Abstract

Radiative transfer models are often employed to derive the surface reflectance for Earth-looking multispectral scanners or imaging spectrometers. For this purpose the calculated radiances have to be resampled with the spectral channel response functions of the instrument. Three methods of bandpass resampling the product terms of the radiative transfer equation are compared: the exact method and two commonly used approximations. Error budgets for the two approximate methods are given for typical multispectral and hyperspectral sensors. The error depends on the wavelength, bandwidth, atmospheric parameters, and atmospheric path length.

© 2000 Optical Society of America

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  1. M. J. Duggin, C. J. Robinove, “Assumptions implicit in remote sensing data acquisition and analysis,” Int. J. Remote Sens. 11, 1669–1694 (1990).
    [CrossRef]
  2. B. M. Herman, S. R. Browning, “The effect of aerosols on the earth–atmosphere albedo,” J. Atmos. Sci. 32, 158–165 (1975).
    [CrossRef]
  3. K. Stamnes, S.-C. Tsay, W. Wiscombe, K. Jayaweera, “Numerically stable discrete-ordinate-method radiative transfer in multiple scattering and emitting layered media,” Appl. Opt. 27, 2502–2509 (1988).
    [CrossRef] [PubMed]
  4. A. Berk, L. S. Bernstein, G. P. Anderson, P. K. Acharya, D. C. Robertson, J. H. Chetwynd, S. M. Adler-Golden, “MODTRAN cloud and multiple scattering upgrades with application to AVIRIS,” Remote Sens. Environ. 65, 367–375 (1998).
    [CrossRef]
  5. E. F. Vermote, D. Tanre, J. L. Deuze, 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]
  6. P. N. Slater, S. F. Biggar, R. G. Holm, R. D. Jackson, Y. Mao, M. S. Moran, J. M. Palmer, B. Yuan, “Reflectance and radiance-based methods for the in-flight absolute calibration of multispectral sensors,” Remote Sens. Environ. 22, 11–37 (1987).
    [CrossRef]
  7. R. Santer, X. F. Gu, G. Guyot, J. L. Deuze, C. Devaux, E. Vermote, M. Verbrugghe, “SPOT calibration at the La Crau test site (France),” Remote Sens. Environ. 41, 227–237 (1992).
    [CrossRef]
  8. R. Richter, “On the in-flight absolute calibration of high spatial resolution spaceborne sensors using small ground targets,” Int. J. Remote Sens. 18, 2827–2833 (1997).
    [CrossRef]
  9. B.-C. Gao, K. B. Heidebrecht, A. F. H. Goetz, “Derivation of scaled surface reflectances from AVIRIS data,” Remote Sens. Environ. 44, 165–178 (1993).
    [CrossRef]
  10. Y. J. Kaufman, C. Sendra, “Algorithm for automatic atmospheric corrections to visible and near-IR satellite imagery,” Int. J. Remote Sens. 9, 1357–1381 (1988).
    [CrossRef]
  11. R. Richter, “A spatially adaptive fast atmospheric correction algorithm,” Int. J. Remote Sens. 17, 1201–1214 (1996).
    [CrossRef]
  12. R. W. Sjoberg, B. K. P. Horn, “Atmospheric effects in satellite imaging of mountainous terrain,” Appl. Opt. 22, 1701–1716 (1983).
    [CrossRef]
  13. S. Sandmeier, K. I. Itten, “A physically-based model to correct atmospheric and illumination effects in optical satellite data of rugged terrain,” IEEE Trans. Geosci. Remote Sens. 35, 708–717 (1997).
    [CrossRef]
  14. R. Richter, “Correction of satellite imagery over mountainous terrain,” Appl. Opt. 37, 4004–4015 (1998).
    [CrossRef]
  15. C. O. Justice, E. Vermote, J. R. G. Townshend, R. Defries, D. O. Roy, D. K. Hall, V. V. Salomonson, J. L. Privette, G. Riggs, A. Strahler, W. Lucht, R. B. Myneni, K. Knyazikhin, S. W. Running, P. R. Nemani, Z. Wan, A. R. Huete, W. van Leeuwen, R. E. Wolfe, L. Giglio, J.-P. Muller, Y. Knyazikhin, M. J. Barnsley, “The moderate resolution imaging spectroradiometer (MODIS): land remote sensing for global change research,” IEEE Trans. Geosci. Remote Sens. 36, 1228–1249 (1998).
    [CrossRef]
  16. K. Thome, F. Palluconi, T. Tashima, K. Matsuda, “Atmospheric correction of ASTER,” IEEE Trans. Geosci. Remote Sens. 36, 1199–1211 (1998).
    [CrossRef]
  17. B. L. Markham, J. L. Barker, “Spectral characterization of the Landsat Thematic Mapper sensors,” Int. J. Remote Sens. 6, 697–716 (1985).
    [CrossRef]
  18. T. Cocks, R. Jenssen, A. Stewart, I. Wilson, T. Shields, “The HYMAP airborne hyperspectral sensor: the system, calibration, and performance,” in Proceedings of the First EARSeL Workshop on Imaging Spectroscopy (Remote Sensing Laboratories, University of Zurich, Zurich, Switzerland, 1998), pp. 37–42.
  19. Z. Wan, J. Dozier, “A generalized split-window algorithm for retrieving land-surface temperature from space,” IEEE Trans. Geosci. Remote Sens. 34, 892–905 (1996).
    [CrossRef]
  20. A. Gillespie, S. R. Okugawa, T. Matsunaga, J. S. Cothern, S. Hook, A. B. Kahle, “A temperature and emissivity separation algorithm for Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) images,” IEEE Trans. Geosci. Remote Sens. 36, 1113–1126 (1998).
    [CrossRef]

1998 (5)

A. Berk, L. S. Bernstein, G. P. Anderson, P. K. Acharya, D. C. Robertson, J. H. Chetwynd, S. M. Adler-Golden, “MODTRAN cloud and multiple scattering upgrades with application to AVIRIS,” Remote Sens. Environ. 65, 367–375 (1998).
[CrossRef]

