Abstract

The retrieval of surface emissivity in the 8–14-µm region from remotely sensed thermal imagery requires channel-averaged values of atmospheric transmittance, path radiance, and downwelling sky flux. Bandpass resampling introduces inherent retrieval errors that depend on atmospheric conditions, spectral region, bandwidth, flight altitude, and surface temperature. This simulation study is performed for clear sky conditions and moderate atmospheric water vapor contents. It shows that relative emissivity retrieval errors can reach as much as 3% for broadband sensors (1–2-µm bandwidth) and 0.8% for narrowband instruments (0.15 µm), even for constant surface emissivity. For spectrally varying surface emissivities the relative retrieval error increases for the broadband instrument by ∼2% in channels with strong emissivity changes of 0.05–0.1. The corresponding retrieval errors for narrowband sensors increase by approximately 3–4%. The channels in the atmospheric window regions with lower transmittance, i.e., 8–8.5 and 12.5–14 µm, are most sensitive to retrieval errors.

© 2002 Optical Society of America

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2001

S. J. Hook, J. J. Myers, K. J. Thome, M. Fitzgerald, A. B. Kahle, “The MODIS/ASTER airborne simulator (MASTER)—a new instrument for earth science studies,” Remote Sens. Environ. 76, 93–102 (2001).
[CrossRef]

2000

C. Coll, V. Caselles, E. Rubio, F. Sospedra, E. Valor, “Temperature and emissivity separation from calibrated data of the Digital Airborne Imaging Spectrometer,” Remote Sens. Environ. 76, 250–259 (2000).
[CrossRef]

R. Richter, “Bandpass-resampling effects on the retrieval of radiance and surface reflectance,” Appl. Opt. 39, 5001–5005 (2000).
[CrossRef]

1998

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]

Y. Yamagushi, A. B. Kahle, H. Tsu, T. Kawakami, M. Pniel, “Overview of Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER),” IEEE Trans. Geosci. Remote Sens. 36, 1062–1071 (1998).
[CrossRef]

A. Gillespie, S. Rokugawa, 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]

1994

R. Richter, “Derivation of temperature and emittance from airborne multispectral thermal infrared scanner data,” Infrared Phys. Technol. 35, 618–626 (1994).
[CrossRef]

1992

J. W. Salibury, D. M. D’Aria, “Emissivity of terrestrial materials in the 8–14-µm atmospheric window,” Remote Sens. Environ. 69, 197–214 (1992).

1985

C. J. Tucker, J. R. G. Townshend, T. E. Goff, “African land-cover classification using satellite data,” Science 227, 369–375 (1985).
[CrossRef] [PubMed]

1981

M. Matson, D. R. Wiesnet, “New database for climate studies,” Nature (London) 289, 451–456 (1981).
[CrossRef]

A. F. H. Goetz, L. C. Rowan, “Geologic remote sensing,” Science 211, 781–791 (1981).
[CrossRef] [PubMed]

1980

A. B. Kahle, D. P. Madura, J. M. Soha, “Middle infrared multispectral aircraft scanner data: analysis for geological applications,” Appl. Opt. 19, 2279–2290 (1980).
[CrossRef] [PubMed]

J. C. Price, “The potential of remotely sensed thermal infrared data to infer surface soil moisture and evaporation,” Water Resour. Res. 16, 787–795 (1980).
[CrossRef]

1975

K. Watson, “Geologic applications of thermal infrared images,” Proc. IEEE 63, 128–137 (1975).
[CrossRef]

1972

R. K. Vincent, F. J. Thomson, “Rock type discrimination from ratioed infrared scanner images of Pisgah Crater, CA,” Science 175, 986–988 (1972).
[CrossRef] [PubMed]

R. J. P. Lyon, “Infrared spectral emittance in geologic mapping: airborne spectrometer data from Pisgah Crater, CA,” Science 175, 983–985 (1972).
[CrossRef] [PubMed]

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]

A. Berk, G. P. Anderson, P. K. Acharya, J. H. Chetwynd, L. S. Bernstein, E. P. Shettle, M. W. Matthew, S. M. Adler-Golden, MODTRAN4 User’s Manual (Air Force Research Laboratory, Hanscom AFB, Mass., 2000).

