Abstract

The assumption of blackbody emission (emissivity, 1.0) for a calm ocean surface can lead to significant underestimates of the sea-surface temperature (SST) derived from IR radiometric data. Taking the optical properties of the atmosphere as known, we calculate the errors stemming from the blackbody assumption for cases of a purely absorbing or a purely scattering atmosphere. It is observed that for an absorbing atmosphere the errors in SST are always reduced and are the same whether measurements are made from space or at any level in the atmosphere. As for atmospheric scattering, the SST errors are slightly reduced when one is viewing from large zenith angles but are slightly enhanced when one is viewing from the zenith. The inferred optical thickness τ of an absorbing layer can be in error under the blackbody assumption by a Δτ of 0.01–0.08, while the inferred optical thickness of a scattering layer can be in error by a larger amount, Δτ of 0.03–0.13. The error Δτ depends only weakly on the actual optical thickness and on the viewing angle, but it is rather sensitive to the wavelength of the measurement. In the absence of steep slopes in the wave-slope distribution, directional emissivities are essentially unchanged by sea state when one is viewing from or near the zenith. When one is viewing from moderately large zenith angles (such as 50°), however, the departures in the directional emissivities from blackbody emission can be much larger under perturbed sea state than under calm conditions.

© 1992 Optical Society of America

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    [CrossRef]
  2. C. Prabhakara, J.-M. Yoo, G. Dalu, R. S. Fraser, “Deep optically thin cirrus clouds in the polar regions: part I. Infrared extinction characteristics,” J. Appl. Meteorol. 29, 1313–1329 (1990).
    [CrossRef]
  3. C. Prabhakara, G. Dalu, V. G. Kunde, “Estimation of sea surface temperature from remote sensing in the 11 to 13 μm window region,” J. Geophys. Res. 79, 5039–5044 (1974).
    [CrossRef]
  4. T. B. Barnett, W. C. Patzert, S. C. Webb, B. R. Bean, “Climatological usefulness of satellite determined sea surface temperatures in the tropical pacific,” Bull. Am. Meteorol. Soc. 60, 197–205 (1979).
    [CrossRef]
  5. J. Susskind, J. Rosenfield, D. Reuter, M. T. Chahine, “Remote sensing of weather and climate parameters from HIRS2/MSU on TIROS-N,” J. Geophys. Res. 89, 4677–4697 (1984).
    [CrossRef]
  6. E. P. McClain, W. G. Pichel, C. C. Walton, “Comparative performance of AVHRR based multi-channel sea surface temperatures,” J. Geophys. Res. 90, 11587–11601 (1985).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  25. C. Cox, W. Munk, “Some problems in optical oceanography,” J. Mar. Res. 14, 63–78 (1955).
  26. K. Masuda, T. Takashima, Y. Takayama, “Emissivity of pure and sea waters for the model sea surface in the infrared window regions,” Remote Sensing Environ. 24, 313–329 (1988).
    [CrossRef]
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  29. R. W. Spencer, J. R. Christy, “Precise monitoring of global temperature trends from satellites,” Science 247, 1558–1562 (1990).
    [CrossRef] [PubMed]

1990 (2)

C. Prabhakara, J.-M. Yoo, G. Dalu, R. S. Fraser, “Deep optically thin cirrus clouds in the polar regions: part I. Infrared extinction characteristics,” J. Appl. Meteorol. 29, 1313–1329 (1990).
[CrossRef]

R. W. Spencer, J. R. Christy, “Precise monitoring of global temperature trends from satellites,” Science 247, 1558–1562 (1990).
[CrossRef] [PubMed]

1989 (4)

A. E. Strong, “Greater global warming revealed by satellite-derived sea surface temperature trends,” Nature (London) 338, 642–645 (1989).
[CrossRef]

R. W. Reynolds, C. K. Folland, D. E. Parker, “Biases in satellite-derived sea-surface-temperature data,” Nature (London) 341, 728–731 (1989).
[CrossRef]

I. J. Barton, A. M. Zavody, D. M. O’Brien, D. R. Cutten, R. W. Saunders, D. T. Llewellyn-Jones, “Theoretical algorithms for satellite-derived sea surface temperatures,” J. Geophys. Res. 94, 3365–3375 (1989).
[CrossRef]

