Abstract

Multiangle algorithms for estimating sea and land surface temperature with Along-Track Scanning Radiometer data require a precise knowledge of the angular variation of surface emissivity in the thermal infrared. Currently, few measurements of this variation exist. Here an experimental investigation of the angular variation of the infrared emissivity in the thermal infrared (8–14-µm) band of some representative samples was made at angles of 0°–65° (at 5° increments) to the surface normal. The results show a decrease of the emissivity with increasing viewing angle, with water showing the highest angular dependence (∼7% from 0° to 65° views). Clay, sand, slime, and gravel show variations of approximately 1–3% for the same range of views, whereas a homogeneous grass cover does not show angular dependence. Finally, we include an evaluation of the impact that these data can produce on the algorithms for determining land and sea surface temperature from double-angle views.

© 1999 Optical Society of America

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References

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  1. F. Nerry, J. Labed, M. P. Stoll, “Spectral properties of land surfaces in the thermal infrared, 1: laboratory measurements of absolute spectral emissivity signatures,” J. Geophys. Res. 95, 7027–7044 (1990).
    [CrossRef]
  2. J. A. Sobrino, Z.-L. Li, M. P. Stoll, F. Becker, “Improvements in the split-window technique for the land surface temperature determination,” IEEE Trans. Geosci. Remote Sens. 32, 243–253 (1994).
    [CrossRef]
  3. ESA/Earthnet, ERS-1 System, P. Vass, B. Battrick, (European Space Agency, European Space Research and Technology Centre, Noordwijk, The Netherlands, 1992).
  4. ESA/Earthnet, ERS-1 Product Specification, P. Vass, B. Battrick, eds., (European Space Agency, European Space Research and Technology Centre, Noordwijk, The Netherlands, 1992).
  5. A. Chédin, N. A. Scott, A. Berroir, “A single-channel double-viewing angle method for sea surface temperature determination from coincident METEOSAT and TIROS-N radiometric measurements,” J. Appl. Meteorol. 21, 613–618 (1982).
    [CrossRef]
  6. M. S. Malkevich, A. K. Gorodetsky, “Determination of ocean surface temperature taking account of atmospheric effects by measurements of the angular IR-radiation distribution of the ‘ocean-atmosphere’ system made from the satellite ‘COSMOS-1151,’” Remote Sens. Rev. 3, 137–161 (1988).
    [CrossRef]
  7. P. M. Saunders, “Aerial measurement of sea surface temperature in the infrared,” J. Geophys. Res. 72, 4109–4117 (1967).
    [CrossRef]
  8. R. J. Holyer, “A two-satellite method for measurement of sea surface temperature,” Int. J. Remote Sens. 5, 115–131 (1984).
    [CrossRef]
  9. H. E. Montgomery, “Simultaneous earth observations from two satellites,” Int. J. Remote Sens. 7, 1083–1087 (1986).
    [CrossRef]
  10. C. T. Mutlow, A. M. Závody, I. J. Barton, D. T. Lewellyn-Jones, “Sea surface temperature measurements by the along-track scanning radiometer on ESA’s ERS-1 satellite: early results,” J. Geophys. Res. 99, 22,578–22,588 (1994).
  11. J. Labed, M. P. Stoll, “Angular variation of land surface spectral emissivity in the thermal infrared: laboratory investigations on bare soils,” Int. J. Remote Sens. 12, 2299–2310 (1991).
    [CrossRef]
  12. W. G. Rees, S. P. James, “Angular variation of the infrared emissivity of ice and water surfaces,” Int. J. Remote Sens. 13, 2873–2886 (1992).
    [CrossRef]
  13. W. C. Snyder, Z. Wan, Y. Zhang, Y.-Z. Feng, “Thermal infrared (3–14 µm) bidirectional reflectance measurements of sands and soils,” Remote Sens. Environ. 60, 101–109 (1997).
    [CrossRef]
  14. F. Becker, “The Impact of spectral emissivity on the measurement of land surface temperature from a satellite,” Int. J. Remote Sens. 8, 1509–1522 (1987).
    [CrossRef]
  15. J. A. Sobrino, V. Caselles, F. Becker, “Significance of the remote sensed thermal infrared measurements obtained over a citrus orchad,” ISPRS J. Photogramm. Remote Sens. 44, 343–354 (1990).
    [CrossRef]
  16. J. A. Sobrino, V. Caselles, “Medida mediante el método de la caja de la emisividad en la banda espectral de los 8–14 µm de algunos suelos agrícolas y de la vegetación,” An. Fis. B85, 220–227 (1989).
  17. E. Rubio, V. Caselles, C. Badenas, “Emissivity measurements of several soils and vegetation types in the 8–14 µm wave band: analysis of two field methods,” Remote Sens. Environ. 59, 490–521 (1997).
    [CrossRef]
  18. W. G. Rees, Physical Principles of Remote Sensing, (Cambridge University Press, Cambridge, UK, 1990).
  19. J. A. Sobrino, Z.-L. Li, M. P. Stoll, F. Becker, “Multi-channel and multi-angle algorithms for estimating sea and land surface temperature with ATSR data,” Int. J. Remote Sens. 17, 2089–2114 (1996).
    [CrossRef]
  20. J. A. Sobrino, V. Caselles, “A methodology for obtaining the crop temperature from NOAA-9 AVHRR data,” Int. J. Remote Sens. 12, 2461–2475 (1991).
    [CrossRef]
  21. I. J. Barton, “Satellite-derived surface temperatures—a comparison between operational, theoretical and experimental algorithms,” J. Appl. Meteorol. 31, 432–442 (1992).
    [CrossRef]

