Abstract

The amplification of UV irradiance at the Earth’s surface that is due to successive reflections between the snow-covered ground and the scattering atmosphere is analyzed by a method based on decoupling the atmosphere and the surface functions. For a uniform Lambertian surface the amplification factor for the global irradiance depends only on the product of the surface reflectance and the atmospheric backscatter. It varies with wavelength, reaching a maximum near 320 nm; this maximum is close to 50% for clean snow. In UV-B the amplification depends strongly on tropospheric ozone. For non-Lambertian, nonuniform surfaces it is possible, by the same method, to define effective or average reflectances.

© 1998 Optical Society of America

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References

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  1. S. Madronich, “Implications of recent total atmospheric ozone measurements for biologically active ultraviolet radiation reaching the Earth’s surface,” Geophys. Res. Lett. 19, 37–40 (1992).
    [CrossRef]
  2. C. S. Weiler, P. A. Penhale, eds., Ultraviolet Radiation in Antarctica: Measurements and Biological Effects, Vol. 62 of Antarctic Research Series (American Geophysical Union, Washington, D.C., 1994).
  3. R. D. Bojkov, L. Bishop, V. E. Fioletov, “Total ozone trends from quality-controlled ground-based data (1964–1994),” J. Geophys. Res. 100, 25,867–25,876 (1995).
    [CrossRef]
  4. K. Stamnes, “The stratosphere as a modulator of ultraviolet radiation into the biosphere,” Surv. Geophys. 14, 167–186 (1993).
    [CrossRef]
  5. B. G. Gardiner, P. J. Kirsch, “Setting standards for European ultraviolet spectroradiometers,” final report, contract STEP- CT 900076 (European Commission, Brussels, Belgium, 1995).
  6. J. Zeng, R. McKenzie, K. Stamnes, M. Wineland, J. Rosen, “Measured UV spectra compared with discrete ordinate method simulations,” J. Geophys. Res. 99, 23,019–23,030 (1994).
    [CrossRef]
  7. P. Weihs, A. Webb, “Accuracy of spectral UV model calculations I. Consideration of uncertainties in input parameters,” J. Geophys. Res. 102, 1541–1550 (1996).
    [CrossRef]
  8. 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]
  9. C. Leroux, “Etude théorique et expérimentale de la réflectance de la neige dans le spectre solaire. Application à la télédétection,” Ph.D. dissertation (Université des Sciences et Technologies de Lille, Lille, France, 1996).
  10. 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]
  11. M. Blumthaler, W. Ambach, “Solar UV albedo of various surfaces,” Photochem. Photobiol. 48, 85–88 (1988).
    [CrossRef] [PubMed]
  12. B. L. Diffey, “A comparison of dosimeters used for solar ultraviolet radiometry,” Photochem. Photobiol. 46, 55–60 (1987).
    [CrossRef] [PubMed]
  13. S. Chandrasekhar, Radiative Transfer (Dover, New York, 1949).
  14. D. Tanré, M. Herman, P. Y. Deschamps, A. de Leffe, “Atmospheric modeling for space measurements of ground reflectances, including bidirectional properties,” Appl. Opt. 18, 3587–3594 (1979).
    [CrossRef]
  15. D. Tanré, M. Herman, P. Y. Deschamps, “Influence of the background contribution upon space measurements of ground reflectance,” Appl. Opt. 20, 3676–3684 (1981).
    [CrossRef]
  16. D. Tanré, M. Herman, P. Y. Deschamps, “Influence of the atmosphere on space measurements of directional properties,” Appl. Opt. 22, 733–741 (1983).
    [CrossRef]
  17. J. Lenoble, Atmospheric Radiative Transfer (Deepak, Hampton, Va., 1993).
  18. J. W. Hovenier, “A unified treatment of polarized light emerging from a homogeneous plane-parallel atmosphere,” Astron. Astrophys. 183, 363–370 (1987).
  19. International Association for Meteorology and Atmospheric Physics, “A preliminary cloudless standard atmosphere for radiation computation,” report WCP-112, WMO/TD-NO.24 (International Association for Meteorology and Atmospheric Physics, World Meteorological Organisation, Geneva, Switzerland, 1986).

