Abstract

The study is based on experimental work conducted in alpine snow. We made microwave radiometric and near-infrared reflectance measurements of snow slabs under different experimental conditions. We used an empirical relation to link near-infrared reflectance of snow to the specific surface area (SSA), and converted the SSA into the correlation length. From the measurements of snow radiances at 21 and 35GHz, we derived the microwave scattering coefficient by inverting two coupled radiative transfer models (the sandwich and six-flux model). The correlation lengths found are in the same range as those determined in the literature using cold laboratory work. The technique shows great potential in the determination of the snow correlation length under field conditions.

© 2008 Optical Society of America

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  1. J. T. Pulliainen, J. Grandell, and M. T. Hallikainen, “HUT snow emission model and its applicability to snow water equivalent retrieval,” IEEE Trans. Geosci. Remote Sens. 37, 1378-1390(1999).
    [CrossRef]
  2. A. Wiesmann and C. Mätzler, “Microwave emission model of layered snowpacks,” Remote Sens. Environ. 70, 307-316 (1999).
    [CrossRef]
  3. L. Tsang, C.-T. Chen, A. T. C. Chang, J. Guo, and K.-H. Ding, “Dense media radiative transfer theory based on quasi-crystalline approximation with application to passive microwave remote sensing of snow,” Radio Sci. 35, 731-749 (2000).
    [CrossRef]
  4. Y.-Q. Jin, Electromagnetic Scattering Modelling for Quantitative Remote Sensing (World Scientific, 1993).
  5. L. Tsang and J. A. Kong, “Application of strong fluctuation random medium theory to scattering from a vegetation-like half space,” IEEE Trans. Geosci. Remote Sens. GE-19, 62-69 (1981).
    [CrossRef]
  6. S. Colbeck, E. Akitaya, R. Armstrong, H. Gubler, J. Lafeuille, K. Lied, D. McClung, and E. Morris, International Classification for Seasonal Snow on the Ground (University of Colorado, 1990).
  7. R. L. Armstrong, A. Chang, A. Rango, and E. Josberger, “Snow depths and grain-size relationships with relevance for passive microwaves studies,” Ann. Glaciol. 17, 171-176 (1993).
  8. C. Mätzler, “Relation between grain size and correlation length of snow,” J. Glaciol. 48, 461-466 (2002).
    [CrossRef]
  9. T. C. Grenfell and S. G. Warren, “Representation of a nonspherical ice particle by a collection of independent spheres for scattering and absorption of radiation,” J. Geophys. Res. 104, 31697-31709 (1999).
    [CrossRef]
  10. C. Mätzler, “Autocorrelation function of granular media with free arrangement of spheres, spherical shells or ellipsoids,” J. Appl. Phys. 81, 1509-1517 (1997).
    [CrossRef]
  11. R. Parwani, “Correlation function, “http://staff.science.nus.edu.sg/~parwani/c1/node2.html.
  12. P. Debye, H. R. Anderson, and H. Brumberger, “Scattering by an inhomogeneous solid II. The correlation function and its applications,” J. Appl. Phys. 28, 679-683 (1957).
    [CrossRef]
  13. A. Stogryn, “Correlation functions for random granular media in strong fluctuation theory,” IEEE Trans. Geosci. Remote Sens. GE-22, 150-154 (1984).
    [CrossRef]
  14. H. Lim, M. E. Veysoglu, S. H. Yueh, R. T. Shin, and J. A. Kong, “Random medium model approach to scattering from a random collection of discrete scatters,” J. Electromagn. Waves Appl. 8, 801-817 (1994).
  15. J. Giddings and E. Lachapelle, “Diffusion theory applied to radiant energy distribution and albedo of snow,” J. Geophys. Res. 66, 181-189 (1961).
    [CrossRef]
  16. S. G. Warren and W. J. Wiscombe, “A model for the spectral albedo of snow. I: Pure snow,” J. Atmos. Sci. 37, 2734-2745(1980).
    [CrossRef]
  17. J. Dozier, S. R. Schneider, J. McGinnis, and F. Davis, “Effect of grain size and snowpack water equivalent on visible and near-infrared,” Water Resour. Res. 17, 1213-1221 (1981).
    [CrossRef]
  18. A. Nolin and J. Dozier, “A hyperspectral method for remotely sensing the grain size of snow,” Remote Sens. Environ. 74, 207-216 (2000).
    [CrossRef]
  19. D. L. Mitchell, “Effective diameter in radiative transfer: general definition, application, and limitation,” J. Atmos. Sci. 59, 2330-2346 (2002).
    [CrossRef]
  20. L. Legagneux, A. Cabanes, and F. Dominé, “Measurement of the specific surface area of 176 snow samples using methane adsorption at 77 K,” J. Geophys. Res. 107, 4335 (2002).
    [CrossRef]
  21. M. Kerbrat, B. Pinzer, T. Huthwelker, H. W. Gäggeler, M. Ammann, and M. Schneebeli, “Measuring the specific surface area of snow with x-ray tomography and gas adsorption: comparison and implications for surface smoothness,” Atmos. Chem. Phys. 8, 1261-1275 (2008).
    [CrossRef]
  22. M. Matzl and M. Schneebeli, “Measuring specific surface area of snow by near-infrared photography,” J. Glaciol. 52, 558-564 (2006).
    [CrossRef]
  23. T. H. Painter, N. P. Molotch, M. Cassidy, M. Flanner, and K. Steffen, “Contact spectroscopy for determination of stratigraphy of snow optical grain size,” J. Glaciol. 53, 121-127 (2007).
    [CrossRef]
  24. A. Wiesmann, C. Mätzler, and T. Wiese, “Radiometric and structural measurements of snow samples,” Radio Sci. 33, 273-289 (1998).
    [CrossRef]
  25. S. Rosenfeld and N. C. Grody, “Metamorphic signature of snow revealed in SSM/I measurements,” IEEE Trans. Geosci. Remote Sens. 38, 53-63 (2000).
    [CrossRef]
  26. J. L. Foster, D. K. Hall, A. T. C. Chang, A. Rango, W. Wergin, and E. Erbe, “Effects of snow crystal shape on the scattering of passive microwave radiation,” IEEE Trans. Geosci. Remote Sens. 37, 1165-1168 (1999).
    [CrossRef]
  27. T. Weise, “Radiometric and structural measurements of snow,” PhD thesis (Inst. of Appl. Physics University of Bern, 1996).
  28. M. Laternser and M. Schneebeli, “Long-term snow climate trends of the Swiss Alps (1931-99),” Int. J. Climatol. 23, 733-750 (2003).
    [CrossRef]
  29. E. Akitaya, “Studies on depth hoar,” Contrib. Inst. Low Temp. Sci. Hokkaido Univ. Ser. A 26, 1-67 (1974).
  30. D. Marbouty, “An experimental study of temperature-gradient metamorphism,” J. Glaciol. 26, 303-312 (1980).

