Engelsen, J. Lenoble, B. Mayer, G. Pfister, A. Ruggaber, B. Walravens, P. Weihs, B. G. Gardiner, D. Gillotay, D. Haferl, A. Kylling, G. Seckmeyer, W. M. F. Wauben, “From model intercomparison towards benchmark UV spectra for six real atmospheric cases,” J. Geophys. Res. 105, 4915–4925 (2000).
[CrossRef]

Wauben, W. M. F.

M. van Weele, T. J. Martin, M. Blumthaler, C. Brogniez, P. N. den Outer, O. Engelsen, J. Lenoble, B. Mayer, G. Pfister, A. Ruggaber, B. Walravens, P. Weihs, B. G. Gardiner, D. Gillotay, D. Haferl, A. Kylling, G. Seckmeyer, W. M. F. Wauben, “From model intercomparison towards benchmark UV spectra for six real atmospheric cases,” J. Geophys. Res. 105, 4915–4925 (2000).
[CrossRef]

Weihs, P.

M. van Weele, T. J. Martin, M. Blumthaler, C. Brogniez, P. N. den Outer, O. Engelsen, J. Lenoble, B. Mayer, G. Pfister, A. Ruggaber, B. Walravens, P. Weihs, B. G. Gardiner, D. Gillotay, D. Haferl, A. Kylling, G. Seckmeyer, W. M. F. Wauben, “From model intercomparison towards benchmark UV spectra for six real atmospheric cases,” J. Geophys. Res. 105, 4915–4925 (2000).
[CrossRef]

Ann. Glaciol. (1)

C. Sergent, E. Pougatch, M. Sudul, B. Bourdelles, “Experimental investigation of optical snow properties,” Ann. Glaciol. 17, 281–287 (1993).

Appl. Opt. (4)

Geophys. Res. Lett. (2)

M. Degünther, R. Meerkötter, A. Albold, G. Seckmeyer, “Case study of inhomogeneous surface albedo on UV irradiance,” Geophys. Res. Lett. 25, 3587–3590 (1998).
[CrossRef]

I. Smolskaia, M. Numez, K. Michael, “Measurements of erythemal irradiance near Davis Station, Antarctica: effect of inhomogeneous surface albedo,” Geophys. Res. Lett. 26, 1381–1384 (1999).
[CrossRef]

J. Geophys. Res. (5)

M. van Weele, T. J. Martin, M. Blumthaler, C. Brogniez, P. N. den Outer, O. Engelsen, J. Lenoble, B. Mayer, G. Pfister, A. Ruggaber, B. Walravens, P. Weihs, B. G. Gardiner, D. Gillotay, D. Haferl, A. Kylling, G. Seckmeyer, W. M. F. Wauben, “From model intercomparison towards benchmark UV spectra for six real atmospheric cases,” J. Geophys. Res. 105, 4915–4925 (2000).
[CrossRef]

P. Ricchiazzi, C. Gautier, “Investigation of the effect of surface heterogeneity and topography on the radiation environment of Palmer Station, Antarctica, with an hybrid 3-D radiative transfer model,” J. Geophys. Res. 103, 6161–6176 (1998).
[CrossRef]

R. L. McKenzie, K. J. Paulin, S. Madronich, “Effects of snow cover on UV irradiance and surface albedo: a case study,” J. Geophys. Res. 103, 28,785–28,792 (1998).
[CrossRef]

E. Pachart, J. Lenoble, C. Brogniez, D. Masserot, J. L. Bocquet, “Ultraviolet spectral irradiance in the French Alps: results of two campaigns,” J. Geophys. Res. 104, 16,777–16,784 (1999).
[CrossRef]

T. F. Eck, P. K. Bhartia, P. H. Hwang, L. L. Stowe, “Reflectivity of Earth’s surface and clouds in ultraviolet from satellite observations,” J. Geophys. Res. 92, 4287–4296 (1987).
[CrossRef]

Photochem. Photobiol. (2)

M. Blumthaler, W. Ambach, “Solar UV albedo of various surfaces,” Photochem. Photobiol. 48, 85–88 (1988).
[CrossRef] [PubMed]

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[CrossRef]

Other (1)

S. Chandrasekhar, Radiative Transfer (Dover, New York, 1949).

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Figures (6)

Fig. 1
Fig. 1

Percent differences between MC and SOS codes [(MC - SOS)/SOS]: (a) 395 nm, Rayleigh, black ground surface; (b) 345 nm, Rayleigh, black gound surface; (c) 345 nm, Rayleigh, ground-surface reflectance 0.6; (d) 345 nm, aerosols, black ground surface.

Fig. 2
Fig. 2

Amplification factor A Lz versus the central disk radius. Various SZA’s; the wavelength is 345 nm. (a) Center reflectance 0.6, black environment, Rayleigh atmosphere; (b) center reflectance 0.6, black environment, aerosols; (c) black center, environment reflectance 0.6, Rayleigh atmosphere.

Fig. 3
Fig. 3

Integral contribution function. Influence of the ground-surface reflectance.

Fig. 4
Fig. 4

Integral contribution function. Influence of aerosols. AOD, aerosol optical depth.

Fig. 5
Fig. 5

Mean integral contribution function [see Eq. (11)].

Fig. 6
Fig. 6

Four cases considered for testing the effective reflectance values (see Table 5).

Tables (5)

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Table 1 Amplification Factors for Zenith Sky Radiance ALz, Diffuse Irradiance Adif, and Global Irradiance AGla

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Table 2 Percentage of Reflected Photonsa

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Table 3 Integral Contribution Function F(R) Computed for a Disk of Radius R, ρ1 = 0.6, and Dark Background

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Table 4 Integral Contribution Function F(R) Computed for a Disk of Radius R, Reflectance ρ1, and Background Reflectance ρ2 a

Tables Icon

Table 5 Comparison of Zenith Sky Radiances Obtained by MC Code and by SOS Code (with Effective Reflectance) for Four Casesa

Equations (12)

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AGl=1+ρRa/1-ρRa=1/1-ρRa,
Adifμ0=1+ρRa/1-ρRaFGlμ0/Fdifμ0;
ALzμ0=1+ρRa1/1-ρRaFGIμ0/πLzμ0,
ALzμ0=1+ADifμ0-1Ra1/RaLμ0/Lzμ0;
ρe=02π0 ρr, ψpr, ψrdrdψ,
pr=rar/Ra,
FR=2π 0R prrdr
Lz0, ρ1, ρ2=Lzhomρ2,  Lz, ρ1, ρ2=Lzhomρ1.
FR=LzR, ρ1, ρ2-Lzhomρ2Lzhomρ1-Lzhomρ2.
FR=Lzhomρ2-LzR, ρ1, ρ2/Lzhomρ2-Lzhomρ1.
FR=1-exp-0.1233R+0.002885R2-0.0000323R3.
ρe= ρiFRi-FRi-1.

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