1997 (2)

W. C. Snyder, Z. Wan, Y. Zhang, Y.-Z. Feng, “Thermal infrared (3–14 µm) bidirectional reflectance measurements of sands and soils,” Remote Sens. Environ. 60, 101–109 (1997).
[CrossRef]

E. Rubio, V. Caselles, C. Badenas, “Emissivity measurements of several soils and vegetation types in the 8–14 µm wave band: analysis of two field methods,” Remote Sens. Environ. 59, 490–521 (1997).
[CrossRef]

1996 (1)

J. A. Sobrino, Z.-L. Li, M. P. Stoll, F. Becker, “Multi-channel and multi-angle algorithms for estimating sea and land surface temperature with ATSR data,” Int. J. Remote Sens. 17, 2089–2114 (1996).
[CrossRef]

1994 (2)

J. A. Sobrino, Z.-L. Li, M. P. Stoll, F. Becker, “Improvements in the split-window technique for the land surface temperature determination,” IEEE Trans. Geosci. Remote Sens. 32, 243–253 (1994).
[CrossRef]

C. T. Mutlow, A. M. Závody, I. J. Barton, D. T. Lewellyn-Jones, “Sea surface temperature measurements by the along-track scanning radiometer on ESA’s ERS-1 satellite: early results,” J. Geophys. Res. 99, 22,578–22,588 (1994).

1992 (2)

W. G. Rees, S. P. James, “Angular variation of the infrared emissivity of ice and water surfaces,” Int. J. Remote Sens. 13, 2873–2886 (1992).
[CrossRef]

I. J. Barton, “Satellite-derived surface temperatures—a comparison between operational, theoretical and experimental algorithms,” J. Appl. Meteorol. 31, 432–442 (1992).
[CrossRef]

1991 (2)

J. A. Sobrino, V. Caselles, “A methodology for obtaining the crop temperature from NOAA-9 AVHRR data,” Int. J. Remote Sens. 12, 2461–2475 (1991).
[CrossRef]

J. Labed, M. P. Stoll, “Angular variation of land surface spectral emissivity in the thermal infrared: laboratory investigations on bare soils,” Int. J. Remote Sens. 12, 2299–2310 (1991).
[CrossRef]

1990 (2)

F. Nerry, J. Labed, M. P. Stoll, “Spectral properties of land surfaces in the thermal infrared, 1: laboratory measurements of absolute spectral emissivity signatures,” J. Geophys. Res. 95, 7027–7044 (1990).
[CrossRef]

J. A. Sobrino, V. Caselles, F. Becker, “Significance of the remote sensed thermal infrared measurements obtained over a citrus orchad,” ISPRS J. Photogramm. Remote Sens. 44, 343–354 (1990).
[CrossRef]

1989 (1)

J. A. Sobrino, V. Caselles, “Medida mediante el método de la caja de la emisividad en la banda espectral de los 8–14 µm de algunos suelos agrícolas y de la vegetación,” An. Fis. B85, 220–227 (1989).