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]

A. Berk, G. P. Anderson, P. K. Acharya, J. H. Chetwynd, L. S. Bernstein, E. P. Shettle, M. W. Matthew, S. M. Adler-Golden, MODTRAN4 User’s Manual (Air Force Research Laboratory, Hanscom AFB, Mass., 2000).

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]

A. Berk, G. P. Anderson, P. K. Acharya, J. H. Chetwynd, L. S. Bernstein, E. P. Shettle, M. W. Matthew, S. M. Adler-Golden, MODTRAN4 User’s Manual (Air Force Research Laboratory, Hanscom AFB, Mass., 2000).

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]

A. Berk, G. P. Anderson, P. K. Acharya, J. H. Chetwynd, L. S. Bernstein, E. P. Shettle, M. W. Matthew, S. M. Adler-Golden, MODTRAN4 User’s Manual (Air Force Research Laboratory, Hanscom AFB, Mass., 2000).

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]

A. Berk, G. P. Anderson, P. K. Acharya, J. H. Chetwynd, L. S. Bernstein, E. P. Shettle, M. W. Matthew, S. M. Adler-Golden, MODTRAN4 User’s Manual (Air Force Research Laboratory, Hanscom AFB, Mass., 2000).

Caselles, V.

C. Coll, V. Caselles, E. Rubio, F. Sospedra, E. Valor, “Temperature and emissivity separation from calibrated data of the Digital Airborne Imaging Spectrometer,” Remote Sens. Environ. 76, 250–259 (2000).
[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]

A. Berk, G. P. Anderson, P. K. Acharya, J. H. Chetwynd, L. S. Bernstein, E. P. Shettle, M. W. Matthew, S. M. Adler-Golden, MODTRAN4 User’s Manual (Air Force Research Laboratory, Hanscom AFB, Mass., 2000).

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, 6–8 Oct. 1998 (Remote Sensing Laboratories, University of Zurich, Zurich, Switzerland, 1998), pp. 37–42.

Coll, C.

C. Coll, V. Caselles, E. Rubio, F. Sospedra, E. Valor, “Temperature and emissivity separation from calibrated data of the Digital Airborne Imaging Spectrometer,” Remote Sens. Environ. 76, 250–259 (2000).
[CrossRef]

Cothern, J. S.

A. Gillespie, S. Rokugawa, 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]

D’Aria, D. M.

J. W. Salibury, D. M. D’Aria, “Emissivity of terrestrial materials in the 8–14-µm atmospheric window,” Remote Sens. Environ. 69, 197–214 (1992).

Fitzgerald, M.

S. J. Hook, J. J. Myers, K. J. Thome, M. Fitzgerald, A. B. Kahle, “The MODIS/ASTER airborne simulator (MASTER)—a new instrument for earth science studies,” Remote Sens. Environ. 76, 93–102 (2001).
[CrossRef]

Gillespie, A.

A. Gillespie, S. Rokugawa, 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]

A. Gillespie, “Lithologic mapping of silicate rocks using TIMS,” in Proceedings of TIMS Data User’s Workshop, 15–18 June 1985, JPL Publ. 83-38 (Jet Propulsion Laboratory, Pasadena, Calif., 1986), pp. 29–44.

Goetz, A. F. H.

A. F. H. Goetz, L. C. Rowan, “Geologic remote sensing,” Science 211, 781–791 (1981).
[CrossRef] [PubMed]

Goff, T. E.

C. J. Tucker, J. R. G. Townshend, T. E. Goff, “African land-cover classification using satellite data,” Science 227, 369–375 (1985).
[CrossRef] [PubMed]

Hook, S.

A. Gillespie, S. Rokugawa, 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]

Hook, S. J.

S. J. Hook, J. J. Myers, K. J. Thome, M. Fitzgerald, A. B. Kahle, “The MODIS/ASTER airborne simulator (MASTER)—a new instrument for earth science studies,” Remote Sens. Environ. 76, 93–102 (2001).
[CrossRef]

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, 6–8 Oct. 1998 (Remote Sensing Laboratories, University of Zurich, Zurich, Switzerland, 1998), pp. 37–42.

