Abstract

An algorithm based on the Monte Carlo method is developed to solve the radiative transfer equation in the reflective domain (0.4–4 µm) of the solar spectrum over rugged terrain. This algorithm takes into account relief, spatial heterogeneity, and ground bidirectional reflectance. The method permits the computation of irradiance components at ground level and radiance terms reaching an airborne or satelliteborne sensor. The Monte Carlo method consists of statistically simulating the paths of photons inside the Earth–atmosphere system to reproduce physical phenomena while introducing neither analytical modeling nor assumption. The potentialities of the code are then depicted over different types of landscape, including a seashore, a desert region, and a steep mountainous valley.

© 1999 Optical Society of America

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References

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  1. B. N. Holben, C. O. Justice, “The topographic effect on spectral response from nadir-pointing sensors,” Photogramm. Eng. Remote Sens. 46, 1191–1200 (1980).
  2. D. S. Kimes, J. A. Kirchner, “Modeling the effects of various radiant transfers in mountainous terrain on sensor response,” IEEE Trans. Geosci. Remote Sens. GE-19, 100–108 (1981).
    [CrossRef]
  3. T. Kusaka, Y. Kawata, S. Ueno, S. Furumoto, “Removal of the atmospheric and topographic effects from the rugged terrain image data remotely sensed by Landsat,” in Proceedings of International Geoscience and Remote Sensing Symposium (Institute of Electrical and Electronic Engineers, Piscataway, N.J., 1987), Vol. 1, pp. 649–652.
  4. T. Kusaka, Y. Kawata, H. Egawa, S. Ueno, “Signature variations due to atmospheric and topographic effects on satellite MSS data over rugged terrain,” in Proceedings of International Geoscience and Remote Sensing Symposium (European Space Agency, Paris, 1988), pp. 825–828.
  5. T. Kusaka, Y. Kawata, “Atmospheric and topographic correction of satellite data over mountainous terrain,” in Proceedings of International Geoscience and Remote Sensing Symposium (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1994), Vol. 1, pp. 58–60.
  6. R. Richter, “Correction of atmospheric and topographic effects for high spatial resolution satellite imagery,” Intl. Remote Sens. 18, 1099–1111 (1997).
    [CrossRef]
  7. C. Proy, D. Tanré, P. Y. Deschamps, “Evaluation of topographic effects on remotely sensed data,” Remote Sens. Environ. 30, 21–32 (1989).
    [CrossRef]
  8. E. Vermote, D. Tanré, J. L. Deuzé, M. Herman, J. J. Morcrette, “Second simulation of the satellite signal in the solar spectrum, 6S: an overview,” IEEE Trans. Geosci. Remote Sens. 35, 675–686 (1997).
    [CrossRef]
  9. G. I. Marchuk, G. A. Mikhailov, M. A. Nazaraliev, R. A. Dacbinjan, B. A. Kargin, B. S. Elepov, The Monte Carlo Methods in Atmospheric Optics, D. L. MacAdam, ed., Vol. 12 of Springer Series in Optical Sciences (Springer-Verlag, Berlin, 1980), pp. 5–17.
    [CrossRef]
  10. J. Lenoble, Atmospheric Radiative Transfer (Deepak, Hampton, Va., 1993).
  11. R. McClatchey, R. W. Fenn, J. E. A. Selby, F. E. Volz, J. S. Garing, “Optical properties of the atmosphere,” (U.S. Air Force Cambridge Research Laboratory, Bedford, Mass., 1971).
  12. ASTER (Advanced Spaceborne Thermal Emission and Reflection Radiometer) spectral library, NASA: http://speclib.jpl.nasa.gov/ ; cognizant scientist, simon.j.hook@jpl.nasa.gov .
  13. Y. J. Kaufman, “Atmospheric effect on spatial resolution of surface imagery: errata,” Appl. Opt. 23, 4164–4172 (1987).
    [CrossRef]
  14. H. Cosnefroy, M. Leroy, X. Briottet, “Selection and characterization of Saharan and Arabian desert sites for the calibration of optical satellite sensors,” Remote Sens. Environ. 58, 101–114 (1996).
    [CrossRef]
  15. J. Dozier, J. Frew, “Atmospheric corrections to satellite radiometric data over rugged terrain,” Remote Sens. Environ. 11, 191–205 (1981).
    [CrossRef]
  16. R. W. Sloberg, B. K. P. Horn, “Atmospheric effects in satellite imaging of mountainous terrain,” Appl. Opt. 22, 1703–1716 (1983).
  17. J. Dozier, R. E. Davis, A. T. C. Chang, K. Brown, “The spectral bidirectional reflectance of snow,” in Proceedings of the 4th International Colloquium on Spectral Signatures of Objects in Remote Sensing (European Space Agency, Paris, 1988), pp. 87–92.
  18. S. G. Warren, “Optical properties of snow,” Rev. Geophys. Space Phys. 20, 67–89 (1982).
    [CrossRef]
  19. M. M. Verstraete, B. Pinty, R. E. Dickinson, “A physical model of the bidirectional reflectance of vegetation canopies. 2. Inversion and validation,” J. Geophys. Res. 95, 11,767–11,775 (1990).
    [CrossRef]
  20. F. E. Nicodemus, “Reflectance nomenclature and directional reflectance and emissivity,” Appl. Opt. 9, 1474–1475 (1970).
    [CrossRef] [PubMed]
  21. Y. M. Govaerts, M. M. Verstraete, “Raytran: a Monte Carlo ray-tracing model to compute light scattering in three-dimensional heterogeneous media,” IEEE Trans. Geosci. Remote Sens. 36, 493–504 (1998).
    [CrossRef]