2008

M. Kerbrat, B. Pinzer, T. Huthwelker, H. W. Gäggeler, M. Ammann, and M. Schneebeli, “Measuring the specific surface area of snow with x-ray tomography and gas adsorption: comparison and implications for surface smoothness,” Atmos. Chem. Phys. 8, 1261-1275 (2008).
[CrossRef]

2007

T. H. Painter, N. P. Molotch, M. Cassidy, M. Flanner, and K. Steffen, “Contact spectroscopy for determination of stratigraphy of snow optical grain size,” J. Glaciol. 53, 121-127 (2007).
[CrossRef]

2006

M. Matzl and M. Schneebeli, “Measuring specific surface area of snow by near-infrared photography,” J. Glaciol. 52, 558-564 (2006).
[CrossRef]

2003

M. Laternser and M. Schneebeli, “Long-term snow climate trends of the Swiss Alps (1931-99),” Int. J. Climatol. 23, 733-750 (2003).
[CrossRef]

2002

C. Mätzler, “Relation between grain size and correlation length of snow,” J. Glaciol. 48, 461-466 (2002).
[CrossRef]

D. L. Mitchell, “Effective diameter in radiative transfer: general definition, application, and limitation,” J. Atmos. Sci. 59, 2330-2346 (2002).
[CrossRef]

L. Legagneux, A. Cabanes, and F. Dominé, “Measurement of the specific surface area of 176 snow samples using methane adsorption at 77 K,” J. Geophys. Res. 107, 4335 (2002).
[CrossRef]