E. P. McClain, “Global sea surface temperatures and cloud clearing for aerosol optical depth estimates,” Int. J. Remote Sensing 10, 763–769 (1989).
[CrossRef]

1988 (2)

C. Prabhakara, R. S. Fraser, G. Dalu, M. -L. C. Wu, R. J. Curran, “Thin cirrus clouds: seasonal distribution over oceans deduced from Nimbus-4 IRIS,” J. Appl. Meteorol. 27, 379–399 (1988).
[CrossRef]

K. Masuda, T. Takashima, Y. Takayama, “Emissivity of pure and sea waters for the model sea surface in the infrared window regions,” Remote Sensing Environ. 24, 313–329 (1988).
[CrossRef]

1986 (1)

A. E. Strong, “Monitoring El Nino using satellite-based sea surface temperatures,” Ocean-Air Interact. 1, 11–28 (1986).

1985 (2)

E. P. McClain, W. G. Pichel, C. C. Walton, “Comparative performance of AVHRR based multi-channel sea surface temperatures,” J. Geophys. Res. 90, 11587–11601 (1985).
[CrossRef]

J. Susskind, D. Reuter, “Retrieval of sea-surface temperatures from HIRS2/MSU,” J. Geophys. Res. 90, 11602–11608 (1985).
[CrossRef]

1984 (1)

J. Susskind, J. Rosenfield, D. Reuter, M. T. Chahine, “Remote sensing of weather and climate parameters from HIRS2/MSU on TIROS-N,” J. Geophys. Res. 89, 4677–4697 (1984).
[CrossRef]

1983 (1)

G. A. Maul, “Zenith angle effects in multichannel infrared sea surface remote sensing,” Remote Sensing Environ. 13, 439–451 (1983).
[CrossRef]

1981 (3)

A. Ben-Shalom, J. Otterman, P. Schechner, “Measured infrared radiances near sea horizon and their interpretation—preliminary results,” Geophys. Res. Lett. 8, 772–774 (1981).
[CrossRef]

M. Sidran, “Broad-band reflectance and emissivity of specular and rough water surface,” Appl. Opt. 20, 3176–3183 (1981).
[CrossRef] [PubMed]

T. Takashima, Y. Takayama, “Emissivity and reflectance of the model sea surface for a use of AVHRR data of NOAA satellites,” Pap. Meteorol. Geophys. 32, 267–274 (1981).
[CrossRef]

1979 (1)

T. B. Barnett, W. C. Patzert, S. C. Webb, B. R. Bean, “Climatological usefulness of satellite determined sea surface temperatures in the tropical pacific,” Bull. Am. Meteorol. Soc. 60, 197–205 (1979).
[CrossRef]

1978 (1)

1977 (1)

J. Kornfeld, J. Susskind, “On the effects of surface emissivity on temperature retrievals,” Mon. Weather Rev. 105, 1605–1608 (1977).
[CrossRef]

1975 (1)

G. Dalu, “Emittance effect on the remotely sensed sea surface temperature,” Int. J. Remote Sensing 6, 733–740 (1975).
[CrossRef]

1974 (1)

C. Prabhakara, G. Dalu, V. G. Kunde, “Estimation of sea surface temperature from remote sensing in the 11 to 13 μm window region,” J. Geophys. Res. 79, 5039–5044 (1974).
[CrossRef]

1969 (1)

1968 (1)

1955 (1)

C. Cox, W. Munk, “Some problems in optical oceanography,” J. Mar. Res. 14, 63–78 (1955).

1954 (2)

C. Cox, W. Munk, “Statistics of the sea surface derived from Sun glitter,” J. Mar. Res. 13, 198–227 (1954).

C. Cox, W. Munk, “Measurement of the roughness of the sea surface from photography of the Sun's glitter,” J. Opt. Soc. Am. 44, 835–850 (1954).
[CrossRef]

Barnett, T. B.

T. B. Barnett, W. C. Patzert, S. C. Webb, B. R. Bean, “Climatological usefulness of satellite determined sea surface temperatures in the tropical pacific,” Bull. Am. Meteorol. Soc. 60, 197–205 (1979).
[CrossRef]

Barton, I. J.