1998 (1)

Y. M. Govaerts, M. M. Verstraete, “Raytran: a Monte Carlo ray-tracing model to compute light scattering in three-dimensional heterogeneous media,” IEEE Trans. Geosci. Remote Sens. 36, 493–504 (1998).
[CrossRef]

1997 (2)

R. Richter, “Correction of atmospheric and topographic effects for high spatial resolution satellite imagery,” Intl. Remote Sens. 18, 1099–1111 (1997).
[CrossRef]

E. Vermote, D. Tanré, J. L. Deuzé, M. Herman, J. J. Morcrette, “Second simulation of the satellite signal in the solar spectrum, 6S: an overview,” IEEE Trans. Geosci. Remote Sens. 35, 675–686 (1997).
[CrossRef]

1996 (1)

H. Cosnefroy, M. Leroy, X. Briottet, “Selection and characterization of Saharan and Arabian desert sites for the calibration of optical satellite sensors,” Remote Sens. Environ. 58, 101–114 (1996).
[CrossRef]

1990 (1)

M. M. Verstraete, B. Pinty, R. E. Dickinson, “A physical model of the bidirectional reflectance of vegetation canopies. 2. Inversion and validation,” J. Geophys. Res. 95, 11,767–11,775 (1990).
[CrossRef]

1989 (1)

C. Proy, D. Tanré, P. Y. Deschamps, “Evaluation of topographic effects on remotely sensed data,” Remote Sens. Environ. 30, 21–32 (1989).
[CrossRef]

1987 (1)

1983 (1)

R. W. Sloberg, B. K. P. Horn, “Atmospheric effects in satellite imaging of mountainous terrain,” Appl. Opt. 22, 1703–1716 (1983).

1982 (1)

S. G. Warren, “Optical properties of snow,” Rev. Geophys. Space Phys. 20, 67–89 (1982).
[CrossRef]

1981 (2)

J. Dozier, J. Frew, “Atmospheric corrections to satellite radiometric data over rugged terrain,” Remote Sens. Environ. 11, 191–205 (1981).
[CrossRef]

D. S. Kimes, J. A. Kirchner, “Modeling the effects of various radiant transfers in mountainous terrain on sensor response,” IEEE Trans. Geosci. Remote Sens. GE-19, 100–108 (1981).
[CrossRef]

1980 (1)

B. N. Holben, C. O. Justice, “The topographic effect on spectral response from nadir-pointing sensors,” Photogramm. Eng. Remote Sens. 46, 1191–1200 (1980).

1970 (1)

Briottet, X.

H. Cosnefroy, M. Leroy, X. Briottet, “Selection and characterization of Saharan and Arabian desert sites for the calibration of optical satellite sensors,” Remote Sens. Environ. 58, 101–114 (1996).
[CrossRef]

Brown, K.