2000

L. Tsang, C.-T. Chen, A. T. C. Chang, J. Guo, and K.-H. Ding, “Dense media radiative transfer theory based on quasi-crystalline approximation with application to passive microwave remote sensing of snow,” Radio Sci. 35, 731-749 (2000).
[CrossRef]

S. Rosenfeld and N. C. Grody, “Metamorphic signature of snow revealed in SSM/I measurements,” IEEE Trans. Geosci. Remote Sens. 38, 53-63 (2000).
[CrossRef]

A. Nolin and J. Dozier, “A hyperspectral method for remotely sensing the grain size of snow,” Remote Sens. Environ. 74, 207-216 (2000).
[CrossRef]

1999

J. L. Foster, D. K. Hall, A. T. C. Chang, A. Rango, W. Wergin, and E. Erbe, “Effects of snow crystal shape on the scattering of passive microwave radiation,” IEEE Trans. Geosci. Remote Sens. 37, 1165-1168 (1999).
[CrossRef]

J. T. Pulliainen, J. Grandell, and M. T. Hallikainen, “HUT snow emission model and its applicability to snow water equivalent retrieval,” IEEE Trans. Geosci. Remote Sens. 37, 1378-1390(1999).
[CrossRef]

A. Wiesmann and C. Mätzler, “Microwave emission model of layered snowpacks,” Remote Sens. Environ. 70, 307-316 (1999).
[CrossRef]

T. C. Grenfell and S. G. Warren, “Representation of a nonspherical ice particle by a collection of independent spheres for scattering and absorption of radiation,” J. Geophys. Res. 104, 31697-31709 (1999).
[CrossRef]

1998

A. Wiesmann, C. Mätzler, and T. Wiese, “Radiometric and structural measurements of snow samples,” Radio Sci. 33, 273-289 (1998).
[CrossRef]

1997

C. Mätzler, “Autocorrelation function of granular media with free arrangement of spheres, spherical shells or ellipsoids,” J. Appl. Phys. 81, 1509-1517 (1997).
[CrossRef]

1994

H. Lim, M. E. Veysoglu, S. H. Yueh, R. T. Shin, and J. A. Kong, “Random medium model approach to scattering from a random collection of discrete scatters,” J. Electromagn. Waves Appl. 8, 801-817 (1994).

1993

R. L. Armstrong, A. Chang, A. Rango, and E. Josberger, “Snow depths and grain-size relationships with relevance for passive microwaves studies,” Ann. Glaciol. 17, 171-176 (1993).

1984

A. Stogryn, “Correlation functions for random granular media in strong fluctuation theory,” IEEE Trans. Geosci. Remote Sens. GE-22, 150-154 (1984).
[CrossRef]

1981

J. Dozier, S. R. Schneider, J. McGinnis, and F. Davis, “Effect of grain size and snowpack water equivalent on visible and near-infrared,” Water Resour. Res. 17, 1213-1221 (1981).
[CrossRef]

L. Tsang and J. A. Kong, “Application of strong fluctuation random medium theory to scattering from a vegetation-like half space,” IEEE Trans. Geosci. Remote Sens. GE-19, 62-69 (1981).
[CrossRef]

1980

S. G. Warren and W. J. Wiscombe, “A model for the spectral albedo of snow. I: Pure snow,” J. Atmos. Sci. 37, 2734-2745(1980).
[CrossRef]

D. Marbouty, “An experimental study of temperature-gradient metamorphism,” J. Glaciol. 26, 303-312 (1980).

1974

E. Akitaya, “Studies on depth hoar,” Contrib. Inst. Low Temp. Sci. Hokkaido Univ. Ser. A 26, 1-67 (1974).

1961

J. Giddings and E. Lachapelle, “Diffusion theory applied to radiant energy distribution and albedo of snow,” J. Geophys. Res. 66, 181-189 (1961).
[CrossRef]

1957

P. Debye, H. R. Anderson, and H. Brumberger, “Scattering by an inhomogeneous solid II. The correlation function and its applications,” J. Appl. Phys. 28, 679-683 (1957).
[CrossRef]

Akitaya, E.

E. Akitaya, “Studies on depth hoar,” Contrib. Inst. Low Temp. Sci. Hokkaido Univ. Ser. A 26, 1-67 (1974).

S. Colbeck, E. Akitaya, R. Armstrong, H. Gubler, J. Lafeuille, K. Lied, D. McClung, and E. Morris, International Classification for Seasonal Snow on the Ground (University of Colorado, 1990).