I. J. Barton, A. M. Zavody, D. M. O’Brien, D. R. Cutten, R. W. Saunders, D. T. Llewellyn-Jones, “Theoretical algorithms for satellite-derived sea surface temperatures,” J. Geophys. Res. 94, 3365–3375 (1989).
[CrossRef]

Bean, B. R.

T. B. Barnett, W. C. Patzert, S. C. Webb, B. R. Bean, “Climatological usefulness of satellite determined sea surface temperatures in the tropical pacific,” Bull. Am. Meteorol. Soc. 60, 197–205 (1979).
[CrossRef]

Ben-Shalom, A.

A. Ben-Shalom, J. Otterman, P. Schechner, “Measured infrared radiances near sea horizon and their interpretation—preliminary results,” Geophys. Res. Lett. 8, 772–774 (1981).
[CrossRef]

Bramson, M. A.

M. A. Bramson, Infrared Radiation: A Handbook of Applications (Plenum, New York, 1968).

Burch, D. E.

D. E. Burch, “Radiative properties of the atmospheric windows,” presented at the Conference on Atmospheric Radiation, Fort Collins, Colo., 7–9 August 1972.

Chahine, M. T.

J. Susskind, J. Rosenfield, D. Reuter, M. T. Chahine, “Remote sensing of weather and climate parameters from HIRS2/MSU on TIROS-N,” J. Geophys. Res. 89, 4677–4697 (1984).
[CrossRef]

Christy, J. R.

R. W. Spencer, J. R. Christy, “Precise monitoring of global temperature trends from satellites,” Science 247, 1558–1562 (1990).
[CrossRef] [PubMed]

Cox, C.

C. Cox, W. Munk, “Some problems in optical oceanography,” J. Mar. Res. 14, 63–78 (1955).

C. Cox, W. Munk, “Measurement of the roughness of the sea surface from photography of the Sun's glitter,” J. Opt. Soc. Am. 44, 835–850 (1954).
[CrossRef]

C. Cox, W. Munk, “Statistics of the sea surface derived from Sun glitter,” J. Mar. Res. 13, 198–227 (1954).

Curran, R. J.

C. Prabhakara, R. S. Fraser, G. Dalu, M. -L. C. Wu, R. J. Curran, “Thin cirrus clouds: seasonal distribution over oceans deduced from Nimbus-4 IRIS,” J. Appl. Meteorol. 27, 379–399 (1988).
[CrossRef]

Cutten, D. R.

I. J. Barton, A. M. Zavody, D. M. O’Brien, D. R. Cutten, R. W. Saunders, D. T. Llewellyn-Jones, “Theoretical algorithms for satellite-derived sea surface temperatures,” J. Geophys. Res. 94, 3365–3375 (1989).
[CrossRef]

Dalu, G.

C. Prabhakara, J.-M. Yoo, G. Dalu, R. S. Fraser, “Deep optically thin cirrus clouds in the polar regions: part I. Infrared extinction characteristics,” J. Appl. Meteorol. 29, 1313–1329 (1990).
[CrossRef]

C. Prabhakara, R. S. Fraser, G. Dalu, M. -L. C. Wu, R. J. Curran, “Thin cirrus clouds: seasonal distribution over oceans deduced from Nimbus-4 IRIS,” J. Appl. Meteorol. 27, 379–399 (1988).
[CrossRef]

G. Dalu, “Emittance effect on the remotely sensed sea surface temperature,” Int. J. Remote Sensing 6, 733–740 (1975).
[CrossRef]

C. Prabhakara, G. Dalu, V. G. Kunde, “Estimation of sea surface temperature from remote sensing in the 11 to 13 μm window region,” J. Geophys. Res. 79, 5039–5044 (1974).
[CrossRef]

Folland, C. K.

R. W. Reynolds, C. K. Folland, D. E. Parker, “Biases in satellite-derived sea-surface-temperature data,” Nature (London) 341, 728–731 (1989).
[CrossRef]

Fraser, R. S.

