Abstract

It is commonly observed that natural multiple-scattering media such as sand and soils become noticeably darker when wet. The primary reason for this is that changing the medium surrounding the particles from air to water decreases their relative refractive index, hence increases the average degree of forwardness of scattering as determined by the asymmetry parameter (mean cosine of the scattering angle). As a consequence, incident photons have to be scattered more times before reemerging from the medium and are, therefore, exposed to a greater probability of being absorbed. A simple theory incorporating this idea yields results that are in reasonable agreement with the few measurements available in the literature, although there are differences. Our measurements of the reflectance of sand wetted with various liquids are in reasonably good agreement with the simple theory. We suggest that the difference between reflectances of wet and dry surfaces may have implications for remote sensing.

© 1986 Optical Society of America

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References

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  1. K. M. Nagler, S. D. Soules, “Cloud Photography from Gemini 4 Spaceflight,” Bull. Am. Meteorol. Soc. 46, 522 (1965).
  2. J. R. Hope, “Path of Heavy Rainfall Photographed from Space,” Bull. Am. Meteorol. Soc. 47, 371 (1966).
  3. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).
  4. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).
  5. P. Debye, “Der Lichtdruck auf Kugeln von beliebigem Material,” Ann. Phys. 30, 57 (1909).
    [CrossRef]
  6. J. E. Hansen, L. D. Travis, “Light Scattering in Planetary Atmospheres,” Space Sci. Rev. 16, 527 (1974).
    [CrossRef]
  7. H. C. van de Hulst, K. Grossman, “Multiple Light Scattering in Planetary Atmospheres,” in The Atmospheres of Venus and Mars, J. C. Brandt, M. B. McEvoy, Eds. (Gordon & Breach, New York, 1968), p. 35.
  8. H. C. van de Hulst, Multiple Light Scattering, 2 Vols. (Academic, New York, 1980).
  9. S. Chandrasekhar, Radiative Transfer (Oxford U. P., London, 1950;Radiative Transfer reprinted by Dover, New York, 1960).
  10. S. Twomey, C. F. Bohren, “Simple Approximations for Calculations of Absorption in Clouds,” J. Atmos. Sci. 37, 2086 (1980).
    [CrossRef]
  11. C. F. Bohren, “Multiple Scattering at the Beach,” Weatherwise 36, 197 (1983).
    [CrossRef]
  12. S. R. Weast, Ed., Handbook of Chemistry and Physics (CRC Press, Boca Raton, FL, 1985), p. E371.
  13. W. D. Sellers, Physical Climatology (University of Chicago, Chicago, 1965).
  14. P. M. Kuhn, V. E. Suomi, “Airborne Observations of Albedo with a Beam Reflector,” J. Meteorol. 15, 172 (1958).
    [CrossRef]
  15. K. Y. Kondratyev, Radiation Characteristics of the Atmosphere and the Earth's Surface (Gidrometeorologicheskoe Press, Leningrad;Radiation Characteristics of the Atmosphere and the Earth's Surface translated by Amerind Publishing Co., New Dehli, 1973).
  16. R. Geiger, The Climate Near the Ground (Harvard U. P., Cambridge, MA, 1965).
  17. K. Büttner, E. Sutter, “Die Abkühlungsgrosse in den Dünen etc.,” Strahlentherapie 54, 156 (1935).
  18. E. A. Milne, “Thermodynamics of the Stars,” in Handbuch der Astrophysik 3/1, 65 (1930).Reprinted in Selected Papers on the Transfer of Radiation, D. H. Menzel, Ed. (Dover, New York, 1966).
    [CrossRef]
  19. M. Planck, The Theory of Heat Radiation (Dover, New York, 1959).
  20. H. von Helmholtz, Treatise on Physiological Optics, Vol. 1 (Dover, New York, 1962).
  21. A. Angström, “The albedo of various surfaces of ground,” Geografiska Ann. 7, 323 (1925).
    [CrossRef]