Ammann, M.

M. Kerbrat, B. Pinzer, T. Huthwelker, H. W. Gäggeler, M. Ammann, and M. Schneebeli, “Measuring the specific surface area of snow with x-ray tomography and gas adsorption: comparison and implications for surface smoothness,” Atmos. Chem. Phys. 8, 1261-1275 (2008).
[CrossRef]

Anderson, H. R.

P. Debye, H. R. Anderson, and H. Brumberger, “Scattering by an inhomogeneous solid II. The correlation function and its applications,” J. Appl. Phys. 28, 679-683 (1957).
[CrossRef]

Armstrong, R.

S. Colbeck, E. Akitaya, R. Armstrong, H. Gubler, J. Lafeuille, K. Lied, D. McClung, and E. Morris, International Classification for Seasonal Snow on the Ground (University of Colorado, 1990).

Armstrong, R. L.

R. L. Armstrong, A. Chang, A. Rango, and E. Josberger, “Snow depths and grain-size relationships with relevance for passive microwaves studies,” Ann. Glaciol. 17, 171-176 (1993).

Brumberger, H.

P. Debye, H. R. Anderson, and H. Brumberger, “Scattering by an inhomogeneous solid II. The correlation function and its applications,” J. Appl. Phys. 28, 679-683 (1957).
[CrossRef]

Cabanes, A.

L. Legagneux, A. Cabanes, and F. Dominé, “Measurement of the specific surface area of 176 snow samples using methane adsorption at 77 K,” J. Geophys. Res. 107, 4335 (2002).
[CrossRef]

Cassidy, M.

T. H. Painter, N. P. Molotch, M. Cassidy, M. Flanner, and K. Steffen, “Contact spectroscopy for determination of stratigraphy of snow optical grain size,” J. Glaciol. 53, 121-127 (2007).
[CrossRef]

Chang, A.

R. L. Armstrong, A. Chang, A. Rango, and E. Josberger, “Snow depths and grain-size relationships with relevance for passive microwaves studies,” Ann. Glaciol. 17, 171-176 (1993).

Chang, A. T. C.

L. Tsang, C.-T. Chen, A. T. C. Chang, J. Guo, and K.-H. Ding, “Dense media radiative transfer theory based on quasi-crystalline approximation with application to passive microwave remote sensing of snow,” Radio Sci. 35, 731-749 (2000).
[CrossRef]

J. L. Foster, D. K. Hall, A. T. C. Chang, A. Rango, W. Wergin, and E. Erbe, “Effects of snow crystal shape on the scattering of passive microwave radiation,” IEEE Trans. Geosci. Remote Sens. 37, 1165-1168 (1999).
[CrossRef]

Chen, C.-T.

L. Tsang, C.-T. Chen, A. T. C. Chang, J. Guo, and K.-H. Ding, “Dense media radiative transfer theory based on quasi-crystalline approximation with application to passive microwave remote sensing of snow,” Radio Sci. 35, 731-749 (2000).
[CrossRef]

Colbeck, S.

S. Colbeck, E. Akitaya, R. Armstrong, H. Gubler, J. Lafeuille, K. Lied, D. McClung, and E. Morris, International Classification for Seasonal Snow on the Ground (University of Colorado, 1990).

Davis, F.

J. Dozier, S. R. Schneider, J. McGinnis, and F. Davis, “Effect of grain size and snowpack water equivalent on visible and near-infrared,” Water Resour. Res. 17, 1213-1221 (1981).
[CrossRef]

Debye, P.

P. Debye, H. R. Anderson, and H. Brumberger, “Scattering by an inhomogeneous solid II. The correlation function and its applications,” J. Appl. Phys. 28, 679-683 (1957).
[CrossRef]

Ding, K.-H.

L. Tsang, C.-T. Chen, A. T. C. Chang, J. Guo, and K.-H. Ding, “Dense media radiative transfer theory based on quasi-crystalline approximation with application to passive microwave remote sensing of snow,” Radio Sci. 35, 731-749 (2000).
[CrossRef]

Dominé, F.