Kahle, A. B.

S. J. Hook, J. J. Myers, K. J. Thome, M. Fitzgerald, A. B. Kahle, “The MODIS/ASTER airborne simulator (MASTER)—a new instrument for earth science studies,” Remote Sens. Environ. 76, 93–102 (2001).
[CrossRef]

Y. Yamagushi, A. B. Kahle, H. Tsu, T. Kawakami, M. Pniel, “Overview of Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER),” IEEE Trans. Geosci. Remote Sens. 36, 1062–1071 (1998).
[CrossRef]

A. Gillespie, S. Rokugawa, 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]

A. B. Kahle, D. P. Madura, J. M. Soha, “Middle infrared multispectral aircraft scanner data: analysis for geological applications,” Appl. Opt. 19, 2279–2290 (1980).
[CrossRef] [PubMed]

Kawakami, T.

Y. Yamagushi, A. B. Kahle, H. Tsu, T. Kawakami, M. Pniel, “Overview of Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER),” IEEE Trans. Geosci. Remote Sens. 36, 1062–1071 (1998).
[CrossRef]

Kondratyev, K. Y.

K. Y. Kondratyev, Radiation in the Atmosphere (Academic, New York, 1969).

Kramer, H. J.

H. J. Kramer, Observation of the Earth and its Environment (Springer-Verlag, Berlin, 1996).
[CrossRef]

Lyon, R. J. P.

R. J. P. Lyon, “Infrared spectral emittance in geologic mapping: airborne spectrometer data from Pisgah Crater, CA,” Science 175, 983–985 (1972).
[CrossRef] [PubMed]

Madura, D. P.

Matson, M.

M. Matson, D. R. Wiesnet, “New database for climate studies,” Nature (London) 289, 451–456 (1981).
[CrossRef]

Matsunaga, T.

A. Gillespie, S. Rokugawa, 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]

Matthew, M. W.

A. Berk, G. P. Anderson, P. K. Acharya, J. H. Chetwynd, L. S. Bernstein, E. P. Shettle, M. W. Matthew, S. M. Adler-Golden, MODTRAN4 User’s Manual (Air Force Research Laboratory, Hanscom AFB, Mass., 2000).

Müller, A.

P. Strobl, A. Müller, D. Schläpfer, M. Schaepman, “Laboratory calibration and in-flight validation of the Digital Airborne Imaging Spectrometer DAIS 7915,” in Algorithms for Multispectral and Hyperspectral Imagery III, A. E. Iverson, S. S. Shen, eds., Proc. SPIE3071, 225–235 (1997).
[CrossRef]

Myers, J. J.

S. J. Hook, J. J. Myers, K. J. Thome, M. Fitzgerald, A. B. Kahle, “The MODIS/ASTER airborne simulator (MASTER)—a new instrument for earth science studies,” Remote Sens. Environ. 76, 93–102 (2001).
[CrossRef]

Pniel, M.

Y. Yamagushi, A. B. Kahle, H. Tsu, T. Kawakami, M. Pniel, “Overview of Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER),” IEEE Trans. Geosci. Remote Sens. 36, 1062–1071 (1998).
[CrossRef]

Price, J. C.

J. C. Price, “The potential of remotely sensed thermal infrared data to infer surface soil moisture and evaporation,” Water Resour. Res. 16, 787–795 (1980).
[CrossRef]

Richter, R.

R. Richter, “Bandpass-resampling effects on the retrieval of radiance and surface reflectance,” Appl. Opt. 39, 5001–5005 (2000).
[CrossRef]

R. Richter, “Derivation of temperature and emittance from airborne multispectral thermal infrared scanner data,” Infrared Phys. Technol. 35, 618–626 (1994).
[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]

Rokugawa, S.

A. Gillespie, S. Rokugawa, 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]

Rowan, L. C.

A. F. H. Goetz, L. C. Rowan, “Geologic remote sensing,” Science 211, 781–791 (1981).
[CrossRef] [PubMed]

Rubio, E.