C. Prabhakara, J.-M. Yoo, G. Dalu, R. S. Fraser, “Deep optically thin cirrus clouds in the polar regions: part I. Infrared extinction characteristics,” J. Appl. Meteorol. 29, 1313–1329 (1990).
[CrossRef]

C. Prabhakara, R. S. Fraser, G. Dalu, M. -L. C. Wu, R. J. Curran, “Thin cirrus clouds: seasonal distribution over oceans deduced from Nimbus-4 IRIS,” J. Appl. Meteorol. 27, 379–399 (1988).
[CrossRef]

Friedman, D.

Kornfeld, J.

J. Kornfeld, J. Susskind, “On the effects of surface emissivity on temperature retrievals,” Mon. Weather Rev. 105, 1605–1608 (1977).
[CrossRef]

Kunde, V. G.

C. Prabhakara, G. Dalu, V. G. Kunde, “Estimation of sea surface temperature from remote sensing in the 11 to 13 μm window region,” J. Geophys. Res. 79, 5039–5044 (1974).
[CrossRef]

Llewellyn-Jones, D. T.

I. J. Barton, A. M. Zavody, D. M. O’Brien, D. R. Cutten, R. W. Saunders, D. T. Llewellyn-Jones, “Theoretical algorithms for satellite-derived sea surface temperatures,” J. Geophys. Res. 94, 3365–3375 (1989).
[CrossRef]

Masuda, K.

K. Masuda, T. Takashima, Y. Takayama, “Emissivity of pure and sea waters for the model sea surface in the infrared window regions,” Remote Sensing Environ. 24, 313–329 (1988).
[CrossRef]

Maul, G. A.

G. A. Maul, “Zenith angle effects in multichannel infrared sea surface remote sensing,” Remote Sensing Environ. 13, 439–451 (1983).
[CrossRef]

McClain, E. P.

E. P. McClain, “Global sea surface temperatures and cloud clearing for aerosol optical depth estimates,” Int. J. Remote Sensing 10, 763–769 (1989).
[CrossRef]

E. P. McClain, W. G. Pichel, C. C. Walton, “Comparative performance of AVHRR based multi-channel sea surface temperatures,” J. Geophys. Res. 90, 11587–11601 (1985).
[CrossRef]

Munk, W.

C. Cox, W. Munk, “Some problems in optical oceanography,” J. Mar. Res. 14, 63–78 (1955).

C. Cox, W. Munk, “Measurement of the roughness of the sea surface from photography of the Sun's glitter,” J. Opt. Soc. Am. 44, 835–850 (1954).
[CrossRef]

C. Cox, W. Munk, “Statistics of the sea surface derived from Sun glitter,” J. Mar. Res. 13, 198–227 (1954).

O’Brien, D. M.

I. J. Barton, A. M. Zavody, D. M. O’Brien, D. R. Cutten, R. W. Saunders, D. T. Llewellyn-Jones, “Theoretical algorithms for satellite-derived sea surface temperatures,” J. Geophys. Res. 94, 3365–3375 (1989).
[CrossRef]

Otterman, J.

A. Ben-Shalom, J. Otterman, P. Schechner, “Measured infrared radiances near sea horizon and their interpretation—preliminary results,” Geophys. Res. Lett. 8, 772–774 (1981).
[CrossRef]

J. Otterman, “Single-scattering solution for radiative transfer through a turbid atmosphere,” Appl. Opt. 17, 3431–3438 (1978).
[CrossRef] [PubMed]

Parker, D. E.

R. W. Reynolds, C. K. Folland, D. E. Parker, “Biases in satellite-derived sea-surface-temperature data,” Nature (London) 341, 728–731 (1989).
[CrossRef]

Patzert, W. C.

T. B. Barnett, W. C. Patzert, S. C. Webb, B. R. Bean, “Climatological usefulness of satellite determined sea surface temperatures in the tropical pacific,” Bull. Am. Meteorol. Soc. 60, 197–205 (1979).
[CrossRef]

Pichel, W. G.

E. P. McClain, W. G. Pichel, C. C. Walton, “Comparative performance of AVHRR based multi-channel sea surface temperatures,” J. Geophys. Res. 90, 11587–11601 (1985).
[CrossRef]

Prabhakara, C.