L. Legagneux, A. Cabanes, and F. Dominé, “Measurement of the specific surface area of 176 snow samples using methane adsorption at 77 K,” J. Geophys. Res. 107, 4335 (2002).
[CrossRef]

Dozier, J.

A. Nolin and J. Dozier, “A hyperspectral method for remotely sensing the grain size of snow,” Remote Sens. Environ. 74, 207-216 (2000).
[CrossRef]

J. Dozier, S. R. Schneider, J. McGinnis, and F. Davis, “Effect of grain size and snowpack water equivalent on visible and near-infrared,” Water Resour. Res. 17, 1213-1221 (1981).
[CrossRef]

Erbe, E.

J. L. Foster, D. K. Hall, A. T. C. Chang, A. Rango, W. Wergin, and E. Erbe, “Effects of snow crystal shape on the scattering of passive microwave radiation,” IEEE Trans. Geosci. Remote Sens. 37, 1165-1168 (1999).
[CrossRef]

Flanner, M.

T. H. Painter, N. P. Molotch, M. Cassidy, M. Flanner, and K. Steffen, “Contact spectroscopy for determination of stratigraphy of snow optical grain size,” J. Glaciol. 53, 121-127 (2007).
[CrossRef]

Foster, J. L.

J. L. Foster, D. K. Hall, A. T. C. Chang, A. Rango, W. Wergin, and E. Erbe, “Effects of snow crystal shape on the scattering of passive microwave radiation,” IEEE Trans. Geosci. Remote Sens. 37, 1165-1168 (1999).
[CrossRef]

Gäggeler, H. W.

M. Kerbrat, B. Pinzer, T. Huthwelker, H. W. Gäggeler, M. Ammann, and M. Schneebeli, “Measuring the specific surface area of snow with x-ray tomography and gas adsorption: comparison and implications for surface smoothness,” Atmos. Chem. Phys. 8, 1261-1275 (2008).
[CrossRef]

Giddings, J.

J. Giddings and E. Lachapelle, “Diffusion theory applied to radiant energy distribution and albedo of snow,” J. Geophys. Res. 66, 181-189 (1961).
[CrossRef]

Grandell, J.

J. T. Pulliainen, J. Grandell, and M. T. Hallikainen, “HUT snow emission model and its applicability to snow water equivalent retrieval,” IEEE Trans. Geosci. Remote Sens. 37, 1378-1390(1999).
[CrossRef]

Grenfell, T. C.

T. C. Grenfell and S. G. Warren, “Representation of a nonspherical ice particle by a collection of independent spheres for scattering and absorption of radiation,” J. Geophys. Res. 104, 31697-31709 (1999).
[CrossRef]

Grody, N. C.

S. Rosenfeld and N. C. Grody, “Metamorphic signature of snow revealed in SSM/I measurements,” IEEE Trans. Geosci. Remote Sens. 38, 53-63 (2000).
[CrossRef]

Gubler, H.

S. Colbeck, E. Akitaya, R. Armstrong, H. Gubler, J. Lafeuille, K. Lied, D. McClung, and E. Morris, International Classification for Seasonal Snow on the Ground (University of Colorado, 1990).

Guo, J.

L. Tsang, C.-T. Chen, A. T. C. Chang, J. Guo, and K.-H. Ding, “Dense media radiative transfer theory based on quasi-crystalline approximation with application to passive microwave remote sensing of snow,” Radio Sci. 35, 731-749 (2000).
[CrossRef]

Hall, D. K.

J. L. Foster, D. K. Hall, A. T. C. Chang, A. Rango, W. Wergin, and E. Erbe, “Effects of snow crystal shape on the scattering of passive microwave radiation,” IEEE Trans. Geosci. Remote Sens. 37, 1165-1168 (1999).
[CrossRef]

Hallikainen, M. T.

J. T. Pulliainen, J. Grandell, and M. T. Hallikainen, “HUT snow emission model and its applicability to snow water equivalent retrieval,” IEEE Trans. Geosci. Remote Sens. 37, 1378-1390(1999).
[CrossRef]

Huthwelker, T.

M. Kerbrat, B. Pinzer, T. Huthwelker, H. W. Gäggeler, M. Ammann, and M. Schneebeli, “Measuring the specific surface area of snow with x-ray tomography and gas adsorption: comparison and implications for surface smoothness,” Atmos. Chem. Phys. 8, 1261-1275 (2008).
[CrossRef]

Jin, Y.-Q.