J. Dozier, R. E. Davis, A. T. C. Chang, K. Brown, “The spectral bidirectional reflectance of snow,” in Proceedings of the 4th International Colloquium on Spectral Signatures of Objects in Remote Sensing (European Space Agency, Paris, 1988), pp. 87–92.

Chang, A. T. C.

J. Dozier, R. E. Davis, A. T. C. Chang, K. Brown, “The spectral bidirectional reflectance of snow,” in Proceedings of the 4th International Colloquium on Spectral Signatures of Objects in Remote Sensing (European Space Agency, Paris, 1988), pp. 87–92.

Cosnefroy, H.

H. Cosnefroy, M. Leroy, X. Briottet, “Selection and characterization of Saharan and Arabian desert sites for the calibration of optical satellite sensors,” Remote Sens. Environ. 58, 101–114 (1996).
[CrossRef]

Dacbinjan, R. A.

G. I. Marchuk, G. A. Mikhailov, M. A. Nazaraliev, R. A. Dacbinjan, B. A. Kargin, B. S. Elepov, The Monte Carlo Methods in Atmospheric Optics, D. L. MacAdam, ed., Vol. 12 of Springer Series in Optical Sciences (Springer-Verlag, Berlin, 1980), pp. 5–17.
[CrossRef]

Davis, R. E.

J. Dozier, R. E. Davis, A. T. C. Chang, K. Brown, “The spectral bidirectional reflectance of snow,” in Proceedings of the 4th International Colloquium on Spectral Signatures of Objects in Remote Sensing (European Space Agency, Paris, 1988), pp. 87–92.

Deschamps, P. Y.

C. Proy, D. Tanré, P. Y. Deschamps, “Evaluation of topographic effects on remotely sensed data,” Remote Sens. Environ. 30, 21–32 (1989).
[CrossRef]

Deuzé, J. L.

E. Vermote, D. Tanré, J. L. Deuzé, M. Herman, J. J. Morcrette, “Second simulation of the satellite signal in the solar spectrum, 6S: an overview,” IEEE Trans. Geosci. Remote Sens. 35, 675–686 (1997).
[CrossRef]

Dickinson, R. E.

M. M. Verstraete, B. Pinty, R. E. Dickinson, “A physical model of the bidirectional reflectance of vegetation canopies. 2. Inversion and validation,” J. Geophys. Res. 95, 11,767–11,775 (1990).
[CrossRef]

Dozier, J.

J. Dozier, J. Frew, “Atmospheric corrections to satellite radiometric data over rugged terrain,” Remote Sens. Environ. 11, 191–205 (1981).
[CrossRef]

J. Dozier, R. E. Davis, A. T. C. Chang, K. Brown, “The spectral bidirectional reflectance of snow,” in Proceedings of the 4th International Colloquium on Spectral Signatures of Objects in Remote Sensing (European Space Agency, Paris, 1988), pp. 87–92.

Egawa, H.

T. Kusaka, Y. Kawata, H. Egawa, S. Ueno, “Signature variations due to atmospheric and topographic effects on satellite MSS data over rugged terrain,” in Proceedings of International Geoscience and Remote Sensing Symposium (European Space Agency, Paris, 1988), pp. 825–828.

Elepov, B. S.

G. I. Marchuk, G. A. Mikhailov, M. A. Nazaraliev, R. A. Dacbinjan, B. A. Kargin, B. S. Elepov, The Monte Carlo Methods in Atmospheric Optics, D. L. MacAdam, ed., Vol. 12 of Springer Series in Optical Sciences (Springer-Verlag, Berlin, 1980), pp. 5–17.
[CrossRef]

Fenn, R. W.

R. McClatchey, R. W. Fenn, J. E. A. Selby, F. E. Volz, J. S. Garing, “Optical properties of the atmosphere,” (U.S. Air Force Cambridge Research Laboratory, Bedford, Mass., 1971).

Frew, J.

J. Dozier, J. Frew, “Atmospheric corrections to satellite radiometric data over rugged terrain,” Remote Sens. Environ. 11, 191–205 (1981).
[CrossRef]

Furumoto, S.