1988 (1)

M. S. Malkevich, A. K. Gorodetsky, “Determination of ocean surface temperature taking account of atmospheric effects by measurements of the angular IR-radiation distribution of the ‘ocean-atmosphere’ system made from the satellite ‘COSMOS-1151,’” Remote Sens. Rev. 3, 137–161 (1988).
[CrossRef]

1987 (1)

F. Becker, “The Impact of spectral emissivity on the measurement of land surface temperature from a satellite,” Int. J. Remote Sens. 8, 1509–1522 (1987).
[CrossRef]

1986 (1)

H. E. Montgomery, “Simultaneous earth observations from two satellites,” Int. J. Remote Sens. 7, 1083–1087 (1986).
[CrossRef]

1984 (1)

R. J. Holyer, “A two-satellite method for measurement of sea surface temperature,” Int. J. Remote Sens. 5, 115–131 (1984).
[CrossRef]

1982 (1)

A. Chédin, N. A. Scott, A. Berroir, “A single-channel double-viewing angle method for sea surface temperature determination from coincident METEOSAT and TIROS-N radiometric measurements,” J. Appl. Meteorol. 21, 613–618 (1982).
[CrossRef]

1967 (1)

P. M. Saunders, “Aerial measurement of sea surface temperature in the infrared,” J. Geophys. Res. 72, 4109–4117 (1967).
[CrossRef]

Badenas, C.

E. Rubio, V. Caselles, C. Badenas, “Emissivity measurements of several soils and vegetation types in the 8–14 µm wave band: analysis of two field methods,” Remote Sens. Environ. 59, 490–521 (1997).
[CrossRef]

Barton, I. J.

C. T. Mutlow, A. M. Závody, I. J. Barton, D. T. Lewellyn-Jones, “Sea surface temperature measurements by the along-track scanning radiometer on ESA’s ERS-1 satellite: early results,” J. Geophys. Res. 99, 22,578–22,588 (1994).

I. J. Barton, “Satellite-derived surface temperatures—a comparison between operational, theoretical and experimental algorithms,” J. Appl. Meteorol. 31, 432–442 (1992).
[CrossRef]

Becker, F.

J. A. Sobrino, Z.-L. Li, M. P. Stoll, F. Becker, “Multi-channel and multi-angle algorithms for estimating sea and land surface temperature with ATSR data,” Int. J. Remote Sens. 17, 2089–2114 (1996).
[CrossRef]

J. A. Sobrino, Z.-L. Li, M. P. Stoll, F. Becker, “Improvements in the split-window technique for the land surface temperature determination,” IEEE Trans. Geosci. Remote Sens. 32, 243–253 (1994).
[CrossRef]

J. A. Sobrino, V. Caselles, F. Becker, “Significance of the remote sensed thermal infrared measurements obtained over a citrus orchad,” ISPRS J. Photogramm. Remote Sens. 44, 343–354 (1990).
[CrossRef]

F. Becker, “The Impact of spectral emissivity on the measurement of land surface temperature from a satellite,” Int. J. Remote Sens. 8, 1509–1522 (1987).
[CrossRef]

Berroir, A.

A. Chédin, N. A. Scott, A. Berroir, “A single-channel double-viewing angle method for sea surface temperature determination from coincident METEOSAT and TIROS-N radiometric measurements,” J. Appl. Meteorol. 21, 613–618 (1982).
[CrossRef]

Caselles, V.