C. O. Justice, E. Vermote, J. R. G. Townshend, R. Defries, D. O. Roy, D. K. Hall, V. V. Salomonson, J. L. Privette, G. Riggs, A. Strahler, W. Lucht, R. B. Myneni, K. Knyazikhin, S. W. Running, P. R. Nemani, Z. Wan, A. R. Huete, W. van Leeuwen, R. E. Wolfe, L. Giglio, J.-P. Muller, Y. Knyazikhin, M. J. Barnsley, “The moderate resolution imaging spectroradiometer (MODIS): land remote sensing for global change research,” IEEE Trans. Geosci. Remote Sens. 36, 1228–1249 (1998).
[CrossRef]

K. Thome, F. Palluconi, T. Tashima, K. Matsuda, “Atmospheric correction of ASTER,” IEEE Trans. Geosci. Remote Sens. 36, 1199–1211 (1998).
[CrossRef]

A. Gillespie, S. R. Okugawa, T. Matsunaga, J. S. Cothern, S. Hook, A. B. Kahle, “A temperature and emissivity separation algorithm for Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) images,” IEEE Trans. Geosci. Remote Sens. 36, 1113–1126 (1998).
[CrossRef]

R. Richter, “Correction of satellite imagery over mountainous terrain,” Appl. Opt. 37, 4004–4015 (1998).
[CrossRef]

1997 (3)

E. F. Vermote, D. Tanre, J. L. Deuze, 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]

R. Richter, “On the in-flight absolute calibration of high spatial resolution spaceborne sensors using small ground targets,” Int. J. Remote Sens. 18, 2827–2833 (1997).
[CrossRef]

S. Sandmeier, K. I. Itten, “A physically-based model to correct atmospheric and illumination effects in optical satellite data of rugged terrain,” IEEE Trans. Geosci. Remote Sens. 35, 708–717 (1997).
[CrossRef]

1996 (2)

R. Richter, “A spatially adaptive fast atmospheric correction algorithm,” Int. J. Remote Sens. 17, 1201–1214 (1996).
[CrossRef]

Z. Wan, J. Dozier, “A generalized split-window algorithm for retrieving land-surface temperature from space,” IEEE Trans. Geosci. Remote Sens. 34, 892–905 (1996).
[CrossRef]

1993 (1)

B.-C. Gao, K. B. Heidebrecht, A. F. H. Goetz, “Derivation of scaled surface reflectances from AVIRIS data,” Remote Sens. Environ. 44, 165–178 (1993).
[CrossRef]

1992 (1)

R. Santer, X. F. Gu, G. Guyot, J. L. Deuze, C. Devaux, E. Vermote, M. Verbrugghe, “SPOT calibration at the La Crau test site (France),” Remote Sens. Environ. 41, 227–237 (1992).
[CrossRef]

1990 (1)

M. J. Duggin, C. J. Robinove, “Assumptions implicit in remote sensing data acquisition and analysis,” Int. J. Remote Sens. 11, 1669–1694 (1990).
[CrossRef]

1988 (2)

K. Stamnes, S.-C. Tsay, W. Wiscombe, K. Jayaweera, “Numerically stable discrete-ordinate-method radiative transfer in multiple scattering and emitting layered media,” Appl. Opt. 27, 2502–2509 (1988).
[CrossRef] [PubMed]

Y. J. Kaufman, C. Sendra, “Algorithm for automatic atmospheric corrections to visible and near-IR satellite imagery,” Int. J. Remote Sens. 9, 1357–1381 (1988).
[CrossRef]

1987 (1)

P. N. Slater, S. F. Biggar, R. G. Holm, R. D. Jackson, Y. Mao, M. S. Moran, J. M. Palmer, B. Yuan, “Reflectance and radiance-based methods for the in-flight absolute calibration of multispectral sensors,” Remote Sens. Environ. 22, 11–37 (1987).
[CrossRef]

1985 (1)

B. L. Markham, J. L. Barker, “Spectral characterization of the Landsat Thematic Mapper sensors,” Int. J. Remote Sens. 6, 697–716 (1985).
[CrossRef]

1983 (1)

R. W. Sjoberg, B. K. P. Horn, “Atmospheric effects in satellite imaging of mountainous terrain,” Appl. Opt. 22, 1701–1716 (1983).
[CrossRef]

1975 (1)

B. M. Herman, S. R. Browning, “The effect of aerosols on the earth–atmosphere albedo,” J. Atmos. Sci. 32, 158–165 (1975).
[CrossRef]

Acharya, P. K.

A. Berk, L. S. Bernstein, G. P. Anderson, P. K. Acharya, D. C. Robertson, J. H. Chetwynd, S. M. Adler-Golden, “MODTRAN cloud and multiple scattering upgrades with application to AVIRIS,” Remote Sens. Environ. 65, 367–375 (1998).
[CrossRef]

Adler-Golden, S. M.

A. Berk, L. S. Bernstein, G. P. Anderson, P. K. Acharya, D. C. Robertson, J. H. Chetwynd, S. M. Adler-Golden, “MODTRAN cloud and multiple scattering upgrades with application to AVIRIS,” Remote Sens. Environ. 65, 367–375 (1998).
[CrossRef]

Anderson, G. P.

A. Berk, L. S. Bernstein, G. P. Anderson, P. K. Acharya, D. C. Robertson, J. H. Chetwynd, S. M. Adler-Golden, “MODTRAN cloud and multiple scattering upgrades with application to AVIRIS,” Remote Sens. Environ. 65, 367–375 (1998).
[CrossRef]

Barker, J. L.

B. L. Markham, J. L. Barker, “Spectral characterization of the Landsat Thematic Mapper sensors,” Int. J. Remote Sens. 6, 697–716 (1985).
[CrossRef]

Barnsley, M. J.

C. O. Justice, E. Vermote, J. R. G. Townshend, R. Defries, D. O. Roy, D. K. Hall, V. V. Salomonson, J. L. Privette, G. Riggs, A. Strahler, W. Lucht, R. B. Myneni, K. Knyazikhin, S. W. Running, P. R. Nemani, Z. Wan, A. R. Huete, W. van Leeuwen, R. E. Wolfe, L. Giglio, J.-P. Muller, Y. Knyazikhin, M. J. Barnsley, “The moderate resolution imaging spectroradiometer (MODIS): land remote sensing for global change research,” IEEE Trans. Geosci. Remote Sens. 36, 1228–1249 (1998).
[CrossRef]

Berk, A.