T. Kusaka, Y. Kawata, S. Ueno, S. Furumoto, “Removal of the atmospheric and topographic effects from the rugged terrain image data remotely sensed by Landsat,” in Proceedings of International Geoscience and Remote Sensing Symposium (Institute of Electrical and Electronic Engineers, Piscataway, N.J., 1987), Vol. 1, pp. 649–652.

Garing, J. S.

R. McClatchey, R. W. Fenn, J. E. A. Selby, F. E. Volz, J. S. Garing, “Optical properties of the atmosphere,” (U.S. Air Force Cambridge Research Laboratory, Bedford, Mass., 1971).

Govaerts, Y. M.

Y. M. Govaerts, M. M. Verstraete, “Raytran: a Monte Carlo ray-tracing model to compute light scattering in three-dimensional heterogeneous media,” IEEE Trans. Geosci. Remote Sens. 36, 493–504 (1998).
[CrossRef]

Herman, M.

E. Vermote, D. Tanré, J. L. Deuzé, M. Herman, J. J. Morcrette, “Second simulation of the satellite signal in the solar spectrum, 6S: an overview,” IEEE Trans. Geosci. Remote Sens. 35, 675–686 (1997).
[CrossRef]

Holben, B. N.

B. N. Holben, C. O. Justice, “The topographic effect on spectral response from nadir-pointing sensors,” Photogramm. Eng. Remote Sens. 46, 1191–1200 (1980).

Horn, B. K. P.

R. W. Sloberg, B. K. P. Horn, “Atmospheric effects in satellite imaging of mountainous terrain,” Appl. Opt. 22, 1703–1716 (1983).

Justice, C. O.

B. N. Holben, C. O. Justice, “The topographic effect on spectral response from nadir-pointing sensors,” Photogramm. Eng. Remote Sens. 46, 1191–1200 (1980).

Kargin, B. A.

G. I. Marchuk, G. A. Mikhailov, M. A. Nazaraliev, R. A. Dacbinjan, B. A. Kargin, B. S. Elepov, The Monte Carlo Methods in Atmospheric Optics, D. L. MacAdam, ed., Vol. 12 of Springer Series in Optical Sciences (Springer-Verlag, Berlin, 1980), pp. 5–17.
[CrossRef]

Kaufman, Y. J.

Kawata, Y.

T. Kusaka, Y. Kawata, S. Ueno, S. Furumoto, “Removal of the atmospheric and topographic effects from the rugged terrain image data remotely sensed by Landsat,” in Proceedings of International Geoscience and Remote Sensing Symposium (Institute of Electrical and Electronic Engineers, Piscataway, N.J., 1987), Vol. 1, pp. 649–652.

T. Kusaka, Y. Kawata, H. Egawa, S. Ueno, “Signature variations due to atmospheric and topographic effects on satellite MSS data over rugged terrain,” in Proceedings of International Geoscience and Remote Sensing Symposium (European Space Agency, Paris, 1988), pp. 825–828.

T. Kusaka, Y. Kawata, “Atmospheric and topographic correction of satellite data over mountainous terrain,” in Proceedings of International Geoscience and Remote Sensing Symposium (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1994), Vol. 1, pp. 58–60.

Kimes, D. S.

D. S. Kimes, J. A. Kirchner, “Modeling the effects of various radiant transfers in mountainous terrain on sensor response,” IEEE Trans. Geosci. Remote Sens. GE-19, 100–108 (1981).
[CrossRef]

Kirchner, J. A.

D. S. Kimes, J. A. Kirchner, “Modeling the effects of various radiant transfers in mountainous terrain on sensor response,” IEEE Trans. Geosci. Remote Sens. GE-19, 100–108 (1981).
[CrossRef]

Kusaka, T.

T. Kusaka, Y. Kawata, S. Ueno, S. Furumoto, “Removal of the atmospheric and topographic effects from the rugged terrain image data remotely sensed by Landsat,” in Proceedings of International Geoscience and Remote Sensing Symposium (Institute of Electrical and Electronic Engineers, Piscataway, N.J., 1987), Vol. 1, pp. 649–652.

T. Kusaka, Y. Kawata, H. Egawa, S. Ueno, “Signature variations due to atmospheric and topographic effects on satellite MSS data over rugged terrain,” in Proceedings of International Geoscience and Remote Sensing Symposium (European Space Agency, Paris, 1988), pp. 825–828.