C. Prabhakara, J.-M. Yoo, G. Dalu, R. S. Fraser, “Deep optically thin cirrus clouds in the polar regions: part I. Infrared extinction characteristics,” J. Appl. Meteorol. 29, 1313–1329 (1990).
[CrossRef]

C. Prabhakara, R. S. Fraser, G. Dalu, M. -L. C. Wu, R. J. Curran, “Thin cirrus clouds: seasonal distribution over oceans deduced from Nimbus-4 IRIS,” J. Appl. Meteorol. 27, 379–399 (1988).
[CrossRef]

C. Prabhakara, G. Dalu, V. G. Kunde, “Estimation of sea surface temperature from remote sensing in the 11 to 13 μm window region,” J. Geophys. Res. 79, 5039–5044 (1974).
[CrossRef]

Reuter, D.

J. Susskind, D. Reuter, “Retrieval of sea-surface temperatures from HIRS2/MSU,” J. Geophys. Res. 90, 11602–11608 (1985).
[CrossRef]

J. Susskind, J. Rosenfield, D. Reuter, M. T. Chahine, “Remote sensing of weather and climate parameters from HIRS2/MSU on TIROS-N,” J. Geophys. Res. 89, 4677–4697 (1984).
[CrossRef]

Reynolds, R. W.

R. W. Reynolds, C. K. Folland, D. E. Parker, “Biases in satellite-derived sea-surface-temperature data,” Nature (London) 341, 728–731 (1989).
[CrossRef]

Rosenfield, J.

J. Susskind, J. Rosenfield, D. Reuter, M. T. Chahine, “Remote sensing of weather and climate parameters from HIRS2/MSU on TIROS-N,” J. Geophys. Res. 89, 4677–4697 (1984).
[CrossRef]

Saunders, P. M.

Saunders, R. W.

I. J. Barton, A. M. Zavody, D. M. O’Brien, D. R. Cutten, R. W. Saunders, D. T. Llewellyn-Jones, “Theoretical algorithms for satellite-derived sea surface temperatures,” J. Geophys. Res. 94, 3365–3375 (1989).
[CrossRef]

Schechner, P.

A. Ben-Shalom, J. Otterman, P. Schechner, “Measured infrared radiances near sea horizon and their interpretation—preliminary results,” Geophys. Res. Lett. 8, 772–774 (1981).
[CrossRef]

Sidran, M.

Spencer, R. W.

R. W. Spencer, J. R. Christy, “Precise monitoring of global temperature trends from satellites,” Science 247, 1558–1562 (1990).
[CrossRef] [PubMed]

Strong, A. E.

A. E. Strong, “Greater global warming revealed by satellite-derived sea surface temperature trends,” Nature (London) 338, 642–645 (1989).
[CrossRef]

A. E. Strong, “Monitoring El Nino using satellite-based sea surface temperatures,” Ocean-Air Interact. 1, 11–28 (1986).

Susskind, J.

J. Susskind, D. Reuter, “Retrieval of sea-surface temperatures from HIRS2/MSU,” J. Geophys. Res. 90, 11602–11608 (1985).
[CrossRef]

J. Susskind, J. Rosenfield, D. Reuter, M. T. Chahine, “Remote sensing of weather and climate parameters from HIRS2/MSU on TIROS-N,” J. Geophys. Res. 89, 4677–4697 (1984).
[CrossRef]

J. Kornfeld, J. Susskind, “On the effects of surface emissivity on temperature retrievals,” Mon. Weather Rev. 105, 1605–1608 (1977).
[CrossRef]

Takashima, T.

K. Masuda, T. Takashima, Y. Takayama, “Emissivity of pure and sea waters for the model sea surface in the infrared window regions,” Remote Sensing Environ. 24, 313–329 (1988).
[CrossRef]

T. Takashima, Y. Takayama, “Emissivity and reflectance of the model sea surface for a use of AVHRR data of NOAA satellites,” Pap. Meteorol. Geophys. 32, 267–274 (1981).
[CrossRef]

Takayama, Y.

K. Masuda, T. Takashima, Y. Takayama, “Emissivity of pure and sea waters for the model sea surface in the infrared window regions,” Remote Sensing Environ. 24, 313–329 (1988).
[CrossRef]

T. Takashima, Y. Takayama, “Emissivity and reflectance of the model sea surface for a use of AVHRR data of NOAA satellites,” Pap. Meteorol. Geophys. 32, 267–274 (1981).
[CrossRef]

Walton, C. C.