1983

C. F. Bohren, “Multiple Scattering at the Beach,” Weatherwise 36, 197 (1983).
[CrossRef]

1980

S. Twomey, C. F. Bohren, “Simple Approximations for Calculations of Absorption in Clouds,” J. Atmos. Sci. 37, 2086 (1980).
[CrossRef]

1974

J. E. Hansen, L. D. Travis, “Light Scattering in Planetary Atmospheres,” Space Sci. Rev. 16, 527 (1974).
[CrossRef]

1966

J. R. Hope, “Path of Heavy Rainfall Photographed from Space,” Bull. Am. Meteorol. Soc. 47, 371 (1966).

1965

K. M. Nagler, S. D. Soules, “Cloud Photography from Gemini 4 Spaceflight,” Bull. Am. Meteorol. Soc. 46, 522 (1965).

1958

P. M. Kuhn, V. E. Suomi, “Airborne Observations of Albedo with a Beam Reflector,” J. Meteorol. 15, 172 (1958).
[CrossRef]

1935

K. Büttner, E. Sutter, “Die Abkühlungsgrosse in den Dünen etc.,” Strahlentherapie 54, 156 (1935).

1930

E. A. Milne, “Thermodynamics of the Stars,” in Handbuch der Astrophysik 3/1, 65 (1930).Reprinted in Selected Papers on the Transfer of Radiation, D. H. Menzel, Ed. (Dover, New York, 1966).
[CrossRef]

1925

A. Angström, “The albedo of various surfaces of ground,” Geografiska Ann. 7, 323 (1925).
[CrossRef]

1909

P. Debye, “Der Lichtdruck auf Kugeln von beliebigem Material,” Ann. Phys. 30, 57 (1909).
[CrossRef]

Angström, A.

A. Angström, “The albedo of various surfaces of ground,” Geografiska Ann. 7, 323 (1925).
[CrossRef]

Bohren, C. F.

C. F. Bohren, “Multiple Scattering at the Beach,” Weatherwise 36, 197 (1983).
[CrossRef]

S. Twomey, C. F. Bohren, “Simple Approximations for Calculations of Absorption in Clouds,” J. Atmos. Sci. 37, 2086 (1980).
[CrossRef]

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Büttner, K.

K. Büttner, E. Sutter, “Die Abkühlungsgrosse in den Dünen etc.,” Strahlentherapie 54, 156 (1935).

Chandrasekhar, S.

S. Chandrasekhar, Radiative Transfer (Oxford U. P., London, 1950;Radiative Transfer reprinted by Dover, New York, 1960).

Debye, P.

P. Debye, “Der Lichtdruck auf Kugeln von beliebigem Material,” Ann. Phys. 30, 57 (1909).
[CrossRef]

Geiger, R.

R. Geiger, The Climate Near the Ground (Harvard U. P., Cambridge, MA, 1965).

Grossman, K.

H. C. van de Hulst, K. Grossman, “Multiple Light Scattering in Planetary Atmospheres,” in The Atmospheres of Venus and Mars, J. C. Brandt, M. B. McEvoy, Eds. (Gordon & Breach, New York, 1968), p. 35.

Hansen, J. E.

J. E. Hansen, L. D. Travis, “Light Scattering in Planetary Atmospheres,” Space Sci. Rev. 16, 527 (1974).
[CrossRef]

Hope, J. R.

J. R. Hope, “Path of Heavy Rainfall Photographed from Space,” Bull. Am. Meteorol. Soc. 47, 371 (1966).

Huffman, D. R.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Kondratyev, K. Y.

K. Y. Kondratyev, Radiation Characteristics of the Atmosphere and the Earth's Surface (Gidrometeorologicheskoe Press, Leningrad;Radiation Characteristics of the Atmosphere and the Earth's Surface translated by Amerind Publishing Co., New Dehli, 1973).

Kuhn, P. M.

P. M. Kuhn, V. E. Suomi, “Airborne Observations of Albedo with a Beam Reflector,” J. Meteorol. 15, 172 (1958).
[CrossRef]

Milne, E. A.