A. Berk, L. S. Bernstein, G. P. Anderson, P. K. Acharya, D. C. Robertson, J. H. Chetwynd, S. M. Adler-Golden, “MODTRAN cloud and multiple scattering upgrades with application to AVIRIS,” Remote Sens. Environ. 65, 367–375 (1998).
[CrossRef]

Bernstein, L. S.

A. Berk, L. S. Bernstein, G. P. Anderson, P. K. Acharya, D. C. Robertson, J. H. Chetwynd, S. M. Adler-Golden, “MODTRAN cloud and multiple scattering upgrades with application to AVIRIS,” Remote Sens. Environ. 65, 367–375 (1998).
[CrossRef]

Biggar, S. F.

P. N. Slater, S. F. Biggar, R. G. Holm, R. D. Jackson, Y. Mao, M. S. Moran, J. M. Palmer, B. Yuan, “Reflectance and radiance-based methods for the in-flight absolute calibration of multispectral sensors,” Remote Sens. Environ. 22, 11–37 (1987).
[CrossRef]

Browning, S. R.

B. M. Herman, S. R. Browning, “The effect of aerosols on the earth–atmosphere albedo,” J. Atmos. Sci. 32, 158–165 (1975).
[CrossRef]

Chetwynd, J. H.

A. Berk, L. S. Bernstein, G. P. Anderson, P. K. Acharya, D. C. Robertson, J. H. Chetwynd, S. M. Adler-Golden, “MODTRAN cloud and multiple scattering upgrades with application to AVIRIS,” Remote Sens. Environ. 65, 367–375 (1998).
[CrossRef]

Cocks, T.

T. Cocks, R. Jenssen, A. Stewart, I. Wilson, T. Shields, “The HYMAP airborne hyperspectral sensor: the system, calibration, and performance,” in Proceedings of the First EARSeL Workshop on Imaging Spectroscopy (Remote Sensing Laboratories, University of Zurich, Zurich, Switzerland, 1998), pp. 37–42.

Cothern, J. S.

A. Gillespie, S. R. Okugawa, T. Matsunaga, J. S. Cothern, S. Hook, A. B. Kahle, “A temperature and emissivity separation algorithm for Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) images,” IEEE Trans. Geosci. Remote Sens. 36, 1113–1126 (1998).
[CrossRef]

Defries, R.

C. O. Justice, E. Vermote, J. R. G. Townshend, R. Defries, D. O. Roy, D. K. Hall, V. V. Salomonson, J. L. Privette, G. Riggs, A. Strahler, W. Lucht, R. B. Myneni, K. Knyazikhin, S. W. Running, P. R. Nemani, Z. Wan, A. R. Huete, W. van Leeuwen, R. E. Wolfe, L. Giglio, J.-P. Muller, Y. Knyazikhin, M. J. Barnsley, “The moderate resolution imaging spectroradiometer (MODIS): land remote sensing for global change research,” IEEE Trans. Geosci. Remote Sens. 36, 1228–1249 (1998).
[CrossRef]

Deuze, J. L.

E. F. Vermote, D. Tanre, J. L. Deuze, 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]

R. Santer, X. F. Gu, G. Guyot, J. L. Deuze, C. Devaux, E. Vermote, M. Verbrugghe, “SPOT calibration at the La Crau test site (France),” Remote Sens. Environ. 41, 227–237 (1992).
[CrossRef]

Devaux, C.

R. Santer, X. F. Gu, G. Guyot, J. L. Deuze, C. Devaux, E. Vermote, M. Verbrugghe, “SPOT calibration at the La Crau test site (France),” Remote Sens. Environ. 41, 227–237 (1992).
[CrossRef]

Dozier, J.

Z. Wan, J. Dozier, “A generalized split-window algorithm for retrieving land-surface temperature from space,” IEEE Trans. Geosci. Remote Sens. 34, 892–905 (1996).
[CrossRef]

Duggin, M. J.

M. J. Duggin, C. J. Robinove, “Assumptions implicit in remote sensing data acquisition and analysis,” Int. J. Remote Sens. 11, 1669–1694 (1990).
[CrossRef]

Gao, B.-C.

B.-C. Gao, K. B. Heidebrecht, A. F. H. Goetz, “Derivation of scaled surface reflectances from AVIRIS data,” Remote Sens. Environ. 44, 165–178 (1993).
[CrossRef]

Giglio, L.

C. O. Justice, E. Vermote, J. R. G. Townshend, R. Defries, D. O. Roy, D. K. Hall, V. V. Salomonson, J. L. Privette, G. Riggs, A. Strahler, W. Lucht, R. B. Myneni, K. Knyazikhin, S. W. Running, P. R. Nemani, Z. Wan, A. R. Huete, W. van Leeuwen, R. E. Wolfe, L. Giglio, J.-P. Muller, Y. Knyazikhin, M. J. Barnsley, “The moderate resolution imaging spectroradiometer (MODIS): land remote sensing for global change research,” IEEE Trans. Geosci. Remote Sens. 36, 1228–1249 (1998).
[CrossRef]

Gillespie, A.

A. Gillespie, S. R. Okugawa, T. Matsunaga, J. S. Cothern, S. Hook, A. B. Kahle, “A temperature and emissivity separation algorithm for Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) images,” IEEE Trans. Geosci. Remote Sens. 36, 1113–1126 (1998).
[CrossRef]

Goetz, A. F. H.

B.-C. Gao, K. B. Heidebrecht, A. F. H. Goetz, “Derivation of scaled surface reflectances from AVIRIS data,” Remote Sens. Environ. 44, 165–178 (1993).
[CrossRef]

Gu, X. F.

R. Santer, X. F. Gu, G. Guyot, J. L. Deuze, C. Devaux, E. Vermote, M. Verbrugghe, “SPOT calibration at the La Crau test site (France),” Remote Sens. Environ. 41, 227–237 (1992).
[CrossRef]

Guyot, G.

R. Santer, X. F. Gu, G. Guyot, J. L. Deuze, C. Devaux, E. Vermote, M. Verbrugghe, “SPOT calibration at the La Crau test site (France),” Remote Sens. Environ. 41, 227–237 (1992).
[CrossRef]

Hall, D. K.