E. P. McClain, W. G. Pichel, C. C. Walton, “Comparative performance of AVHRR based multi-channel sea surface temperatures,” J. Geophys. Res. 90, 11587–11601 (1985).
[CrossRef]

Webb, S. C.

T. B. Barnett, W. C. Patzert, S. C. Webb, B. R. Bean, “Climatological usefulness of satellite determined sea surface temperatures in the tropical pacific,” Bull. Am. Meteorol. Soc. 60, 197–205 (1979).
[CrossRef]

Wolfe, W. L.

W. L. Wolfe, G. Zissis, The Infrared Handbook (U.S. Department of the Navy, Washington, D.C., 1978).

Wu, M. -L. C.

C. Prabhakara, R. S. Fraser, G. Dalu, M. -L. C. Wu, R. J. Curran, “Thin cirrus clouds: seasonal distribution over oceans deduced from Nimbus-4 IRIS,” J. Appl. Meteorol. 27, 379–399 (1988).
[CrossRef]

Yoo, J.-M.

C. Prabhakara, J.-M. Yoo, G. Dalu, R. S. Fraser, “Deep optically thin cirrus clouds in the polar regions: part I. Infrared extinction characteristics,” J. Appl. Meteorol. 29, 1313–1329 (1990).
[CrossRef]

Zavody, A. M.

I. J. Barton, A. M. Zavody, D. M. O’Brien, D. R. Cutten, R. W. Saunders, D. T. Llewellyn-Jones, “Theoretical algorithms for satellite-derived sea surface temperatures,” J. Geophys. Res. 94, 3365–3375 (1989).
[CrossRef]

Zissis, G.

W. L. Wolfe, G. Zissis, The Infrared Handbook (U.S. Department of the Navy, Washington, D.C., 1978).

Appl. Opt. (3)

Bull. Am. Meteorol. Soc. (1)

T. B. Barnett, W. C. Patzert, S. C. Webb, B. R. Bean, “Climatological usefulness of satellite determined sea surface temperatures in the tropical pacific,” Bull. Am. Meteorol. Soc. 60, 197–205 (1979).
[CrossRef]

Geophys. Res. Lett. (1)

A. Ben-Shalom, J. Otterman, P. Schechner, “Measured infrared radiances near sea horizon and their interpretation—preliminary results,” Geophys. Res. Lett. 8, 772–774 (1981).
[CrossRef]

Int. J. Remote Sensing (2)

G. Dalu, “Emittance effect on the remotely sensed sea surface temperature,” Int. J. Remote Sensing 6, 733–740 (1975).
[CrossRef]

E. P. McClain, “Global sea surface temperatures and cloud clearing for aerosol optical depth estimates,” Int. J. Remote Sensing 10, 763–769 (1989).
[CrossRef]

J. Appl. Meteorol. (2)

C. Prabhakara, R. S. Fraser, G. Dalu, M. -L. C. Wu, R. J. Curran, “Thin cirrus clouds: seasonal distribution over oceans deduced from Nimbus-4 IRIS,” J. Appl. Meteorol. 27, 379–399 (1988).
[CrossRef]

C. Prabhakara, J.-M. Yoo, G. Dalu, R. S. Fraser, “Deep optically thin cirrus clouds in the polar regions: part I. Infrared extinction characteristics,” J. Appl. Meteorol. 29, 1313–1329 (1990).
[CrossRef]

J. Geophys. Res. (5)

C. Prabhakara, G. Dalu, V. G. Kunde, “Estimation of sea surface temperature from remote sensing in the 11 to 13 μm window region,” J. Geophys. Res. 79, 5039–5044 (1974).
[CrossRef]

I. J. Barton, A. M. Zavody, D. M. O’Brien, D. R. Cutten, R. W. Saunders, D. T. Llewellyn-Jones, “Theoretical algorithms for satellite-derived sea surface temperatures,” J. Geophys. Res. 94, 3365–3375 (1989).
[CrossRef]

J. Susskind, J. Rosenfield, D. Reuter, M. T. Chahine, “Remote sensing of weather and climate parameters from HIRS2/MSU on TIROS-N,” J. Geophys. Res. 89, 4677–4697 (1984).
[CrossRef]

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J. Kornfeld, J. Susskind, “On the effects of surface emissivity on temperature retrievals,” Mon. Weather Rev. 105, 1605–1608 (1977).
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Figures (8)

Fig. 1
Fig. 1

A Spectral reflectances versus wavelength, directional reflectances 1 − ∊(0°) and 1 − ∊(50°) from Bramson’s tabulation,14 and hemispheric reflectance 1 − ∊ h fitted to Bramson’s data. B Coefficients c − 1 and m in the approximate representation of the spectral directional emissivity.