E. A. Milne, “Thermodynamics of the Stars,” in Handbuch der Astrophysik 3/1, 65 (1930).Reprinted in Selected Papers on the Transfer of Radiation, D. H. Menzel, Ed. (Dover, New York, 1966).
[CrossRef]

Nagler, K. M.

K. M. Nagler, S. D. Soules, “Cloud Photography from Gemini 4 Spaceflight,” Bull. Am. Meteorol. Soc. 46, 522 (1965).

Planck, M.

M. Planck, The Theory of Heat Radiation (Dover, New York, 1959).

Sellers, W. D.

W. D. Sellers, Physical Climatology (University of Chicago, Chicago, 1965).

Soules, S. D.

K. M. Nagler, S. D. Soules, “Cloud Photography from Gemini 4 Spaceflight,” Bull. Am. Meteorol. Soc. 46, 522 (1965).

Suomi, V. E.

P. M. Kuhn, V. E. Suomi, “Airborne Observations of Albedo with a Beam Reflector,” J. Meteorol. 15, 172 (1958).
[CrossRef]

Sutter, E.

K. Büttner, E. Sutter, “Die Abkühlungsgrosse in den Dünen etc.,” Strahlentherapie 54, 156 (1935).

Travis, L. D.

J. E. Hansen, L. D. Travis, “Light Scattering in Planetary Atmospheres,” Space Sci. Rev. 16, 527 (1974).
[CrossRef]

Twomey, S.

S. Twomey, C. F. Bohren, “Simple Approximations for Calculations of Absorption in Clouds,” J. Atmos. Sci. 37, 2086 (1980).
[CrossRef]

van de Hulst, H. C.

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

H. C. van de Hulst, Multiple Light Scattering, 2 Vols. (Academic, New York, 1980).

H. C. van de Hulst, K. Grossman, “Multiple Light Scattering in Planetary Atmospheres,” in The Atmospheres of Venus and Mars, J. C. Brandt, M. B. McEvoy, Eds. (Gordon & Breach, New York, 1968), p. 35.

von Helmholtz, H.

H. von Helmholtz, Treatise on Physiological Optics, Vol. 1 (Dover, New York, 1962).

Ann. Phys.

P. Debye, “Der Lichtdruck auf Kugeln von beliebigem Material,” Ann. Phys. 30, 57 (1909).
[CrossRef]

Bull. Am. Meteorol. Soc.

K. M. Nagler, S. D. Soules, “Cloud Photography from Gemini 4 Spaceflight,” Bull. Am. Meteorol. Soc. 46, 522 (1965).

J. R. Hope, “Path of Heavy Rainfall Photographed from Space,” Bull. Am. Meteorol. Soc. 47, 371 (1966).

Geografiska Ann.

A. Angström, “The albedo of various surfaces of ground,” Geografiska Ann. 7, 323 (1925).
[CrossRef]

Handbuch der Astrophysik

E. A. Milne, “Thermodynamics of the Stars,” in Handbuch der Astrophysik 3/1, 65 (1930).Reprinted in Selected Papers on the Transfer of Radiation, D. H. Menzel, Ed. (Dover, New York, 1966).
[CrossRef]

J. Atmos. Sci.

S. Twomey, C. F. Bohren, “Simple Approximations for Calculations of Absorption in Clouds,” J. Atmos. Sci. 37, 2086 (1980).
[CrossRef]

J. Meteorol.

P. M. Kuhn, V. E. Suomi, “Airborne Observations of Albedo with a Beam Reflector,” J. Meteorol. 15, 172 (1958).
[CrossRef]

Space Sci. Rev.