C. Coll, V. Caselles, E. Rubio, F. Sospedra, E. Valor, “Temperature and emissivity separation from calibrated data of the Digital Airborne Imaging Spectrometer,” Remote Sens. Environ. 76, 250–259 (2000).
[CrossRef]

Salibury, J. W.

J. W. Salibury, D. M. D’Aria, “Emissivity of terrestrial materials in the 8–14-µm atmospheric window,” Remote Sens. Environ. 69, 197–214 (1992).

Schaepman, M.

P. Strobl, A. Müller, D. Schläpfer, M. Schaepman, “Laboratory calibration and in-flight validation of the Digital Airborne Imaging Spectrometer DAIS 7915,” in Algorithms for Multispectral and Hyperspectral Imagery III, A. E. Iverson, S. S. Shen, eds., Proc. SPIE3071, 225–235 (1997).
[CrossRef]

Schläpfer, D.

P. Strobl, A. Müller, D. Schläpfer, M. Schaepman, “Laboratory calibration and in-flight validation of the Digital Airborne Imaging Spectrometer DAIS 7915,” in Algorithms for Multispectral and Hyperspectral Imagery III, A. E. Iverson, S. S. Shen, eds., Proc. SPIE3071, 225–235 (1997).
[CrossRef]

Shettle, E. P.

A. Berk, G. P. Anderson, P. K. Acharya, J. H. Chetwynd, L. S. Bernstein, E. P. Shettle, M. W. Matthew, S. M. Adler-Golden, MODTRAN4 User’s Manual (Air Force Research Laboratory, Hanscom AFB, Mass., 2000).

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, 6–8 Oct. 1998 (Remote Sensing Laboratories, University of Zurich, Zurich, Switzerland, 1998), pp. 37–42.

Soha, J. M.

Sospedra, F.

C. Coll, V. Caselles, E. Rubio, F. Sospedra, E. Valor, “Temperature and emissivity separation from calibrated data of the Digital Airborne Imaging Spectrometer,” Remote Sens. Environ. 76, 250–259 (2000).
[CrossRef]

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, 6–8 Oct. 1998 (Remote Sensing Laboratories, University of Zurich, Zurich, Switzerland, 1998), pp. 37–42.

Strobl, P.

P. Strobl, A. Müller, D. Schläpfer, M. Schaepman, “Laboratory calibration and in-flight validation of the Digital Airborne Imaging Spectrometer DAIS 7915,” in Algorithms for Multispectral and Hyperspectral Imagery III, A. E. Iverson, S. S. Shen, eds., Proc. SPIE3071, 225–235 (1997).
[CrossRef]

Thome, K. J.

S. J. Hook, J. J. Myers, K. J. Thome, M. Fitzgerald, A. B. Kahle, “The MODIS/ASTER airborne simulator (MASTER)—a new instrument for earth science studies,” Remote Sens. Environ. 76, 93–102 (2001).
[CrossRef]

Thomson, F. J.

R. K. Vincent, F. J. Thomson, “Rock type discrimination from ratioed infrared scanner images of Pisgah Crater, CA,” Science 175, 986–988 (1972).
[CrossRef] [PubMed]

Townshend, J. R. G.

C. J. Tucker, J. R. G. Townshend, T. E. Goff, “African land-cover classification using satellite data,” Science 227, 369–375 (1985).
[CrossRef] [PubMed]

Tsu, H.

Y. Yamagushi, A. B. Kahle, H. Tsu, T. Kawakami, M. Pniel, “Overview of Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER),” IEEE Trans. Geosci. Remote Sens. 36, 1062–1071 (1998).
[CrossRef]

Tucker, C. J.

C. J. Tucker, J. R. G. Townshend, T. E. Goff, “African land-cover classification using satellite data,” Science 227, 369–375 (1985).
[CrossRef] [PubMed]

Valor, E.

C. Coll, V. Caselles, E. Rubio, F. Sospedra, E. Valor, “Temperature and emissivity separation from calibrated data of the Digital Airborne Imaging Spectrometer,” Remote Sens. Environ. 76, 250–259 (2000).
[CrossRef]

Vincent, R. K.