Fig. 2
Fig. 2

Temperature differences versus wavelength T m T s , when T m is measured from the zenith: A without an atmosphere and over an absorbing layer τ b , T c = 230 K; B as in Fig. 2A, but T c is equal to SST, T c = 300 K; C over a scattering layer τ s .

Fig. 3
Fig. 3

Temperature differences T m T s as in Fig. 2 but with T m measured at θ = 50°.

Fig. 4
Fig. 4

Errors ΔT s = TsbbT s in the SST retrieval under the blackbody assumption viewing from the zenith: A without an atmosphere and over an absorbing layer τ b , T c = 230 K; B as in Fig. 4A but with T c equal to the water temperature, T c = 300 K; C over a scattering layer τ s .

Fig. 5
Fig. 5

Errors ΔT s = TsbbT s in the SST retrieval as in Fig. 4 but for viewing from θ = 50°.

Fig. 6
Fig. 6

Error in the inferred optical thickness under the black-body assumption, viewing from the zenith: A error Δτ b in the cirrus cloud-absorbing optical thickness, T c = 230 K; B error Δτ s in the scattering optical thickness.

Fig. 7
Fig. 7

Error in the inferred optical thickness as in Fig. 6 but with viewing from θ = 50°.

Fig. 8
Fig. 8

Geometry of emission and reflection under sea-state conditions.

Tables (1)

Tables Icon

Table 1 Directional Reflectances 1 − ∊(θ), Directional Reflectances 1 − ∊1(θ), and Conical-To-Directional Reflectances ρ1 for the Same Sea State as a Function of Optical Thickness of the Atmospheric Layer τ s a

Equations (30)