Y.-Q. Jin, Electromagnetic Scattering Modelling for Quantitative Remote Sensing (World Scientific, 1993).

Josberger, E.

R. L. Armstrong, A. Chang, A. Rango, and E. Josberger, “Snow depths and grain-size relationships with relevance for passive microwaves studies,” Ann. Glaciol. 17, 171-176 (1993).

Kerbrat, M.

M. Kerbrat, B. Pinzer, T. Huthwelker, H. W. Gäggeler, M. Ammann, and M. Schneebeli, “Measuring the specific surface area of snow with x-ray tomography and gas adsorption: comparison and implications for surface smoothness,” Atmos. Chem. Phys. 8, 1261-1275 (2008).
[CrossRef]

Kong, J. A.

H. Lim, M. E. Veysoglu, S. H. Yueh, R. T. Shin, and J. A. Kong, “Random medium model approach to scattering from a random collection of discrete scatters,” J. Electromagn. Waves Appl. 8, 801-817 (1994).

L. Tsang and J. A. Kong, “Application of strong fluctuation random medium theory to scattering from a vegetation-like half space,” IEEE Trans. Geosci. Remote Sens. GE-19, 62-69 (1981).
[CrossRef]

Lachapelle, E.

J. Giddings and E. Lachapelle, “Diffusion theory applied to radiant energy distribution and albedo of snow,” J. Geophys. Res. 66, 181-189 (1961).
[CrossRef]

Lafeuille, J.

S. Colbeck, E. Akitaya, R. Armstrong, H. Gubler, J. Lafeuille, K. Lied, D. McClung, and E. Morris, International Classification for Seasonal Snow on the Ground (University of Colorado, 1990).

Laternser, M.

M. Laternser and M. Schneebeli, “Long-term snow climate trends of the Swiss Alps (1931-99),” Int. J. Climatol. 23, 733-750 (2003).
[CrossRef]

Legagneux, L.

L. Legagneux, A. Cabanes, and F. Dominé, “Measurement of the specific surface area of 176 snow samples using methane adsorption at 77 K,” J. Geophys. Res. 107, 4335 (2002).
[CrossRef]

Lied, K.

S. Colbeck, E. Akitaya, R. Armstrong, H. Gubler, J. Lafeuille, K. Lied, D. McClung, and E. Morris, International Classification for Seasonal Snow on the Ground (University of Colorado, 1990).

Lim, H.

H. Lim, M. E. Veysoglu, S. H. Yueh, R. T. Shin, and J. A. Kong, “Random medium model approach to scattering from a random collection of discrete scatters,” J. Electromagn. Waves Appl. 8, 801-817 (1994).

Marbouty, D.

D. Marbouty, “An experimental study of temperature-gradient metamorphism,” J. Glaciol. 26, 303-312 (1980).

Matzl, M.

M. Matzl and M. Schneebeli, “Measuring specific surface area of snow by near-infrared photography,” J. Glaciol. 52, 558-564 (2006).
[CrossRef]

Mätzler, C.

C. Mätzler, “Relation between grain size and correlation length of snow,” J. Glaciol. 48, 461-466 (2002).
[CrossRef]

A. Wiesmann and C. Mätzler, “Microwave emission model of layered snowpacks,” Remote Sens. Environ. 70, 307-316 (1999).
[CrossRef]

A. Wiesmann, C. Mätzler, and T. Wiese, “Radiometric and structural measurements of snow samples,” Radio Sci. 33, 273-289 (1998).
[CrossRef]

C. Mätzler, “Autocorrelation function of granular media with free arrangement of spheres, spherical shells or ellipsoids,” J. Appl. Phys. 81, 1509-1517 (1997).
[CrossRef]

McClung, D.

S. Colbeck, E. Akitaya, R. Armstrong, H. Gubler, J. Lafeuille, K. Lied, D. McClung, and E. Morris, International Classification for Seasonal Snow on the Ground (University of Colorado, 1990).

McGinnis, J.

J. Dozier, S. R. Schneider, J. McGinnis, and F. Davis, “Effect of grain size and snowpack water equivalent on visible and near-infrared,” Water Resour. Res. 17, 1213-1221 (1981).
[CrossRef]

Mitchell, D. L.