C. O. Justice, E. Vermote, J. R. G. Townshend, R. Defries, D. O. Roy, D. K. Hall, V. V. Salomonson, J. L. Privette, G. Riggs, A. Strahler, W. Lucht, R. B. Myneni, K. Knyazikhin, S. W. Running, P. R. Nemani, Z. Wan, A. R. Huete, W. van Leeuwen, R. E. Wolfe, L. Giglio, J.-P. Muller, Y. Knyazikhin, M. J. Barnsley, “The moderate resolution imaging spectroradiometer (MODIS): land remote sensing for global change research,” IEEE Trans. Geosci. Remote Sens. 36, 1228–1249 (1998).
[CrossRef]

Heidebrecht, K. B.

B.-C. Gao, K. B. Heidebrecht, A. F. H. Goetz, “Derivation of scaled surface reflectances from AVIRIS data,” Remote Sens. Environ. 44, 165–178 (1993).
[CrossRef]

Herman, B. M.

B. M. Herman, S. R. Browning, “The effect of aerosols on the earth–atmosphere albedo,” J. Atmos. Sci. 32, 158–165 (1975).
[CrossRef]

Herman, M.

E. F. Vermote, D. Tanre, J. L. Deuze, 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]

Holm, R. G.

P. N. Slater, S. F. Biggar, R. G. Holm, R. D. Jackson, Y. Mao, M. S. Moran, J. M. Palmer, B. Yuan, “Reflectance and radiance-based methods for the in-flight absolute calibration of multispectral sensors,” Remote Sens. Environ. 22, 11–37 (1987).
[CrossRef]

Hook, S.

A. Gillespie, S. R. Okugawa, T. Matsunaga, J. S. Cothern, S. Hook, A. B. Kahle, “A temperature and emissivity separation algorithm for Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) images,” IEEE Trans. Geosci. Remote Sens. 36, 1113–1126 (1998).
[CrossRef]

Horn, B. K. P.

R. W. Sjoberg, B. K. P. Horn, “Atmospheric effects in satellite imaging of mountainous terrain,” Appl. Opt. 22, 1701–1716 (1983).
[CrossRef]

Huete, A. R.

C. O. Justice, E. Vermote, J. R. G. Townshend, R. Defries, D. O. Roy, D. K. Hall, V. V. Salomonson, J. L. Privette, G. Riggs, A. Strahler, W. Lucht, R. B. Myneni, K. Knyazikhin, S. W. Running, P. R. Nemani, Z. Wan, A. R. Huete, W. van Leeuwen, R. E. Wolfe, L. Giglio, J.-P. Muller, Y. Knyazikhin, M. J. Barnsley, “The moderate resolution imaging spectroradiometer (MODIS): land remote sensing for global change research,” IEEE Trans. Geosci. Remote Sens. 36, 1228–1249 (1998).
[CrossRef]

Itten, K. I.

S. Sandmeier, K. I. Itten, “A physically-based model to correct atmospheric and illumination effects in optical satellite data of rugged terrain,” IEEE Trans. Geosci. Remote Sens. 35, 708–717 (1997).
[CrossRef]

Jackson, R. D.

P. N. Slater, S. F. Biggar, R. G. Holm, R. D. Jackson, Y. Mao, M. S. Moran, J. M. Palmer, B. Yuan, “Reflectance and radiance-based methods for the in-flight absolute calibration of multispectral sensors,” Remote Sens. Environ. 22, 11–37 (1987).
[CrossRef]

Jayaweera, K.

Jenssen, R.

T. Cocks, R. Jenssen, A. Stewart, I. Wilson, T. Shields, “The HYMAP airborne hyperspectral sensor: the system, calibration, and performance,” in Proceedings of the First EARSeL Workshop on Imaging Spectroscopy (Remote Sensing Laboratories, University of Zurich, Zurich, Switzerland, 1998), pp. 37–42.

Justice, C. O.

C. O. Justice, E. Vermote, J. R. G. Townshend, R. Defries, D. O. Roy, D. K. Hall, V. V. Salomonson, J. L. Privette, G. Riggs, A. Strahler, W. Lucht, R. B. Myneni, K. Knyazikhin, S. W. Running, P. R. Nemani, Z. Wan, A. R. Huete, W. van Leeuwen, R. E. Wolfe, L. Giglio, J.-P. Muller, Y. Knyazikhin, M. J. Barnsley, “The moderate resolution imaging spectroradiometer (MODIS): land remote sensing for global change research,” IEEE Trans. Geosci. Remote Sens. 36, 1228–1249 (1998).
[CrossRef]

Kahle, A. B.

A. Gillespie, S. R. Okugawa, T. Matsunaga, J. S. Cothern, S. Hook, A. B. Kahle, “A temperature and emissivity separation algorithm for Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) images,” IEEE Trans. Geosci. Remote Sens. 36, 1113–1126 (1998).
[CrossRef]

Kaufman, Y. J.

Y. J. Kaufman, C. Sendra, “Algorithm for automatic atmospheric corrections to visible and near-IR satellite imagery,” Int. J. Remote Sens. 9, 1357–1381 (1988).
[CrossRef]

Knyazikhin, K.

C. O. Justice, E. Vermote, J. R. G. Townshend, R. Defries, D. O. Roy, D. K. Hall, V. V. Salomonson, J. L. Privette, G. Riggs, A. Strahler, W. Lucht, R. B. Myneni, K. Knyazikhin, S. W. Running, P. R. Nemani, Z. Wan, A. R. Huete, W. van Leeuwen, R. E. Wolfe, L. Giglio, J.-P. Muller, Y. Knyazikhin, M. J. Barnsley, “The moderate resolution imaging spectroradiometer (MODIS): land remote sensing for global change research,” IEEE Trans. Geosci. Remote Sens. 36, 1228–1249 (1998).
[CrossRef]

Knyazikhin, Y.

C. O. Justice, E. Vermote, J. R. G. Townshend, R. Defries, D. O. Roy, D. K. Hall, V. V. Salomonson, J. L. Privette, G. Riggs, A. Strahler, W. Lucht, R. B. Myneni, K. Knyazikhin, S. W. Running, P. R. Nemani, Z. Wan, A. R. Huete, W. van Leeuwen, R. E. Wolfe, L. Giglio, J.-P. Muller, Y. Knyazikhin, M. J. Barnsley, “The moderate resolution imaging spectroradiometer (MODIS): land remote sensing for global change research,” IEEE Trans. Geosci. Remote Sens. 36, 1228–1249 (1998).
[CrossRef]

Lucht, W.