1996

P. Weihs, A. Webb, “Accuracy of spectral UV model calculations I. Consideration of uncertainties in input parameters,” J. Geophys. Res. 102, 1541–1550 (1996).
[CrossRef]

1995

R. D. Bojkov, L. Bishop, V. E. Fioletov, “Total ozone trends from quality-controlled ground-based data (1964–1994),” J. Geophys. Res. 100, 25,867–25,876 (1995).
[CrossRef]

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]

1994

J. Zeng, R. McKenzie, K. Stamnes, M. Wineland, J. Rosen, “Measured UV spectra compared with discrete ordinate method simulations,” J. Geophys. Res. 99, 23,019–23,030 (1994).
[CrossRef]

1993

K. Stamnes, “The stratosphere as a modulator of ultraviolet radiation into the biosphere,” Surv. Geophys. 14, 167–186 (1993).
[CrossRef]

1992

S. Madronich, “Implications of recent total atmospheric ozone measurements for biologically active ultraviolet radiation reaching the Earth’s surface,” Geophys. Res. Lett. 19, 37–40 (1992).
[CrossRef]

1988

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

1987

B. L. Diffey, “A comparison of dosimeters used for solar ultraviolet radiometry,” Photochem. Photobiol. 46, 55–60 (1987).
[CrossRef] [PubMed]

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]

J. W. Hovenier, “A unified treatment of polarized light emerging from a homogeneous plane-parallel atmosphere,” Astron. Astrophys. 183, 363–370 (1987).

1983

1981

1979

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]

Bishop, L.

R. D. Bojkov, L. Bishop, V. E. Fioletov, “Total ozone trends from quality-controlled ground-based data (1964–1994),” J. Geophys. Res. 100, 25,867–25,876 (1995).
[CrossRef]

Blumthaler, M.

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

Bojkov, R. D.

R. D. Bojkov, L. Bishop, V. E. Fioletov, “Total ozone trends from quality-controlled ground-based data (1964–1994),” J. Geophys. Res. 100, 25,867–25,876 (1995).
[CrossRef]

Chandrasekhar, S.

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

de Leffe, A.

Deschamps, P. Y.

Diffey, B. L.

B. L. Diffey, “A comparison of dosimeters used for solar ultraviolet radiometry,” Photochem. Photobiol. 46, 55–60 (1987).
[CrossRef] [PubMed]

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]

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]

Fioletov, V. E.

R. D. Bojkov, L. Bishop, V. E. Fioletov, “Total ozone trends from quality-controlled ground-based data (1964–1994),” J. Geophys. Res. 100, 25,867–25,876 (1995).
[CrossRef]

Gardiner, B. G.

B. G. Gardiner, P. J. Kirsch, “Setting standards for European ultraviolet spectroradiometers,” final report, contract STEP- CT 900076 (European Commission, Brussels, Belgium, 1995).

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]

Herman, M.

Hovenier, J. W.

J. W. Hovenier, “A unified treatment of polarized light emerging from a homogeneous plane-parallel atmosphere,” Astron. Astrophys. 183, 363–370 (1987).

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]

Kirsch, P. J.

B. G. Gardiner, P. J. Kirsch, “Setting standards for European ultraviolet spectroradiometers,” final report, contract STEP- CT 900076 (European Commission, Brussels, Belgium, 1995).

Lenoble, J.

J. Lenoble, Atmospheric Radiative Transfer (Deepak, Hampton, Va., 1993).

Leroux, C.

C. Leroux, “Etude théorique et expérimentale de la réflectance de la neige dans le spectre solaire. Application à la télédétection,” Ph.D. dissertation (Université des Sciences et Technologies de Lille, Lille, France, 1996).

Madronich, S.

S. Madronich, “Implications of recent total atmospheric ozone measurements for biologically active ultraviolet radiation reaching the Earth’s surface,” Geophys. Res. Lett. 19, 37–40 (1992).
[CrossRef]

McKenzie, R.

J. Zeng, R. McKenzie, K. Stamnes, M. Wineland, J. Rosen, “Measured UV spectra compared with discrete ordinate method simulations,” J. Geophys. Res. 99, 23,019–23,030 (1994).
[CrossRef]

Rosen, J.

J. Zeng, R. McKenzie, K. Stamnes, M. Wineland, J. Rosen, “Measured UV spectra compared with discrete ordinate method simulations,” J. Geophys. Res. 99, 23,019–23,030 (1994).
[CrossRef]

Stamnes, K.

J. Zeng, R. McKenzie, K. Stamnes, M. Wineland, J. Rosen, “Measured UV spectra compared with discrete ordinate method simulations,” J. Geophys. Res. 99, 23,019–23,030 (1994).
[CrossRef]

K. Stamnes, “The stratosphere as a modulator of ultraviolet radiation into the biosphere,” Surv. Geophys. 14, 167–186 (1993).
[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]

Tanré, D.

Webb, A.