T. Kusaka, Y. Kawata, “Atmospheric and topographic correction of satellite data over mountainous terrain,” in Proceedings of International Geoscience and Remote Sensing Symposium (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1994), Vol. 1, pp. 58–60.

Lenoble, J.

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

Leroy, M.

H. Cosnefroy, M. Leroy, X. Briottet, “Selection and characterization of Saharan and Arabian desert sites for the calibration of optical satellite sensors,” Remote Sens. Environ. 58, 101–114 (1996).
[CrossRef]

Marchuk, G. I.

G. I. Marchuk, G. A. Mikhailov, M. A. Nazaraliev, R. A. Dacbinjan, B. A. Kargin, B. S. Elepov, The Monte Carlo Methods in Atmospheric Optics, D. L. MacAdam, ed., Vol. 12 of Springer Series in Optical Sciences (Springer-Verlag, Berlin, 1980), pp. 5–17.
[CrossRef]

McClatchey, R.

R. McClatchey, R. W. Fenn, J. E. A. Selby, F. E. Volz, J. S. Garing, “Optical properties of the atmosphere,” (U.S. Air Force Cambridge Research Laboratory, Bedford, Mass., 1971).

Mikhailov, G. A.

G. I. Marchuk, G. A. Mikhailov, M. A. Nazaraliev, R. A. Dacbinjan, B. A. Kargin, B. S. Elepov, The Monte Carlo Methods in Atmospheric Optics, D. L. MacAdam, ed., Vol. 12 of Springer Series in Optical Sciences (Springer-Verlag, Berlin, 1980), pp. 5–17.
[CrossRef]

Morcrette, J. J.

E. Vermote, D. Tanré, J. L. Deuzé, M. Herman, J. J. Morcrette, “Second simulation of the satellite signal in the solar spectrum, 6S: an overview,” IEEE Trans. Geosci. Remote Sens. 35, 675–686 (1997).
[CrossRef]

Nazaraliev, M. A.

G. I. Marchuk, G. A. Mikhailov, M. A. Nazaraliev, R. A. Dacbinjan, B. A. Kargin, B. S. Elepov, The Monte Carlo Methods in Atmospheric Optics, D. L. MacAdam, ed., Vol. 12 of Springer Series in Optical Sciences (Springer-Verlag, Berlin, 1980), pp. 5–17.
[CrossRef]

Nicodemus, F. E.

Pinty, B.

M. M. Verstraete, B. Pinty, R. E. Dickinson, “A physical model of the bidirectional reflectance of vegetation canopies. 2. Inversion and validation,” J. Geophys. Res. 95, 11,767–11,775 (1990).
[CrossRef]

Proy, C.

C. Proy, D. Tanré, P. Y. Deschamps, “Evaluation of topographic effects on remotely sensed data,” Remote Sens. Environ. 30, 21–32 (1989).
[CrossRef]

Richter, R.

R. Richter, “Correction of atmospheric and topographic effects for high spatial resolution satellite imagery,” Intl. Remote Sens. 18, 1099–1111 (1997).
[CrossRef]

Selby, J. E. A.

R. McClatchey, R. W. Fenn, J. E. A. Selby, F. E. Volz, J. S. Garing, “Optical properties of the atmosphere,” (U.S. Air Force Cambridge Research Laboratory, Bedford, Mass., 1971).

Sloberg, R. W.

R. W. Sloberg, B. K. P. Horn, “Atmospheric effects in satellite imaging of mountainous terrain,” Appl. Opt. 22, 1703–1716 (1983).

Tanré, D.

E. Vermote, D. Tanré, J. L. Deuzé, M. Herman, J. J. Morcrette, “Second simulation of the satellite signal in the solar spectrum, 6S: an overview,” IEEE Trans. Geosci. Remote Sens. 35, 675–686 (1997).
[CrossRef]

C. Proy, D. Tanré, P. Y. Deschamps, “Evaluation of topographic effects on remotely sensed data,” Remote Sens. Environ. 30, 21–32 (1989).
[CrossRef]

Ueno, S.

T. Kusaka, Y. Kawata, H. Egawa, S. Ueno, “Signature variations due to atmospheric and topographic effects on satellite MSS data over rugged terrain,” in Proceedings of International Geoscience and Remote Sensing Symposium (European Space Agency, Paris, 1988), pp. 825–828.