C. O. Justice, E. Vermote, J. R. G. Townshend, R. Defries, D. O. Roy, D. K. Hall, V. V. Salomonson, J. L. Privette, G. Riggs, A. Strahler, W. Lucht, R. B. Myneni, K. Knyazikhin, S. W. Running, P. R. Nemani, Z. Wan, A. R. Huete, W. van Leeuwen, R. E. Wolfe, L. Giglio, J.-P. Muller, Y. Knyazikhin, M. J. Barnsley, “The moderate resolution imaging spectroradiometer (MODIS): land remote sensing for global change research,” IEEE Trans. Geosci. Remote Sens. 36, 1228–1249 (1998).
[CrossRef]

Mao, Y.

P. N. Slater, S. F. Biggar, R. G. Holm, R. D. Jackson, Y. Mao, M. S. Moran, J. M. Palmer, B. Yuan, “Reflectance and radiance-based methods for the in-flight absolute calibration of multispectral sensors,” Remote Sens. Environ. 22, 11–37 (1987).
[CrossRef]

Markham, B. L.

B. L. Markham, J. L. Barker, “Spectral characterization of the Landsat Thematic Mapper sensors,” Int. J. Remote Sens. 6, 697–716 (1985).
[CrossRef]

Matsuda, K.

K. Thome, F. Palluconi, T. Tashima, K. Matsuda, “Atmospheric correction of ASTER,” IEEE Trans. Geosci. Remote Sens. 36, 1199–1211 (1998).
[CrossRef]

Matsunaga, T.

A. Gillespie, S. R. Okugawa, T. Matsunaga, J. S. Cothern, S. Hook, A. B. Kahle, “A temperature and emissivity separation algorithm for Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) images,” IEEE Trans. Geosci. Remote Sens. 36, 1113–1126 (1998).
[CrossRef]

Moran, M. S.

P. N. Slater, S. F. Biggar, R. G. Holm, R. D. Jackson, Y. Mao, M. S. Moran, J. M. Palmer, B. Yuan, “Reflectance and radiance-based methods for the in-flight absolute calibration of multispectral sensors,” Remote Sens. Environ. 22, 11–37 (1987).
[CrossRef]

Morcrette, J. J.

E. F. Vermote, D. Tanre, J. L. Deuze, 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]

Muller, J.-P.

C. O. Justice, E. Vermote, J. R. G. Townshend, R. Defries, D. O. Roy, D. K. Hall, V. V. Salomonson, J. L. Privette, G. Riggs, A. Strahler, W. Lucht, R. B. Myneni, K. Knyazikhin, S. W. Running, P. R. Nemani, Z. Wan, A. R. Huete, W. van Leeuwen, R. E. Wolfe, L. Giglio, J.-P. Muller, Y. Knyazikhin, M. J. Barnsley, “The moderate resolution imaging spectroradiometer (MODIS): land remote sensing for global change research,” IEEE Trans. Geosci. Remote Sens. 36, 1228–1249 (1998).
[CrossRef]

Myneni, R. B.

C. O. Justice, E. Vermote, J. R. G. Townshend, R. Defries, D. O. Roy, D. K. Hall, V. V. Salomonson, J. L. Privette, G. Riggs, A. Strahler, W. Lucht, R. B. Myneni, K. Knyazikhin, S. W. Running, P. R. Nemani, Z. Wan, A. R. Huete, W. van Leeuwen, R. E. Wolfe, L. Giglio, J.-P. Muller, Y. Knyazikhin, M. J. Barnsley, “The moderate resolution imaging spectroradiometer (MODIS): land remote sensing for global change research,” IEEE Trans. Geosci. Remote Sens. 36, 1228–1249 (1998).
[CrossRef]

Nemani, P. R.

C. O. Justice, E. Vermote, J. R. G. Townshend, R. Defries, D. O. Roy, D. K. Hall, V. V. Salomonson, J. L. Privette, G. Riggs, A. Strahler, W. Lucht, R. B. Myneni, K. Knyazikhin, S. W. Running, P. R. Nemani, Z. Wan, A. R. Huete, W. van Leeuwen, R. E. Wolfe, L. Giglio, J.-P. Muller, Y. Knyazikhin, M. J. Barnsley, “The moderate resolution imaging spectroradiometer (MODIS): land remote sensing for global change research,” IEEE Trans. Geosci. Remote Sens. 36, 1228–1249 (1998).
[CrossRef]

Okugawa, S. R.

A. Gillespie, S. R. Okugawa, T. Matsunaga, J. S. Cothern, S. Hook, A. B. Kahle, “A temperature and emissivity separation algorithm for Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) images,” IEEE Trans. Geosci. Remote Sens. 36, 1113–1126 (1998).
[CrossRef]

Palluconi, F.

K. Thome, F. Palluconi, T. Tashima, K. Matsuda, “Atmospheric correction of ASTER,” IEEE Trans. Geosci. Remote Sens. 36, 1199–1211 (1998).
[CrossRef]

Palmer, J. M.

P. N. Slater, S. F. Biggar, R. G. Holm, R. D. Jackson, Y. Mao, M. S. Moran, J. M. Palmer, B. Yuan, “Reflectance and radiance-based methods for the in-flight absolute calibration of multispectral sensors,” Remote Sens. Environ. 22, 11–37 (1987).
[CrossRef]

Privette, J. L.

C. O. Justice, E. Vermote, J. R. G. Townshend, R. Defries, D. O. Roy, D. K. Hall, V. V. Salomonson, J. L. Privette, G. Riggs, A. Strahler, W. Lucht, R. B. Myneni, K. Knyazikhin, S. W. Running, P. R. Nemani, Z. Wan, A. R. Huete, W. van Leeuwen, R. E. Wolfe, L. Giglio, J.-P. Muller, Y. Knyazikhin, M. J. Barnsley, “The moderate resolution imaging spectroradiometer (MODIS): land remote sensing for global change research,” IEEE Trans. Geosci. Remote Sens. 36, 1228–1249 (1998).
[CrossRef]

Richter, R.

R. Richter, “Correction of satellite imagery over mountainous terrain,” Appl. Opt. 37, 4004–4015 (1998).
[CrossRef]

R. Richter, “On the in-flight absolute calibration of high spatial resolution spaceborne sensors using small ground targets,” Int. J. Remote Sens. 18, 2827–2833 (1997).
[CrossRef]

R. Richter, “A spatially adaptive fast atmospheric correction algorithm,” Int. J. Remote Sens. 17, 1201–1214 (1996).
[CrossRef]

Riggs, G.