E. Rubio, V. Caselles, C. Badenas, “Emissivity measurements of several soils and vegetation types in the 8–14 µm wave band: analysis of two field methods,” Remote Sens. Environ. 59, 490–521 (1997).
[CrossRef]

J. A. Sobrino, V. Caselles, “A methodology for obtaining the crop temperature from NOAA-9 AVHRR data,” Int. J. Remote Sens. 12, 2461–2475 (1991).
[CrossRef]

J. A. Sobrino, V. Caselles, F. Becker, “Significance of the remote sensed thermal infrared measurements obtained over a citrus orchad,” ISPRS J. Photogramm. Remote Sens. 44, 343–354 (1990).
[CrossRef]

J. A. Sobrino, V. Caselles, “Medida mediante el método de la caja de la emisividad en la banda espectral de los 8–14 µm de algunos suelos agrícolas y de la vegetación,” An. Fis. B85, 220–227 (1989).

Chédin, A.

A. Chédin, N. A. Scott, A. Berroir, “A single-channel double-viewing angle method for sea surface temperature determination from coincident METEOSAT and TIROS-N radiometric measurements,” J. Appl. Meteorol. 21, 613–618 (1982).
[CrossRef]

Feng, Y.-Z.

W. C. Snyder, Z. Wan, Y. Zhang, Y.-Z. Feng, “Thermal infrared (3–14 µm) bidirectional reflectance measurements of sands and soils,” Remote Sens. Environ. 60, 101–109 (1997).
[CrossRef]

Gorodetsky, A. K.

M. S. Malkevich, A. K. Gorodetsky, “Determination of ocean surface temperature taking account of atmospheric effects by measurements of the angular IR-radiation distribution of the ‘ocean-atmosphere’ system made from the satellite ‘COSMOS-1151,’” Remote Sens. Rev. 3, 137–161 (1988).
[CrossRef]

Holyer, R. J.

R. J. Holyer, “A two-satellite method for measurement of sea surface temperature,” Int. J. Remote Sens. 5, 115–131 (1984).
[CrossRef]

James, S. P.

W. G. Rees, S. P. James, “Angular variation of the infrared emissivity of ice and water surfaces,” Int. J. Remote Sens. 13, 2873–2886 (1992).
[CrossRef]

Labed, J.

J. Labed, M. P. Stoll, “Angular variation of land surface spectral emissivity in the thermal infrared: laboratory investigations on bare soils,” Int. J. Remote Sens. 12, 2299–2310 (1991).
[CrossRef]

F. Nerry, J. Labed, M. P. Stoll, “Spectral properties of land surfaces in the thermal infrared, 1: laboratory measurements of absolute spectral emissivity signatures,” J. Geophys. Res. 95, 7027–7044 (1990).
[CrossRef]

Lewellyn-Jones, D. T.

C. T. Mutlow, A. M. Závody, I. J. Barton, D. T. Lewellyn-Jones, “Sea surface temperature measurements by the along-track scanning radiometer on ESA’s ERS-1 satellite: early results,” J. Geophys. Res. 99, 22,578–22,588 (1994).

Li, Z.-L.

J. A. Sobrino, Z.-L. Li, M. P. Stoll, F. Becker, “Multi-channel and multi-angle algorithms for estimating sea and land surface temperature with ATSR data,” Int. J. Remote Sens. 17, 2089–2114 (1996).
[CrossRef]

J. A. Sobrino, Z.-L. Li, M. P. Stoll, F. Becker, “Improvements in the split-window technique for the land surface temperature determination,” IEEE Trans. Geosci. Remote Sens. 32, 243–253 (1994).
[CrossRef]

Malkevich, M. S.

M. S. Malkevich, A. K. Gorodetsky, “Determination of ocean surface temperature taking account of atmospheric effects by measurements of the angular IR-radiation distribution of the ‘ocean-atmosphere’ system made from the satellite ‘COSMOS-1151,’” Remote Sens. Rev. 3, 137–161 (1988).
[CrossRef]

Montgomery, H. E.

H. E. Montgomery, “Simultaneous earth observations from two satellites,” Int. J. Remote Sens. 7, 1083–1087 (1986).
[CrossRef]

Mutlow, C. T.