T. Kusaka, Y. Kawata, S. Ueno, S. Furumoto, “Removal of the atmospheric and topographic effects from the rugged terrain image data remotely sensed by Landsat,” in Proceedings of International Geoscience and Remote Sensing Symposium (Institute of Electrical and Electronic Engineers, Piscataway, N.J., 1987), Vol. 1, pp. 649–652.

Vermote, E.

E. Vermote, D. Tanré, J. L. Deuzé, M. Herman, J. J. Morcrette, “Second simulation of the satellite signal in the solar spectrum, 6S: an overview,” IEEE Trans. Geosci. Remote Sens. 35, 675–686 (1997).
[CrossRef]

Verstraete, M. M.

Y. M. Govaerts, M. M. Verstraete, “Raytran: a Monte Carlo ray-tracing model to compute light scattering in three-dimensional heterogeneous media,” IEEE Trans. Geosci. Remote Sens. 36, 493–504 (1998).
[CrossRef]

M. M. Verstraete, B. Pinty, R. E. Dickinson, “A physical model of the bidirectional reflectance of vegetation canopies. 2. Inversion and validation,” J. Geophys. Res. 95, 11,767–11,775 (1990).
[CrossRef]

Volz, F. E.

R. McClatchey, R. W. Fenn, J. E. A. Selby, F. E. Volz, J. S. Garing, “Optical properties of the atmosphere,” (U.S. Air Force Cambridge Research Laboratory, Bedford, Mass., 1971).

Warren, S. G.

S. G. Warren, “Optical properties of snow,” Rev. Geophys. Space Phys. 20, 67–89 (1982).
[CrossRef]

Appl. Opt. (3)

IEEE Trans. Geosci. Remote Sens. (3)

Y. M. Govaerts, M. M. Verstraete, “Raytran: a Monte Carlo ray-tracing model to compute light scattering in three-dimensional heterogeneous media,” IEEE Trans. Geosci. Remote Sens. 36, 493–504 (1998).
[CrossRef]

D. S. Kimes, J. A. Kirchner, “Modeling the effects of various radiant transfers in mountainous terrain on sensor response,” IEEE Trans. Geosci. Remote Sens. GE-19, 100–108 (1981).
[CrossRef]

E. Vermote, D. Tanré, J. L. Deuzé, M. Herman, J. J. Morcrette, “Second simulation of the satellite signal in the solar spectrum, 6S: an overview,” IEEE Trans. Geosci. Remote Sens. 35, 675–686 (1997).
[CrossRef]

Intl. Remote Sens. (1)

R. Richter, “Correction of atmospheric and topographic effects for high spatial resolution satellite imagery,” Intl. Remote Sens. 18, 1099–1111 (1997).
[CrossRef]

J. Geophys. Res. (1)

M. M. Verstraete, B. Pinty, R. E. Dickinson, “A physical model of the bidirectional reflectance of vegetation canopies. 2. Inversion and validation,” J. Geophys. Res. 95, 11,767–11,775 (1990).
[CrossRef]

Photogramm. Eng. Remote Sens. (1)

B. N. Holben, C. O. Justice, “The topographic effect on spectral response from nadir-pointing sensors,” Photogramm. Eng. Remote Sens. 46, 1191–1200 (1980).

Remote Sens. Environ. (3)

C. Proy, D. Tanré, P. Y. Deschamps, “Evaluation of topographic effects on remotely sensed data,” Remote Sens. Environ. 30, 21–32 (1989).
[CrossRef]

H. Cosnefroy, M. Leroy, X. Briottet, “Selection and characterization of Saharan and Arabian desert sites for the calibration of optical satellite sensors,” Remote Sens. Environ. 58, 101–114 (1996).
[CrossRef]

J. Dozier, J. Frew, “Atmospheric corrections to satellite radiometric data over rugged terrain,” Remote Sens. Environ. 11, 191–205 (1981).
[CrossRef]

Rev. Geophys. Space Phys. (1)

S. G. Warren, “Optical properties of snow,” Rev. Geophys. Space Phys. 20, 67–89 (1982).
[CrossRef]

Other (8)

J. Dozier, R. E. Davis, A. T. C. Chang, K. Brown, “The spectral bidirectional reflectance of snow,” in Proceedings of the 4th International Colloquium on Spectral Signatures of Objects in Remote Sensing (European Space Agency, Paris, 1988), pp. 87–92.