P. Weihs, A. Webb, “Accuracy of spectral UV model calculations I. Consideration of uncertainties in input parameters,” J. Geophys. Res. 102, 1541–1550 (1996).
[CrossRef]

Weihs, P.

P. Weihs, A. Webb, “Accuracy of spectral UV model calculations I. Consideration of uncertainties in input parameters,” J. Geophys. Res. 102, 1541–1550 (1996).
[CrossRef]

Wineland, M.

J. Zeng, R. McKenzie, K. Stamnes, M. Wineland, J. Rosen, “Measured UV spectra compared with discrete ordinate method simulations,” J. Geophys. Res. 99, 23,019–23,030 (1994).
[CrossRef]

Zeng, J.

J. Zeng, R. McKenzie, K. Stamnes, M. Wineland, J. Rosen, “Measured UV spectra compared with discrete ordinate method simulations,” J. Geophys. Res. 99, 23,019–23,030 (1994).
[CrossRef]

Appl. Opt.

Astron. Astrophys.

J. W. Hovenier, “A unified treatment of polarized light emerging from a homogeneous plane-parallel atmosphere,” Astron. Astrophys. 183, 363–370 (1987).

Geophys. Res. Lett.

S. Madronich, “Implications of recent total atmospheric ozone measurements for biologically active ultraviolet radiation reaching the Earth’s surface,” Geophys. Res. Lett. 19, 37–40 (1992).
[CrossRef]

J. Geophys. Res.

R. D. Bojkov, L. Bishop, V. E. Fioletov, “Total ozone trends from quality-controlled ground-based data (1964–1994),” J. Geophys. Res. 100, 25,867–25,876 (1995).
[CrossRef]

J. Zeng, R. McKenzie, K. Stamnes, M. Wineland, J. Rosen, “Measured UV spectra compared with discrete ordinate method simulations,” J. Geophys. Res. 99, 23,019–23,030 (1994).
[CrossRef]

P. Weihs, A. Webb, “Accuracy of spectral UV model calculations I. Consideration of uncertainties in input parameters,” J. Geophys. Res. 102, 1541–1550 (1996).
[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.

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]

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

B. L. Diffey, “A comparison of dosimeters used for solar ultraviolet radiometry,” Photochem. Photobiol. 46, 55–60 (1987).
[CrossRef] [PubMed]

Surv. Geophys.

K. Stamnes, “The stratosphere as a modulator of ultraviolet radiation into the biosphere,” Surv. Geophys. 14, 167–186 (1993).
[CrossRef]

Other

B. G. Gardiner, P. J. Kirsch, “Setting standards for European ultraviolet spectroradiometers,” final report, contract STEP- CT 900076 (European Commission, Brussels, Belgium, 1995).

C. S. Weiler, P. A. Penhale, eds., Ultraviolet Radiation in Antarctica: Measurements and Biological Effects, Vol. 62 of Antarctic Research Series (American Geophysical Union, Washington, D.C., 1994).

C. Leroux, “Etude théorique et expérimentale de la réflectance de la neige dans le spectre solaire. Application à la télédétection,” Ph.D. dissertation (Université des Sciences et Technologies de Lille, Lille, France, 1996).

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

J. Lenoble, Atmospheric Radiative Transfer (Deepak, Hampton, Va., 1993).

International Association for Meteorology and Atmospheric Physics, “A preliminary cloudless standard atmosphere for radiation computation,” report WCP-112, WMO/TD-NO.24 (International Association for Meteorology and Atmospheric Physics, World Meteorological Organisation, Geneva, Switzerland, 1986).

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Figures (8)

Fig. 1
Fig. 1

Geometry of the problem. Successive reflections at the ground surface.

Fig. 2
Fig. 2

Atmospheric reflectance: Rayleigh, z = 0 m (solid curve); z = 1300 m (dashed curve).

Fig. 3
Fig. 3

Influence of total ozone on atmospheric reflectance for a molecular atmosphere: 250 DU (dashed curve), 324 DU (solid curve), 400 DU (dotted curve).

Fig. 4
Fig. 4

Influence of tropospheric ozone on atmospheric reflectance for a molecular atmosphere: standard profile, 324 DU (solid curve); same with no ozone below 10 km, 292 DU (dashed curve); same with no ozone below 2 km, 319 DU (dotted curve).

Fig. 5
Fig. 5

Influence of aerosol on atmospheric reflectance with a standard ozone profile, 324 DU: no aerosol (solid curve); aerosol, OD of 0.22, SSA of 0.9 (long-dashed curve); aerosol, OD of 0.80, SSA of 0.9 (short-dashed curve); aerosol, OD of 0.22, SSA of 1 (dashed–dotted curve).