R. K. Vincent, F. J. Thomson, “Rock type discrimination from ratioed infrared scanner images of Pisgah Crater, CA,” Science 175, 986–988 (1972).
[CrossRef] [PubMed]

Watson, K.

K. Watson, “Geologic applications of thermal infrared images,” Proc. IEEE 63, 128–137 (1975).
[CrossRef]

Wiesnet, D. R.

M. Matson, D. R. Wiesnet, “New database for climate studies,” Nature (London) 289, 451–456 (1981).
[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, 6–8 Oct. 1998 (Remote Sensing Laboratories, University of Zurich, Zurich, Switzerland, 1998), pp. 37–42.

Yamagushi, Y.

Y. Yamagushi, A. B. Kahle, H. Tsu, T. Kawakami, M. Pniel, “Overview of Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER),” IEEE Trans. Geosci. Remote Sens. 36, 1062–1071 (1998).
[CrossRef]

Appl. Opt.

IEEE Trans. Geosci. Remote Sens.

Y. Yamagushi, A. B. Kahle, H. Tsu, T. Kawakami, M. Pniel, “Overview of Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER),” IEEE Trans. Geosci. Remote Sens. 36, 1062–1071 (1998).
[CrossRef]

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Figures (9)

Fig. 1
Fig. 1

Normalized spectral response functions of the six thermal channels of DAIS.

Fig. 2
Fig. 2

Normalized spectral response functions of the five thermal channels of ASTER.

Fig. 3
Fig. 3

Spectral emissivity of quartz: solid curve, full resolution; dotted curve, DAIS resampled; dashed curve, ASTER resampled emissivity spectrum. Diamonds, and triangles, center wavelengths of the DAIS and ASTER channels, respectively.

Fig. 4
Fig. 4

Atmospheric transmittance in the 7–14-µm region (compare Table 1 for the atmospheric parameters).

Fig. 5
Fig. 5

Results for the airborne case with a constant surface emissivity of 0.95. Air temperature 21 °C; top to bottom curves, T surf = 41, 21, 16 °C, respectively.

Fig. 6
Fig. 6

Results for the airborne case, spectrally varying surface emissivity. Air temperature, 21 °C; top to bottom curves, T surf = 41, 21, 16 °C, respectively; dotted curve, resampled spectral emissivity of quartz.

Fig. 7
Fig. 7

Results for ASTER (spaceborne case): top, constant surface emissivity = 0.95; bottom, spectrally varying surface emissivity. Air temperature, 21 °C; top to bottom curves, T surf = 41, 21, 16 °C, respectively; dotted curve, resampled spectral emissivity of quartz.

Fig. 8
Fig. 8

Results with Eq. (10), spaceborne case, quartz emissivity: top, HT32, corresponds to the bottom graphics of Fig. 6; bottom, ASTER, corresponds to the bottom graphics of Fig. 7.

Fig. 9
Fig. 9

Satellite platform, surface emissivity ε = 1. Air temperature, 21 °C; top to bottom curves, T surf = 41, 21, 16 °C; respectively.

Tables (1)

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Table 1 Parameters of Simulation

Equations (11)

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Lλ=Lpλ+τλελBλ, T+τλ1-ελFλ/π,
λ1λ2 LλRλdλλ1λ2 Rλdλ=λ1λ2 LpλRλdλλ1λ2 Rλdλ+λ1λ2 ελτλBλ, TRλdλλ1λ2 Rλdλ+1πλ1λ21-ελτλFλRλdλλ1λ2 Rλdλ.
Lk=Lp,k+εk*τkBkT+1-εk*τkFk/π,
τk=λ1λ2 τλRkλdλλ1λ2 Rkλdλ,
Bk=exp-1T+akbk.
εk*=Lk-Lp,k/τk-Fk/πBkT-Fk/π.
εk=λ1λ2 ελRkλdλλ1λ2 Rkλdλ.
ek=100*εk*-εkεk.
Ek=λ1λ2 τλFλRkλdλλ1λ2 Rkλdλ.
εk*=Lk-Lp,k-Ek/πτkBkT-Ek/π.
Bk*=λ1λ2 τλBλ, TRkλdλλ1λ2 Rkλdλ.

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