C. O. Justice, E. Vermote, J. R. G. Townshend, R. Defries, D. O. Roy, D. K. Hall, V. V. Salomonson, J. L. Privette, G. Riggs, A. Strahler, W. Lucht, R. B. Myneni, K. Knyazikhin, S. W. Running, P. R. Nemani, Z. Wan, A. R. Huete, W. van Leeuwen, R. E. Wolfe, L. Giglio, J.-P. Muller, Y. Knyazikhin, M. J. Barnsley, “The moderate resolution imaging spectroradiometer (MODIS): land remote sensing for global change research,” IEEE Trans. Geosci. Remote Sens. 36, 1228–1249 (1998).
[CrossRef]

Robertson, D. C.

A. Berk, L. S. Bernstein, G. P. Anderson, P. K. Acharya, D. C. Robertson, J. H. Chetwynd, S. M. Adler-Golden, “MODTRAN cloud and multiple scattering upgrades with application to AVIRIS,” Remote Sens. Environ. 65, 367–375 (1998).
[CrossRef]

Robinove, C. J.

M. J. Duggin, C. J. Robinove, “Assumptions implicit in remote sensing data acquisition and analysis,” Int. J. Remote Sens. 11, 1669–1694 (1990).
[CrossRef]

Roy, D. O.

C. O. Justice, E. Vermote, J. R. G. Townshend, R. Defries, D. O. Roy, D. K. Hall, V. V. Salomonson, J. L. Privette, G. Riggs, A. Strahler, W. Lucht, R. B. Myneni, K. Knyazikhin, S. W. Running, P. R. Nemani, Z. Wan, A. R. Huete, W. van Leeuwen, R. E. Wolfe, L. Giglio, J.-P. Muller, Y. Knyazikhin, M. J. Barnsley, “The moderate resolution imaging spectroradiometer (MODIS): land remote sensing for global change research,” IEEE Trans. Geosci. Remote Sens. 36, 1228–1249 (1998).
[CrossRef]

Running, S. W.

C. O. Justice, E. Vermote, J. R. G. Townshend, R. Defries, D. O. Roy, D. K. Hall, V. V. Salomonson, J. L. Privette, G. Riggs, A. Strahler, W. Lucht, R. B. Myneni, K. Knyazikhin, S. W. Running, P. R. Nemani, Z. Wan, A. R. Huete, W. van Leeuwen, R. E. Wolfe, L. Giglio, J.-P. Muller, Y. Knyazikhin, M. J. Barnsley, “The moderate resolution imaging spectroradiometer (MODIS): land remote sensing for global change research,” IEEE Trans. Geosci. Remote Sens. 36, 1228–1249 (1998).
[CrossRef]

Salomonson, V. V.

C. O. Justice, E. Vermote, J. R. G. Townshend, R. Defries, D. O. Roy, D. K. Hall, V. V. Salomonson, J. L. Privette, G. Riggs, A. Strahler, W. Lucht, R. B. Myneni, K. Knyazikhin, S. W. Running, P. R. Nemani, Z. Wan, A. R. Huete, W. van Leeuwen, R. E. Wolfe, L. Giglio, J.-P. Muller, Y. Knyazikhin, M. J. Barnsley, “The moderate resolution imaging spectroradiometer (MODIS): land remote sensing for global change research,” IEEE Trans. Geosci. Remote Sens. 36, 1228–1249 (1998).
[CrossRef]

Sandmeier, S.

S. Sandmeier, K. I. Itten, “A physically-based model to correct atmospheric and illumination effects in optical satellite data of rugged terrain,” IEEE Trans. Geosci. Remote Sens. 35, 708–717 (1997).
[CrossRef]

Santer, R.

R. Santer, X. F. Gu, G. Guyot, J. L. Deuze, C. Devaux, E. Vermote, M. Verbrugghe, “SPOT calibration at the La Crau test site (France),” Remote Sens. Environ. 41, 227–237 (1992).
[CrossRef]

Sendra, C.

Y. J. Kaufman, C. Sendra, “Algorithm for automatic atmospheric corrections to visible and near-IR satellite imagery,” Int. J. Remote Sens. 9, 1357–1381 (1988).
[CrossRef]

Shields, T.

T. Cocks, R. Jenssen, A. Stewart, I. Wilson, T. Shields, “The HYMAP airborne hyperspectral sensor: the system, calibration, and performance,” in Proceedings of the First EARSeL Workshop on Imaging Spectroscopy (Remote Sensing Laboratories, University of Zurich, Zurich, Switzerland, 1998), pp. 37–42.

Sjoberg, R. W.

R. W. Sjoberg, B. K. P. Horn, “Atmospheric effects in satellite imaging of mountainous terrain,” Appl. Opt. 22, 1701–1716 (1983).
[CrossRef]

Slater, P. N.

P. N. Slater, S. F. Biggar, R. G. Holm, R. D. Jackson, Y. Mao, M. S. Moran, J. M. Palmer, B. Yuan, “Reflectance and radiance-based methods for the in-flight absolute calibration of multispectral sensors,” Remote Sens. Environ. 22, 11–37 (1987).
[CrossRef]

Stamnes, K.

Stewart, A.

T. Cocks, R. Jenssen, A. Stewart, I. Wilson, T. Shields, “The HYMAP airborne hyperspectral sensor: the system, calibration, and performance,” in Proceedings of the First EARSeL Workshop on Imaging Spectroscopy (Remote Sensing Laboratories, University of Zurich, Zurich, Switzerland, 1998), pp. 37–42.

Strahler, A.

C. O. Justice, E. Vermote, J. R. G. Townshend, R. Defries, D. O. Roy, D. K. Hall, V. V. Salomonson, J. L. Privette, G. Riggs, A. Strahler, W. Lucht, R. B. Myneni, K. Knyazikhin, S. W. Running, P. R. Nemani, Z. Wan, A. R. Huete, W. van Leeuwen, R. E. Wolfe, L. Giglio, J.-P. Muller, Y. Knyazikhin, M. J. Barnsley, “The moderate resolution imaging spectroradiometer (MODIS): land remote sensing for global change research,” IEEE Trans. Geosci. Remote Sens. 36, 1228–1249 (1998).
[CrossRef]

Tanre, D.