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dB ( T m ) dB ( T s ) = t [ + h ( 1 - ) b h ] + h f ¯ [ 1 - h ) b ¯ h ] ;
d B ( T m ) d = B ( T s ) t ( 1 - h b h ) - D ( τ a ) t [ 1 + 2 ( 1 - ) b ] ;
d B ( T m ) d h = B ( T s ) { f ¯ [ 1 + ( 1 - 2 h ) b ¯ h ] + ( 1 - ) t b h } - F d ( τ a ) f ¯ [ 1 + 2 ( 1 - h ) b ¯ h ] ,
Δ B ( T s ) d B ( T m ) d B ( T s ) = - Δ d B ( T m ) d - Δ h d B ( T m ) d h .
Δ B ( T s ) { t [ + h ( 1 - ) b h ] + h f ¯ [ 1 + ( 1 - h ) b ¯ h ] } = - ( 1 - ) t { B ( T s ) ( 1 - h b h ) - D ( τ a ) [ 1 + 2 ( 1 - ) b ] } - ( 1 - h ) { f ¯ B ( T s ) [ 1 + ( 1 - 2 h ) b ¯ h ] + t B ( T s ) ( 1 - ) b h - f ¯ F d ( τ a ) [ 1 + 2 ( 1 - h ) b ¯ h ] } .
Δ a B ( T s ) = - ( 1 - ) B ( T s ) - D ( τ a ) ,
Δ s B ( T s ) B ( T s ) = - ( 1 - ) t [ 1 + ( 1 - 2 h ) b h ] + ( 1 - h ) f ¯ [ 1 + ( 1 - 2 h ) b ¯ h ] t [ + h ( 1 - ) b h ] + h f ¯ [ 1 + ( 1 - h ) b ¯ h ] .
1 - h = 1 - 2 π 0 π / 2 cos θ sin θ ( θ ) d θ / π = 1 - 2 0 1 μ ( μ ) d μ ,
h = ( 10 80 cos θ sin θ ) - 1 10 80 cos θ sin θ ( θ ) ,
a ( u ) = c exp ( - m / μ ) .
T m ( θ ) = B - 1 [ ( θ ) B ( T s ) ] ,
Δ T s = T m ( θ ) - T s = B - 1 [ ( θ ) B ( T s ) ] - T s .
Δ T s = - ( 1 - ) - 1 λ T s 2 c 2 - 1 ,
B ( T m ) = ( μ ) B ( T s ) exp ( - τ b / μ ) + B ( T c ) [ 1 - exp ( - τ b / μ ) ] × { 1 + [ 1 - ( μ ) ] exp ( - τ b / μ ) } .
B ( T c ) [ 1 + 2 ( 1 - ) exp ( - τ b / μ ) ] > B ( T s )
T sia = B - 1 [ exp ( τ b / μ ) ( μ ) ( B ( T m ) - { 1 + [ 1 - ( μ ) ] exp ( - τ b / μ ) } × B ( T c ) [ 1 - exp ( - τ b / μ ) ] ) ] ,
B ( T m ) = B ( T sbb ) exp ( - τ b / μ ) + B ( T c ) [ 1 - exp ( - τ b / μ ) ] ,
T sbb = B - 1 { exp ( τ b / μ ) [ B ( T m ) - B ( T c ) ] × [ 1 - exp ( - τ b / μ ) ] } .
τ inf = μ ln B ( T s ) - B ( T c ) B ( T m ) - B ( T c ) .
B ( T m ) = c exp ( - m / μ ) B ( T s ) exp ( - τ s / μ ) + B sc [ 1 - exp ( - τ s / μ ) ] × { 1 + [ 1 - c exp ( - m / μ ) ] exp ( - τ s / μ ) } .
ϕ 0 = 2 π c B ( T s ) 0 1 μ exp ( - m / μ ) [ 1 - exp ( - τ s / μ ) ] d μ / π = 2 c B ( T s ) [ E 3 ( m ) - E 3 ( m + τ s ) ] ,
Δ ϕ = 2 B s c × 0 1 μ [ 1 - exp ( - τ s / μ ) ] 2 [ 1 - c exp ( - m / μ ) ] d μ = B sc { 1 + 2 [ E 3 ( 2 τ s ) - c E 3 ( m ) - 2 E 3 ( τ s ) - c E 3 ( 2 τ s + m ) + 2 c E 3 ( τ s + m ) ] } = B sc ( 1 + 2 Σ E 3 ) ,
0.5 ϕ = 0.5 ( ϕ 0 + Δ ϕ ) = 2 B sc 0 1 μ [ 1 - exp ( - τ s / μ ) ] d μ = B sc [ 1 - 2 E 3 ( τ s ) ] .
B sc = 2 c B ( T s ) [ E 3 ( m ) - E 3 ( m + τ s ) ] 1 - 4 E 3 ( τ s ) - 2 Σ E 3 .
B ( T m ) = c B ( T s ) ( exp [ - ( m + τ s ) / μ ] + 2 [ E 3 ( m ) - E 3 ( m + τ s ) ] [ 1 - exp ( - τ s / μ ) ] { 1 + [ 1 - c exp ( - m / μ ) ] exp ( - τ s / μ ) } 1 - 4 E 3 ( τ s ) - 2 Σ E 3 ) .
T sbb = B - 1 { B ( T m ) 2 [ 1 + exp ( - τ s / μ ) ] - 1 } .
τ inf = - μ ln [ 2 B ( T m ) B ( T s ) - 1 ] .
1 ( 50 ° ) B ( T s ) = [ cos ( θ + α ) ( θ + α ) + cos ( θ - α ) ( θ - α ) ] cos ( θ + α ) + cos ( θ - α ) B ( T s ) .
B ( T c ) { 1 - exp [ - τ b / cos ( θ + 2 α ) ] } × cos ( θ + α ) [ 1 - ( θ + α ) ] ,
ρ 1 ( θ ) = α cos ( θ + α ) { 1 - exp [ - τ b / cos ( θ + 2 α ) ] } [ 1 - ( θ + α ) ] α cos ( θ + α ) { 1 - exp [ - τ b / cos ( θ + 2 α ) ] } ,

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