D. L. Mitchell, “Effective diameter in radiative transfer: general definition, application, and limitation,” J. Atmos. Sci. 59, 2330-2346 (2002).
[CrossRef]

Molotch, N. P.

T. H. Painter, N. P. Molotch, M. Cassidy, M. Flanner, and K. Steffen, “Contact spectroscopy for determination of stratigraphy of snow optical grain size,” J. Glaciol. 53, 121-127 (2007).
[CrossRef]

Morris, E.

S. Colbeck, E. Akitaya, R. Armstrong, H. Gubler, J. Lafeuille, K. Lied, D. McClung, and E. Morris, International Classification for Seasonal Snow on the Ground (University of Colorado, 1990).

Nolin, A.

A. Nolin and J. Dozier, “A hyperspectral method for remotely sensing the grain size of snow,” Remote Sens. Environ. 74, 207-216 (2000).
[CrossRef]

Painter, T. H.

T. H. Painter, N. P. Molotch, M. Cassidy, M. Flanner, and K. Steffen, “Contact spectroscopy for determination of stratigraphy of snow optical grain size,” J. Glaciol. 53, 121-127 (2007).
[CrossRef]

Parwani, R.

R. Parwani, “Correlation function, “http://staff.science.nus.edu.sg/~parwani/c1/node2.html.

Pinzer, B.

M. Kerbrat, B. Pinzer, T. Huthwelker, H. W. Gäggeler, M. Ammann, and M. Schneebeli, “Measuring the specific surface area of snow with x-ray tomography and gas adsorption: comparison and implications for surface smoothness,” Atmos. Chem. Phys. 8, 1261-1275 (2008).
[CrossRef]

Pulliainen, J. T.

J. T. Pulliainen, J. Grandell, and M. T. Hallikainen, “HUT snow emission model and its applicability to snow water equivalent retrieval,” IEEE Trans. Geosci. Remote Sens. 37, 1378-1390(1999).
[CrossRef]

Rango, A.

J. L. Foster, D. K. Hall, A. T. C. Chang, A. Rango, W. Wergin, and E. Erbe, “Effects of snow crystal shape on the scattering of passive microwave radiation,” IEEE Trans. Geosci. Remote Sens. 37, 1165-1168 (1999).
[CrossRef]

R. L. Armstrong, A. Chang, A. Rango, and E. Josberger, “Snow depths and grain-size relationships with relevance for passive microwaves studies,” Ann. Glaciol. 17, 171-176 (1993).

Rosenfeld, S.

S. Rosenfeld and N. C. Grody, “Metamorphic signature of snow revealed in SSM/I measurements,” IEEE Trans. Geosci. Remote Sens. 38, 53-63 (2000).
[CrossRef]

Schneebeli, M.

M. Kerbrat, B. Pinzer, T. Huthwelker, H. W. Gäggeler, M. Ammann, and M. Schneebeli, “Measuring the specific surface area of snow with x-ray tomography and gas adsorption: comparison and implications for surface smoothness,” Atmos. Chem. Phys. 8, 1261-1275 (2008).
[CrossRef]

M. Matzl and M. Schneebeli, “Measuring specific surface area of snow by near-infrared photography,” J. Glaciol. 52, 558-564 (2006).
[CrossRef]

M. Laternser and M. Schneebeli, “Long-term snow climate trends of the Swiss Alps (1931-99),” Int. J. Climatol. 23, 733-750 (2003).
[CrossRef]

Schneider, S. R.

J. Dozier, S. R. Schneider, J. McGinnis, and F. Davis, “Effect of grain size and snowpack water equivalent on visible and near-infrared,” Water Resour. Res. 17, 1213-1221 (1981).
[CrossRef]

Shin, R. T.

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Figures (9)

Fig. 1
Fig. 1

Experimental setup: the radiometer is mounted on a frame directed at the snow sample (9 to 20 cm ) which is placed on a 3 cm thick styrofoam plate on a metal table. Between the snow and the sample an absorber or metal plate was inserted. The polycorder (PC) and the battery box are also shown.

Fig. 2
Fig. 2

Preparation of the snow slab for the NIR photography. Four gray-white targets are placed on a smoothed snow side.