E. F. Vermote, D. Tanre, J. L. Deuze, 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]

Tashima, T.

K. Thome, F. Palluconi, T. Tashima, K. Matsuda, “Atmospheric correction of ASTER,” IEEE Trans. Geosci. Remote Sens. 36, 1199–1211 (1998).
[CrossRef]

Thome, K.

K. Thome, F. Palluconi, T. Tashima, K. Matsuda, “Atmospheric correction of ASTER,” IEEE Trans. Geosci. Remote Sens. 36, 1199–1211 (1998).
[CrossRef]

Townshend, J. R. G.

C. O. Justice, E. Vermote, J. R. G. Townshend, R. Defries, D. O. Roy, D. K. Hall, V. V. Salomonson, J. L. Privette, G. Riggs, A. Strahler, W. Lucht, R. B. Myneni, K. Knyazikhin, S. W. Running, P. R. Nemani, Z. Wan, A. R. Huete, W. van Leeuwen, R. E. Wolfe, L. Giglio, J.-P. Muller, Y. Knyazikhin, M. J. Barnsley, “The moderate resolution imaging spectroradiometer (MODIS): land remote sensing for global change research,” IEEE Trans. Geosci. Remote Sens. 36, 1228–1249 (1998).
[CrossRef]

Tsay, S.-C.

van Leeuwen, W.

C. O. Justice, E. Vermote, J. R. G. Townshend, R. Defries, D. O. Roy, D. K. Hall, V. V. Salomonson, J. L. Privette, G. Riggs, A. Strahler, W. Lucht, R. B. Myneni, K. Knyazikhin, S. W. Running, P. R. Nemani, Z. Wan, A. R. Huete, W. van Leeuwen, R. E. Wolfe, L. Giglio, J.-P. Muller, Y. Knyazikhin, M. J. Barnsley, “The moderate resolution imaging spectroradiometer (MODIS): land remote sensing for global change research,” IEEE Trans. Geosci. Remote Sens. 36, 1228–1249 (1998).
[CrossRef]

Verbrugghe, M.

R. Santer, X. F. Gu, G. Guyot, J. L. Deuze, C. Devaux, E. Vermote, M. Verbrugghe, “SPOT calibration at the La Crau test site (France),” Remote Sens. Environ. 41, 227–237 (1992).
[CrossRef]

Vermote, E.

C. O. Justice, E. Vermote, J. R. G. Townshend, R. Defries, D. O. Roy, D. K. Hall, V. V. Salomonson, J. L. Privette, G. Riggs, A. Strahler, W. Lucht, R. B. Myneni, K. Knyazikhin, S. W. Running, P. R. Nemani, Z. Wan, A. R. Huete, W. van Leeuwen, R. E. Wolfe, L. Giglio, J.-P. Muller, Y. Knyazikhin, M. J. Barnsley, “The moderate resolution imaging spectroradiometer (MODIS): land remote sensing for global change research,” IEEE Trans. Geosci. Remote Sens. 36, 1228–1249 (1998).
[CrossRef]

R. Santer, X. F. Gu, G. Guyot, J. L. Deuze, C. Devaux, E. Vermote, M. Verbrugghe, “SPOT calibration at the La Crau test site (France),” Remote Sens. Environ. 41, 227–237 (1992).
[CrossRef]

Vermote, E. F.

E. F. Vermote, D. Tanre, J. L. Deuze, 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]

Wan, Z.

C. O. Justice, E. Vermote, J. R. G. Townshend, R. Defries, D. O. Roy, D. K. Hall, V. V. Salomonson, J. L. Privette, G. Riggs, A. Strahler, W. Lucht, R. B. Myneni, K. Knyazikhin, S. W. Running, P. R. Nemani, Z. Wan, A. R. Huete, W. van Leeuwen, R. E. Wolfe, L. Giglio, J.-P. Muller, Y. Knyazikhin, M. J. Barnsley, “The moderate resolution imaging spectroradiometer (MODIS): land remote sensing for global change research,” IEEE Trans. Geosci. Remote Sens. 36, 1228–1249 (1998).
[CrossRef]

Z. Wan, J. Dozier, “A generalized split-window algorithm for retrieving land-surface temperature from space,” IEEE Trans. Geosci. Remote Sens. 34, 892–905 (1996).
[CrossRef]

Wilson, I.

T. Cocks, R. Jenssen, A. Stewart, I. Wilson, T. Shields, “The HYMAP airborne hyperspectral sensor: the system, calibration, and performance,” in Proceedings of the First EARSeL Workshop on Imaging Spectroscopy (Remote Sensing Laboratories, University of Zurich, Zurich, Switzerland, 1998), pp. 37–42.

Wiscombe, W.

Wolfe, R. E.

C. O. Justice, E. Vermote, J. R. G. Townshend, R. Defries, D. O. Roy, D. K. Hall, V. V. Salomonson, J. L. Privette, G. Riggs, A. Strahler, W. Lucht, R. B. Myneni, K. Knyazikhin, S. W. Running, P. R. Nemani, Z. Wan, A. R. Huete, W. van Leeuwen, R. E. Wolfe, L. Giglio, J.-P. Muller, Y. Knyazikhin, M. J. Barnsley, “The moderate resolution imaging spectroradiometer (MODIS): land remote sensing for global change research,” IEEE Trans. Geosci. Remote Sens. 36, 1228–1249 (1998).
[CrossRef]

Yuan, B.