C. T. Mutlow, A. M. Závody, I. J. Barton, D. T. Lewellyn-Jones, “Sea surface temperature measurements by the along-track scanning radiometer on ESA’s ERS-1 satellite: early results,” J. Geophys. Res. 99, 22,578–22,588 (1994).

Nerry, F.

F. Nerry, J. Labed, M. P. Stoll, “Spectral properties of land surfaces in the thermal infrared, 1: laboratory measurements of absolute spectral emissivity signatures,” J. Geophys. Res. 95, 7027–7044 (1990).
[CrossRef]

Rees, W. G.

W. G. Rees, S. P. James, “Angular variation of the infrared emissivity of ice and water surfaces,” Int. J. Remote Sens. 13, 2873–2886 (1992).
[CrossRef]

W. G. Rees, Physical Principles of Remote Sensing, (Cambridge University Press, Cambridge, UK, 1990).

Rubio, E.

E. Rubio, V. Caselles, C. Badenas, “Emissivity measurements of several soils and vegetation types in the 8–14 µm wave band: analysis of two field methods,” Remote Sens. Environ. 59, 490–521 (1997).
[CrossRef]

Saunders, P. M.

P. M. Saunders, “Aerial measurement of sea surface temperature in the infrared,” J. Geophys. Res. 72, 4109–4117 (1967).
[CrossRef]

Scott, N. A.

A. Chédin, N. A. Scott, A. Berroir, “A single-channel double-viewing angle method for sea surface temperature determination from coincident METEOSAT and TIROS-N radiometric measurements,” J. Appl. Meteorol. 21, 613–618 (1982).
[CrossRef]

Snyder, W. C.

W. C. Snyder, Z. Wan, Y. Zhang, Y.-Z. Feng, “Thermal infrared (3–14 µm) bidirectional reflectance measurements of sands and soils,” Remote Sens. Environ. 60, 101–109 (1997).
[CrossRef]

Sobrino, J. A.

J. A. Sobrino, Z.-L. Li, M. P. Stoll, F. Becker, “Multi-channel and multi-angle algorithms for estimating sea and land surface temperature with ATSR data,” Int. J. Remote Sens. 17, 2089–2114 (1996).
[CrossRef]

J. A. Sobrino, Z.-L. Li, M. P. Stoll, F. Becker, “Improvements in the split-window technique for the land surface temperature determination,” IEEE Trans. Geosci. Remote Sens. 32, 243–253 (1994).
[CrossRef]

J. A. Sobrino, V. Caselles, “A methodology for obtaining the crop temperature from NOAA-9 AVHRR data,” Int. J. Remote Sens. 12, 2461–2475 (1991).
[CrossRef]

J. A. Sobrino, V. Caselles, F. Becker, “Significance of the remote sensed thermal infrared measurements obtained over a citrus orchad,” ISPRS J. Photogramm. Remote Sens. 44, 343–354 (1990).
[CrossRef]

J. A. Sobrino, V. Caselles, “Medida mediante el método de la caja de la emisividad en la banda espectral de los 8–14 µm de algunos suelos agrícolas y de la vegetación,” An. Fis. B85, 220–227 (1989).

Stoll, M. P.

J. A. Sobrino, Z.-L. Li, M. P. Stoll, F. Becker, “Multi-channel and multi-angle algorithms for estimating sea and land surface temperature with ATSR data,” Int. J. Remote Sens. 17, 2089–2114 (1996).
[CrossRef]

J. A. Sobrino, Z.-L. Li, M. P. Stoll, F. Becker, “Improvements in the split-window technique for the land surface temperature determination,” IEEE Trans. Geosci. Remote Sens. 32, 243–253 (1994).
[CrossRef]

J. Labed, M. P. Stoll, “Angular variation of land surface spectral emissivity in the thermal infrared: laboratory investigations on bare soils,” Int. J. Remote Sens. 12, 2299–2310 (1991).
[CrossRef]

F. Nerry, J. Labed, M. P. Stoll, “Spectral properties of land surfaces in the thermal infrared, 1: laboratory measurements of absolute spectral emissivity signatures,” J. Geophys. Res. 95, 7027–7044 (1990).
[CrossRef]

Wan, Z.