Fig. 3
Fig. 3

NIR photo of a 13 cm thick inhomogeneous slab laying on a blackbody and styrofoam slabs: the top layer is newly fallen snow with high NIR ( SSA = 38.5 / mm ), the middle layer is refrozen snow with very low NIR ( SSA = 7.7 / mm ), and the bottom layer consists of rounded snow ( SSA = 17.5 / mm ).

Fig. 4
Fig. 4

Principles of snow sample measurements: (a) brightness temperature Tb met of snow on metal plate and (b) brightness temperature Tb abs of snow on absorber. Corresponding values of blackbody radiation Tb bb were also measured.

Fig. 5
Fig. 5

Scatterplot of SSA and snow mean density. Three different types of snow are distinguished: snow with density ρ < 200 kg m 3 (shown as triangles), density 200 < ρ < 300 kg m 3 (shown as filled circles), and snow with density ρ > 300 kg m 3 (shown as diamonds).

Fig. 6
Fig. 6

Representation of the scattering coefficient at (a)  21 GHz vertical polarization, (b)  35 GHz vertical polarization, (c)  21 GHz horizontal polarization, and (d)  35 GHz horizontal polarization versus the SSA. Samples with density ρ < 200 kg m 3 are shown as triangles. Samples with density ρ > 200 kg m 3 are shown as filled circles. The numbers on the right of the symbols indicate the sample’s number. The solid curve is the exponential fit of the dense samples.

Fig. 7
Fig. 7

Representation of the scattering coefficient at (a)  21 GHz vertical polarization, (b)  35 GHz vertical polarization, (c)  21 GHz horizontal polarization, and (d)  35 GHz horizontal polarization versus snow density. The numbers on the right of the symbols indicate the sample’s number.

Fig. 8
Fig. 8

Double logarithmic representation of the scattering coefficients at (a)  21 GHz vertical polarization, (b)  35 GHz vertical polarization, (c)  21 GHz horizontal polarization, and (d)  35 GHz horizontal polarization versus the correlation length. Samples with a density ρ < 200 kg m 3 are shown as triangles; samples with a density ρ > 200 kg m 3 are shown as filled circles. The numbers on the right of the symbols indicate the sample’s number. The solid lines are the power law fit of the dense samples; the broken lines represent the power law fit found by Wiesmann et al. [24].

Fig. 9
Fig. 9

Comparison of measured Tb of snow placed on a metal plate with snow emission model (MEMLS) predictions: (a) and (b) represent the results at 21 GHz vertical and horizontal polarization; (c) and (d) represent the results at 35 GHz vertical and horizontal polarization.

Tables (2)

Tables Icon

Table 1 Properties of the Portable Dicke Radiometers

Tables Icon

Table 2 Fit Parameters for the Six-Flux Scattering Coefficient Versus the Correlation Length and the Correlation Coefficients a

Equations (21)

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

nir = a + b i ,
SSA = A e nir / b ,
Tb met = ( 1 r met ) T snow + r met T sky ,
r met = r i + ( 1 + r i ) 2 R met ,
R met = r + t 2 ( 1 r ) 1 1 r r i r i t 2 ( 1 r ) 1 .
Tb abs = ( 1 r abs ) T snow + r abs T sky ,
r abs = r i + ( 1 r i ) 2 R abs ,
R abs = r + r i t 2 ( 1 r r i ) 1 1 r r i ( r i t ) 2 ( 1 r r i ) 1 .
θ > θ c = arcsin 1 / ε ,
γ a = γ a ( 1 + 4 γ c ( γ a + 2 γ c ) 1 ) ,
γ b = γ b + 4 γ c 2 ( γ a + 2 γ c ) 1 ,
r = r 0 ( 1 t 0 2 ) ( 1 r 0 2 t 0 2 ) 1 ,
t = t 0 ( 1 r 0 2 ) ( 1 r 0 2 t 0 2 ) 1 ,
t 0 = exp ( γ d / ( cos θ ) ) ,
r 0 = γ b ( γ a + γ b + γ ) 1
γ = ( γ a ( γ a + 2 γ b ) ) 1 / 2 .
γ s = 2 γ b + 4 γ c ,
2 γ c / γ b = x / ( 1 x ) ,
x = ( ( ε 1 ) / ε ) 1 / 2 .
pc = 4 ( 1 v ) SSA ,
γ s p = d 2 p . ( pc ) c 3 p .

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