P. N. Slater, S. F. Biggar, R. G. Holm, R. D. Jackson, Y. Mao, M. S. Moran, J. M. Palmer, B. Yuan, “Reflectance and radiance-based methods for the in-flight absolute calibration of multispectral sensors,” Remote Sens. Environ. 22, 11–37 (1987).
[CrossRef]

Appl. Opt. (3)

IEEE Trans. Geosci. Remote Sens. (6)

Z. Wan, J. Dozier, “A generalized split-window algorithm for retrieving land-surface temperature from space,” IEEE Trans. Geosci. Remote Sens. 34, 892–905 (1996).
[CrossRef]

A. Gillespie, S. R. Okugawa, T. Matsunaga, J. S. Cothern, S. Hook, A. B. Kahle, “A temperature and emissivity separation algorithm for Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) images,” IEEE Trans. Geosci. Remote Sens. 36, 1113–1126 (1998).
[CrossRef]

S. Sandmeier, K. I. Itten, “A physically-based model to correct atmospheric and illumination effects in optical satellite data of rugged terrain,” IEEE Trans. Geosci. Remote Sens. 35, 708–717 (1997).
[CrossRef]

C. O. Justice, E. Vermote, J. R. G. Townshend, R. Defries, D. O. Roy, D. K. Hall, V. V. Salomonson, J. L. Privette, G. Riggs, A. Strahler, W. Lucht, R. B. Myneni, K. Knyazikhin, S. W. Running, P. R. Nemani, Z. Wan, A. R. Huete, W. van Leeuwen, R. E. Wolfe, L. Giglio, J.-P. Muller, Y. Knyazikhin, M. J. Barnsley, “The moderate resolution imaging spectroradiometer (MODIS): land remote sensing for global change research,” IEEE Trans. Geosci. Remote Sens. 36, 1228–1249 (1998).
[CrossRef]

K. Thome, F. Palluconi, T. Tashima, K. Matsuda, “Atmospheric correction of ASTER,” IEEE Trans. Geosci. Remote Sens. 36, 1199–1211 (1998).
[CrossRef]

E. F. Vermote, D. Tanre, J. L. Deuze, 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]

Int. J. Remote Sens. (5)

R. Richter, “On the in-flight absolute calibration of high spatial resolution spaceborne sensors using small ground targets,” Int. J. Remote Sens. 18, 2827–2833 (1997).
[CrossRef]

B. L. Markham, J. L. Barker, “Spectral characterization of the Landsat Thematic Mapper sensors,” Int. J. Remote Sens. 6, 697–716 (1985).
[CrossRef]

M. J. Duggin, C. J. Robinove, “Assumptions implicit in remote sensing data acquisition and analysis,” Int. J. Remote Sens. 11, 1669–1694 (1990).
[CrossRef]

Y. J. Kaufman, C. Sendra, “Algorithm for automatic atmospheric corrections to visible and near-IR satellite imagery,” Int. J. Remote Sens. 9, 1357–1381 (1988).
[CrossRef]

R. Richter, “A spatially adaptive fast atmospheric correction algorithm,” Int. J. Remote Sens. 17, 1201–1214 (1996).
[CrossRef]

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B. M. Herman, S. R. Browning, “The effect of aerosols on the earth–atmosphere albedo,” J. Atmos. Sci. 32, 158–165 (1975).
[CrossRef]

Remote Sens. Environ. (4)

B.-C. Gao, K. B. Heidebrecht, A. F. H. Goetz, “Derivation of scaled surface reflectances from AVIRIS data,” Remote Sens. Environ. 44, 165–178 (1993).
[CrossRef]

P. N. Slater, S. F. Biggar, R. G. Holm, R. D. Jackson, Y. Mao, M. S. Moran, J. M. Palmer, B. Yuan, “Reflectance and radiance-based methods for the in-flight absolute calibration of multispectral sensors,” Remote Sens. Environ. 22, 11–37 (1987).
[CrossRef]

R. Santer, X. F. Gu, G. Guyot, J. L. Deuze, C. Devaux, E. Vermote, M. Verbrugghe, “SPOT calibration at the La Crau test site (France),” Remote Sens. Environ. 41, 227–237 (1992).
[CrossRef]

A. Berk, L. S. Bernstein, G. P. Anderson, P. K. Acharya, D. C. Robertson, J. H. Chetwynd, S. M. Adler-Golden, “MODTRAN cloud and multiple scattering upgrades with application to AVIRIS,” Remote Sens. Environ. 65, 367–375 (1998).
[CrossRef]

Other (1)

T. Cocks, R. Jenssen, A. Stewart, I. Wilson, T. Shields, “The HYMAP airborne hyperspectral sensor: the system, calibration, and performance,” in Proceedings of the First EARSeL Workshop on Imaging Spectroscopy (Remote Sensing Laboratories, University of Zurich, Zurich, Switzerland, 1998), pp. 37–42.

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Figures (3)

Fig. 1
Fig. 1

Error budget for Landsat-5 Thematic Mapper (see text). Solid curve, approximation (a1); dashed curve, approximation (a2), solar zenith θ s = 30°; dotted curve, approximation (a1); dotted–dashed curve, approximation (a2), solar zenith θ s = 60°.

Fig. 2
Fig. 2

Error budget for HyMap (see text). Solid curve, approximation (a1), solar zenith θ s = 30°; dashed curve, approximation (a1) with θ s = 60°. Approximation method (a2) yields nearly the same results. The magnitude of the spikes at 1.4 µm is as great as 600% and 1100% for θ s = 30° and θ s = 60°, respectively. HyMap has no bands in the 1.80–1.95-µm region, so a straight line connects this wavelength gap.

Fig. 3
Fig. 3

Relative errors in reflectance retrieval for three spectrally varying surfaces (Landsat Thematic Mapper bands). Diamonds, vegetation; triangles, soil; squares, water surface.

Equations (14)

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

Lλ=Lpλ+ρλ/πτλEgλ,
Lλ=Lpλ+ρλ/πτλEsλτsλcos θs+Edifλ,
λ1λ2 LλRλdλλ1λ2 Rλdλ=λ1λ2 LpλRλdλλ1λ2 Rλdλ+1πλ1λ2 ρλτλEgλRλdλλ1λ2 Rλdλ.
L=λ1λ2 LλRλdλλ1λ2 Rλdλnormalized at-sensor radiance,
Lp=λ1λ2 LpλRλdλλ1λ2 Rλdλnormalized path radiance,
Et=λ1λ2 τλEgλRλdλλ1λ2 Rλdλ=λ1λ2 τλ[Esλτsλcos θs+Edifλ}Rλdλλ1λ2 Rλdλ,
L=Lp+ρ/πEt,
La1=Lp+ρ/πτa1Ega1,
τa1=λ1λ2 τλRλdλλ1λ2 Rλdλ,
Ega1=λ1λ2 EgλRλdλλ1λ2 Rλdλ.
La2=Lp+ρ/πτa2Esa2τsa2 cos θs+Edifa2,
L=Lp+ρπEst cos β+Edift,
Est=λ1λ2 τλEsλτsλRλdλλ1λ2 Rλdλ,
Edift=λ1λ2 τλEdifλRλdλλ1λ2 Rλdλ.

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