J. E. Hansen, L. D. Travis, “Light Scattering in Planetary Atmospheres,” Space Sci. Rev. 16, 527 (1974).
[CrossRef]

Strahlentherapie

K. Büttner, E. Sutter, “Die Abkühlungsgrosse in den Dünen etc.,” Strahlentherapie 54, 156 (1935).

Weatherwise

C. F. Bohren, “Multiple Scattering at the Beach,” Weatherwise 36, 197 (1983).
[CrossRef]

Other

S. R. Weast, Ed., Handbook of Chemistry and Physics (CRC Press, Boca Raton, FL, 1985), p. E371.

W. D. Sellers, Physical Climatology (University of Chicago, Chicago, 1965).

K. Y. Kondratyev, Radiation Characteristics of the Atmosphere and the Earth's Surface (Gidrometeorologicheskoe Press, Leningrad;Radiation Characteristics of the Atmosphere and the Earth's Surface translated by Amerind Publishing Co., New Dehli, 1973).

R. Geiger, The Climate Near the Ground (Harvard U. P., Cambridge, MA, 1965).

M. Planck, The Theory of Heat Radiation (Dover, New York, 1959).

H. von Helmholtz, Treatise on Physiological Optics, Vol. 1 (Dover, New York, 1962).

H. C. van de Hulst, K. Grossman, “Multiple Light Scattering in Planetary Atmospheres,” in The Atmospheres of Venus and Mars, J. C. Brandt, M. B. McEvoy, Eds. (Gordon & Breach, New York, 1968), p. 35.

H. C. van de Hulst, Multiple Light Scattering, 2 Vols. (Academic, New York, 1980).

S. Chandrasekhar, Radiative Transfer (Oxford U. P., London, 1950;Radiative Transfer reprinted by Dover, New York, 1960).

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

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

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Figures (8)

Fig. 1
Fig. 1

Dependence of the mean cosine of the angle of scattering by a sphere (asymmetry parameter) on the refractive index (real part) relative to that of the surrounding medium. These calculations were made using both Mie theory and geometrical optics. The size parameter x is the sphere circumference divided by the wavelength, and mi is the imaginary part of its refractive index.

Fig. 2
Fig. 2

Scaled single-scattering albedo vs asymmetry parameter. Curves are labeled with the actual (unscaled) single-scattering albedo.

Fig. 3
Fig. 3

Dependence of albedo and zenith reflectance (for incident light at 41.4° from zenith) on scaled single-scattering albedo ω ̅ 0

Fig. 4
Fig. 4

(a) Scaled single-scattering albedos for an infinitely deep scattering layer wet by a liquid with refractive index m0. The particles are much larger than the wavelength and have a refractive index of 1.5. (b) Inference of the reflectance produced by wetting.

Fig. 5
Fig. 5

Wet vs dry albedos obtained by the method indicated in Fig. 4. The wetting liquid is water (m0 = 1.33). The crosses are experimental data given by Sellers13 for natural surfaces; the circles are similar experimental data reported by Kondratyev.15

Fig. 6
Fig. 6

Sand wet by water and benzene (from Ref. 11).

Fig. 7
Fig. 7

Computed curves of zenith reflectance for a range of values of (unscaled) single-scattering albedo. The dark circle shows the measured value for Ottawa sand before wetting. The crosses are experimental results for wetting by sugar solutions with refractive index ranging from 1.33 to 1.48. The open circles are for wetting by benzene and glycerol.

Fig. 8
Fig. 8

Calculated dependence of albedo (for representative single-scattering albedos) on the direction of incident illumination [Eq. (4)] compared with data from Sellers13 and from Kondratyev.15

Equations (5)

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( 1 ω ̅ 0 ) τ = ( 1 ω ̅ 0 ) τ , ( 1 g ) ω ̅ 0 τ ( 1 g ) ω ¯ 0 τ .
ω ̅ 0 = ω ̅ 0 1 g 1 g ω ̅ 0 .
I ( μ ) = 1 4 π ω ̅ 0 μ 0 μ + μ 0 H ( μ ) H ( μ 0 ) F 0 ,
R = 1 1 ω ̅ 0 H ( μ 0 ) .
ω ̅ 0 wet = r ω ̅ 0 dry r ω ̅ 0 dry + 1 ω ̅ 0 dry , r = 1 g wet 1 g dry ,

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