G. I. Marchuk, G. A. Mikhailov, M. A. Nazaraliev, R. A. Dacbinjan, B. A. Kargin, B. S. Elepov, The Monte Carlo Methods in Atmospheric Optics, D. L. MacAdam, ed., Vol. 12 of Springer Series in Optical Sciences (Springer-Verlag, Berlin, 1980), pp. 5–17.
[CrossRef]

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

R. McClatchey, R. W. Fenn, J. E. A. Selby, F. E. Volz, J. S. Garing, “Optical properties of the atmosphere,” (U.S. Air Force Cambridge Research Laboratory, Bedford, Mass., 1971).

ASTER (Advanced Spaceborne Thermal Emission and Reflection Radiometer) spectral library, NASA: http://speclib.jpl.nasa.gov/ ; cognizant scientist, simon.j.hook@jpl.nasa.gov .

T. Kusaka, Y. Kawata, S. Ueno, S. Furumoto, “Removal of the atmospheric and topographic effects from the rugged terrain image data remotely sensed by Landsat,” in Proceedings of International Geoscience and Remote Sensing Symposium (Institute of Electrical and Electronic Engineers, Piscataway, N.J., 1987), Vol. 1, pp. 649–652.

T. Kusaka, Y. Kawata, H. Egawa, S. Ueno, “Signature variations due to atmospheric and topographic effects on satellite MSS data over rugged terrain,” in Proceedings of International Geoscience and Remote Sensing Symposium (European Space Agency, Paris, 1988), pp. 825–828.

T. Kusaka, Y. Kawata, “Atmospheric and topographic correction of satellite data over mountainous terrain,” in Proceedings of International Geoscience and Remote Sensing Symposium (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1994), Vol. 1, pp. 58–60.

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Figures (13)

Fig. 1
Fig. 1

Irradiance components at ground level.

Fig. 2
Fig. 2

Radiance components at sensor level.

Fig. 3
Fig. 3

Earth–atmosphere system.

Fig. 4
Fig. 4

Seashore landscape.

Fig. 5
Fig. 5

Irradiance components at ground level on the seashore.

Fig. 6
Fig. 6

Radiance components received by the sensor over the seashore.

Fig. 7
Fig. 7

Linear sand dunes.

Fig. 8
Fig. 8

Irradiance terms over linear sand dunes.

Fig. 9
Fig. 9

Radiance terms observed over linear sand dunes.

Fig. 10
Fig. 10

Deep valley between snow-covered hilltops.

Fig. 11
Fig. 11

Reflectance models of snow and grass. Negative values of zenith are used for backward scattering.

Fig. 12
Fig. 12

Irradiance terms over the deep valley.

Fig. 13
Fig. 13

Radiance components over the deep valley.

Tables (2)

Tables Icon

Table 1 Comparison of Monte Carlo and 6S Codes for θs = 30°, θv = 0°, and v = 23 km

Tables Icon

Table 2 Comparison of Monte Carlo and 6S Codes for θs = 30°, θv = 30°, and v = 10 kma

Equations (11)

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

ΔLm=Δω1ΩΔω2ΩnMΔω1SMρΔω1, Δω2π×nMm, Δω2NSTOAN ETOA cos θs,
Latmm=natmm, ΔωsNETOAΔωs.
Lm=Latmm+MDEMΔω1ΩΔω2ΩnMΔω1SM×ρΔω1, Δω2πnMm, Δω2N×SN ETOA cos θs.
dL=-σeBLBdB,
dpB, B+dB=exp-AB σeCdCσeBdB.
σeB=σs,molB+σs,aeroB+σa,molB+σa,aeroB,
pmolξ=3/41+cos2 ξ,
paeroξ=1-gλ21+gλ2-2gλ cos ξ3/2,
ρpθs, ϕs=ϕ=02πθ=0π/2ρθs, ϕs, θ, ϕπcosθsinθdθdϕ,
EP=nMSMSTOAN ETOA cos θs,
Lm=nmsmΔωmSTOAN ETOA cos θs.

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