Fig. 6
Fig. 6

Influence of aerosol on the atmospheric reflectance with no ozone absorption: no aerosol (solid curve); aerosol, OD of 0.22, SSA of 0.9 (long-dashed curve); aerosol, OD of 0.22, SSA of 1 (short-dashed).

Fig. 7
Fig. 7

Amplification factor. Top, spectral distribution, surface reflectance (RO) of 0.2 (solid curve), 0.4 (dashed curve), 0.6 (dotted curve), and 0.8 (dashed–dotted curve). Bottom, function of RO, atmospheric reflectance R′ = 0.40 (solid curve) and R′ = 0.25 (dashed curve).

Fig. 8
Fig. 8

Modeled bidirectional reflectance of snow in the solar plane; SZA, 50°. The observation angle is considered positive when one is looking toward the Sun. (After Leroux9.)

Tables (1)

Tables Icon

Table 1 Ratio of Reflectance and Transmittance Functions for a Standard Atmospherea

Equations (28)

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R μ , ϕ ; μ 0 , ϕ 0 = π L + μ , ϕ / μ 0 f ,
T dif μ , ϕ ; μ 0 , ϕ 0 = π L - μ , ϕ / μ 0 f ,
R μ 0 = 1 π 0 2 π 0 1   R μ , ϕ ; μ 0 , ϕ 0 μ d μ d ϕ
R = 2   0 1   R μ μ d μ .
T gl μ 0 = T dif μ 0 + exp - τ / μ 0 ,
L * μ , ϕ = L μ , ϕ +   n = 1   L n μ ,
L 1 μ = ρ F gl μ 0 R μ / π ,
F dif 1 μ 0 = ρ F gl μ 0 R ,
F gl μ 0 = F dif μ 0 + μ 0 f   exp - τ / μ 0 = μ 0 fT gl μ 0
L 2 μ = ρ F dif 1 μ 0 R μ / π = ρ 2 F gl μ 0 R R μ / π ,
L * μ , ϕ = L μ , ϕ + ρ F gl μ 0 R μ / π 1 - ρ R ,
F dif * μ 0 = F dif μ 0 + F gl μ 0 ρ R / 1 - ρ R .
F gl * μ 0 = F gl μ 0 / 1 - ρ R
A = 1 / 1 - ρ R ,
L 1 μ , ϕ = L 1 s μ , ϕ + L 1 d μ , ϕ ,
L 1 s μ , ϕ = μ 0 f π 2 exp - τ / μ 0 0 2 π 0 1   ρ μ , ϕ ; μ 0 , ϕ 0 × R μ , ϕ ; μ , ϕ μ d μ d ϕ
L 1 d μ , ϕ = μ 0 f π 3 0 2 π 0 1 0 2 π 0 1   T dif μ , ϕ ; μ 0 , ϕ 0 × ρ μ , ϕ ; μ , ϕ R μ , ϕ ; μ , ϕ × μ d μ d ϕ μ d μ d ϕ .
L 1 s μ , ϕ = ρ av μ , ϕ ; μ 0 , ϕ 0 μ 0 f   exp - τ / μ 0 R μ / π ,
ρ av μ , ϕ ; μ 0 , ϕ 0 = 1 π R μ 0 2 π 0 1   ρ μ , ϕ ; μ 0 , ϕ 0 × R μ , ϕ ; μ ; ϕ μ d μ d ϕ .
F dif 1 s μ 0 = μ 0 f   exp - τ / μ 0 ρ e μ 0 R ,
ρ e μ 0 = 1 π R 0 2 π 0 1   ρ av μ , ϕ ; μ 0 , ϕ 0 R μ μ d μ d ϕ
ρ e μ 0 = 2 R 0 1   ρ 0 μ ; μ 0 R μ μ d μ .
F dif * μ 0 = F dif μ 0 + ρ e μ 0 μ 0 f exp - τ / μ 0 R + ρ F dif μ 0 R + ρ F gl μ 0 ρ 2 R 2 1 - ρ R .
p r , ψ ; μ , ϕ = R r , ψ ; μ , ϕ / R μ , ϕ ;
L 1 μ ; ϕ = ρ μ ; ϕ π   F gl μ 0 R μ ,
ρ μ ; ϕ = 0 2 π 0   ρ r , ψ p r , ψ ; μ ; ϕ r d r d ψ
F dif 1 μ 0 = ρ F gl μ 0 R ,
ρ = 0 2 π 0   ρ r , ψ p r , ψ r d r d ψ .

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