W. C. Snyder, Z. Wan, Y. Zhang, Y.-Z. Feng, “Thermal infrared (3–14 µm) bidirectional reflectance measurements of sands and soils,” Remote Sens. Environ. 60, 101–109 (1997).
[CrossRef]

Závody, A. M.

C. T. Mutlow, A. M. Závody, I. J. Barton, D. T. Lewellyn-Jones, “Sea surface temperature measurements by the along-track scanning radiometer on ESA’s ERS-1 satellite: early results,” J. Geophys. Res. 99, 22,578–22,588 (1994).

Zhang, Y.

W. C. Snyder, Z. Wan, Y. Zhang, Y.-Z. Feng, “Thermal infrared (3–14 µm) bidirectional reflectance measurements of sands and soils,” Remote Sens. Environ. 60, 101–109 (1997).
[CrossRef]

An. Fis. (1)

J. A. Sobrino, V. Caselles, “Medida mediante el método de la caja de la emisividad en la banda espectral de los 8–14 µm de algunos suelos agrícolas y de la vegetación,” An. Fis. B85, 220–227 (1989).

IEEE Trans. Geosci. Remote Sens. (1)

J. A. Sobrino, Z.-L. Li, M. P. Stoll, F. Becker, “Improvements in the split-window technique for the land surface temperature determination,” IEEE Trans. Geosci. Remote Sens. 32, 243–253 (1994).
[CrossRef]

Int. J. Remote Sens. (7)

R. J. Holyer, “A two-satellite method for measurement of sea surface temperature,” Int. J. Remote Sens. 5, 115–131 (1984).
[CrossRef]

H. E. Montgomery, “Simultaneous earth observations from two satellites,” Int. J. Remote Sens. 7, 1083–1087 (1986).
[CrossRef]

J. A. Sobrino, Z.-L. Li, M. P. Stoll, F. Becker, “Multi-channel and multi-angle algorithms for estimating sea and land surface temperature with ATSR data,” Int. J. Remote Sens. 17, 2089–2114 (1996).
[CrossRef]

J. A. Sobrino, V. Caselles, “A methodology for obtaining the crop temperature from NOAA-9 AVHRR data,” Int. J. Remote Sens. 12, 2461–2475 (1991).
[CrossRef]

J. Labed, M. P. Stoll, “Angular variation of land surface spectral emissivity in the thermal infrared: laboratory investigations on bare soils,” Int. J. Remote Sens. 12, 2299–2310 (1991).
[CrossRef]

W. G. Rees, S. P. James, “Angular variation of the infrared emissivity of ice and water surfaces,” Int. J. Remote Sens. 13, 2873–2886 (1992).
[CrossRef]

F. Becker, “The Impact of spectral emissivity on the measurement of land surface temperature from a satellite,” Int. J. Remote Sens. 8, 1509–1522 (1987).
[CrossRef]

ISPRS J. Photogramm. Remote Sens. (1)

J. A. Sobrino, V. Caselles, F. Becker, “Significance of the remote sensed thermal infrared measurements obtained over a citrus orchad,” ISPRS J. Photogramm. Remote Sens. 44, 343–354 (1990).
[CrossRef]

J. Appl. Meteorol. (2)

I. J. Barton, “Satellite-derived surface temperatures—a comparison between operational, theoretical and experimental algorithms,” J. Appl. Meteorol. 31, 432–442 (1992).
[CrossRef]

A. Chédin, N. A. Scott, A. Berroir, “A single-channel double-viewing angle method for sea surface temperature determination from coincident METEOSAT and TIROS-N radiometric measurements,” J. Appl. Meteorol. 21, 613–618 (1982).
[CrossRef]

J. Geophys. Res. (3)

C. T. Mutlow, A. M. Závody, I. J. Barton, D. T. Lewellyn-Jones, “Sea surface temperature measurements by the along-track scanning radiometer on ESA’s ERS-1 satellite: early results,” J. Geophys. Res. 99, 22,578–22,588 (1994).

F. Nerry, J. Labed, M. P. Stoll, “Spectral properties of land surfaces in the thermal infrared, 1: laboratory measurements of absolute spectral emissivity signatures,” J. Geophys. Res. 95, 7027–7044 (1990).
[CrossRef]

P. M. Saunders, “Aerial measurement of sea surface temperature in the infrared,” J. Geophys. Res. 72, 4109–4117 (1967).
[CrossRef]

Remote Sens. Environ. (2)

E. Rubio, V. Caselles, C. Badenas, “Emissivity measurements of several soils and vegetation types in the 8–14 µm wave band: analysis of two field methods,” Remote Sens. Environ. 59, 490–521 (1997).
[CrossRef]

W. C. Snyder, Z. Wan, Y. Zhang, Y.-Z. Feng, “Thermal infrared (3–14 µm) bidirectional reflectance measurements of sands and soils,” Remote Sens. Environ. 60, 101–109 (1997).
[CrossRef]

Remote Sens. Rev. (1)

M. S. Malkevich, A. K. Gorodetsky, “Determination of ocean surface temperature taking account of atmospheric effects by measurements of the angular IR-radiation distribution of the ‘ocean-atmosphere’ system made from the satellite ‘COSMOS-1151,’” Remote Sens. Rev. 3, 137–161 (1988).
[CrossRef]

Other (3)

ESA/Earthnet, ERS-1 System, P. Vass, B. Battrick, (European Space Agency, European Space Research and Technology Centre, Noordwijk, The Netherlands, 1992).

ESA/Earthnet, ERS-1 Product Specification, P. Vass, B. Battrick, eds., (European Space Agency, European Space Research and Technology Centre, Noordwijk, The Netherlands, 1992).

W. G. Rees, Physical Principles of Remote Sensing, (Cambridge University Press, Cambridge, UK, 1990).

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Figures (5)

Fig. 1
Fig. 1

Schematic representation of the goniometric frame. α is the measuring angle.

Fig. 2
Fig. 2

Angular variation of relative-to-nadir emissivity.

Fig. 3
Fig. 3

Angular variation of absolute emissivity.

Fig. 4
Fig. 4

Comparison of the results of Rees and James12 with those obtained in the current paper for water.

Fig. 5
Fig. 5

Comparison of the results of Labed and Stoll11 with those obtained in the current paper for sand.

Tables (2)

Tables Icon

Table 1 Absolute and Relative Emissivity Decreases Between the Angles of the Subsatellite Tracks in the Nadir and Forward Operation Modes of the ATSR (0° and 55°)

Tables Icon

Table 2 Error in the Surface Temperature Estimation, ΔTs∊, ΔTs(Δ∊ = 0) - Ts(Δ∊55°), when the Angular Variation of Emissivity is Not Considereda

Equations (15)

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

BiTiθ=iθBiTs+1-iθLatm,
iθ=BiTiθ-LatmBiTs-Latm.
θ=exp-α/Trad-1.3 exp-α/Tatm0exp-α/Ts-1.3 exp-α/Tatm0
BiTiθ=λ1=8 μmλ2=14 μm iθBiTsfλdλλ1=8 μmλ2=14 μm fλdλ+λ1=8 μmλ2=14 μm1iθLatmfλdλλ1=8 μmλ2=14 μm fλdλ,
BTj=C1λ-5expC2/λTj-1,
C1=1.1911×108 W m-2 μm4 sr-1,
C2=14388 K μm.
r,θ=θ0=BiTiθ-BiTatmBiTi0-BiTatm,
r,θ=exp-α/Trad-1.3 exp-α/Tatm0exp-α/Trad0-1.3 exp-α/Tatm0.
δθ=αB-C2AB-CTrad2 δTrad2+A-CBTi2 δTi2+B-ACTatm02 δTatm021/2,
A=exp-α/Trad,
B=exp-α/Ts for Eq. 3, B=exp-α/Trad0 for Eq. 8,
C=1.3 exp-α/Tatm0,
R=A expB/T  T=BlnR/A,
ΔTs=57-7W1-0+84-15W0-θ,

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