Abstract

Light coming from a cloud to the detector of a multispectral satellite (Landsat) consists of light reflected from the cloud and light scattered by the layer of atmosphere between the cloud and satellite. Because of the strong wavelength dependence of Rayleigh scattering, the comparison of the signals in two spectral channels allows one to find the thickness of the scattering layer and hence the height of the cloud top.

© 1985 Optical Society of America

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References

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  1. R. J. Curran, H. L. Kyle, L. R. Blaine, J. Smith, T. D. Clem, “Multispectral Scanning Radiometer for Remote Sensing Cloud Physical Parameters,” Rev. Sci. Instrum. 52, 1546 (1981).
    [CrossRef]
  2. K.-N. Liou, Introduction to Atmospheric Radiation (Academic, New York, 1980).
  3. A. K. Khargian, The Physics of Atmospheric Ozone (Israel Program for Scientific Translations, Jerusalem, 1975).
  4. K. Y. Kondratyev, Radiation in the Atmosphere (Academic, New York, 1975).
  5. J. Joseph, W. Wiscombe, J. Weinman, “The Delta-Eddington Approximation for Radiative Transfer,” J. Atmos. Sci. 33, 2452 (1976).
    [CrossRef]
  6. E. McCartney, Optics of the Atmosphere; Scattering by Molecules and Particles (Wiley, New York, 1976).
  7. W. Irvine, J. Pollack, “Infrared Optical Properties of Water and Ice Spheres,” Icarus 8, 324 (1968).
    [CrossRef]
  8. M. Podolak, R. E. Danielson, “Axel Dust on Saturn and Titan,” Icarus 37, 361 (1977).
    [CrossRef]

1981 (1)

R. J. Curran, H. L. Kyle, L. R. Blaine, J. Smith, T. D. Clem, “Multispectral Scanning Radiometer for Remote Sensing Cloud Physical Parameters,” Rev. Sci. Instrum. 52, 1546 (1981).
[CrossRef]

1977 (1)

M. Podolak, R. E. Danielson, “Axel Dust on Saturn and Titan,” Icarus 37, 361 (1977).
[CrossRef]

1976 (1)

J. Joseph, W. Wiscombe, J. Weinman, “The Delta-Eddington Approximation for Radiative Transfer,” J. Atmos. Sci. 33, 2452 (1976).
[CrossRef]

1968 (1)

W. Irvine, J. Pollack, “Infrared Optical Properties of Water and Ice Spheres,” Icarus 8, 324 (1968).
[CrossRef]

Blaine, L. R.

R. J. Curran, H. L. Kyle, L. R. Blaine, J. Smith, T. D. Clem, “Multispectral Scanning Radiometer for Remote Sensing Cloud Physical Parameters,” Rev. Sci. Instrum. 52, 1546 (1981).
[CrossRef]

Clem, T. D.

R. J. Curran, H. L. Kyle, L. R. Blaine, J. Smith, T. D. Clem, “Multispectral Scanning Radiometer for Remote Sensing Cloud Physical Parameters,” Rev. Sci. Instrum. 52, 1546 (1981).
[CrossRef]

Curran, R. J.

R. J. Curran, H. L. Kyle, L. R. Blaine, J. Smith, T. D. Clem, “Multispectral Scanning Radiometer for Remote Sensing Cloud Physical Parameters,” Rev. Sci. Instrum. 52, 1546 (1981).
[CrossRef]

Danielson, R. E.

M. Podolak, R. E. Danielson, “Axel Dust on Saturn and Titan,” Icarus 37, 361 (1977).
[CrossRef]

Irvine, W.

W. Irvine, J. Pollack, “Infrared Optical Properties of Water and Ice Spheres,” Icarus 8, 324 (1968).
[CrossRef]

Joseph, J.

J. Joseph, W. Wiscombe, J. Weinman, “The Delta-Eddington Approximation for Radiative Transfer,” J. Atmos. Sci. 33, 2452 (1976).
[CrossRef]

Khargian, A. K.

A. K. Khargian, The Physics of Atmospheric Ozone (Israel Program for Scientific Translations, Jerusalem, 1975).

Kondratyev, K. Y.

K. Y. Kondratyev, Radiation in the Atmosphere (Academic, New York, 1975).

Kyle, H. L.

R. J. Curran, H. L. Kyle, L. R. Blaine, J. Smith, T. D. Clem, “Multispectral Scanning Radiometer for Remote Sensing Cloud Physical Parameters,” Rev. Sci. Instrum. 52, 1546 (1981).
[CrossRef]

Liou, K.-N.

K.-N. Liou, Introduction to Atmospheric Radiation (Academic, New York, 1980).

McCartney, E.

E. McCartney, Optics of the Atmosphere; Scattering by Molecules and Particles (Wiley, New York, 1976).

Podolak, M.

M. Podolak, R. E. Danielson, “Axel Dust on Saturn and Titan,” Icarus 37, 361 (1977).
[CrossRef]

Pollack, J.

W. Irvine, J. Pollack, “Infrared Optical Properties of Water and Ice Spheres,” Icarus 8, 324 (1968).
[CrossRef]

Smith, J.

R. J. Curran, H. L. Kyle, L. R. Blaine, J. Smith, T. D. Clem, “Multispectral Scanning Radiometer for Remote Sensing Cloud Physical Parameters,” Rev. Sci. Instrum. 52, 1546 (1981).
[CrossRef]

Weinman, J.

J. Joseph, W. Wiscombe, J. Weinman, “The Delta-Eddington Approximation for Radiative Transfer,” J. Atmos. Sci. 33, 2452 (1976).
[CrossRef]

Wiscombe, W.

J. Joseph, W. Wiscombe, J. Weinman, “The Delta-Eddington Approximation for Radiative Transfer,” J. Atmos. Sci. 33, 2452 (1976).
[CrossRef]

Icarus (2)

W. Irvine, J. Pollack, “Infrared Optical Properties of Water and Ice Spheres,” Icarus 8, 324 (1968).
[CrossRef]

M. Podolak, R. E. Danielson, “Axel Dust on Saturn and Titan,” Icarus 37, 361 (1977).
[CrossRef]

J. Atmos. Sci. (1)

J. Joseph, W. Wiscombe, J. Weinman, “The Delta-Eddington Approximation for Radiative Transfer,” J. Atmos. Sci. 33, 2452 (1976).
[CrossRef]

Rev. Sci. Instrum. (1)

R. J. Curran, H. L. Kyle, L. R. Blaine, J. Smith, T. D. Clem, “Multispectral Scanning Radiometer for Remote Sensing Cloud Physical Parameters,” Rev. Sci. Instrum. 52, 1546 (1981).
[CrossRef]

Other (4)

K.-N. Liou, Introduction to Atmospheric Radiation (Academic, New York, 1980).

A. K. Khargian, The Physics of Atmospheric Ozone (Israel Program for Scientific Translations, Jerusalem, 1975).

K. Y. Kondratyev, Radiation in the Atmosphere (Academic, New York, 1975).

E. McCartney, Optics of the Atmosphere; Scattering by Molecules and Particles (Wiley, New York, 1976).

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Figures (2)

Fig. 1
Fig. 1

Observational geometry.

Fig. 2
Fig. 2

Comparison of the heights obtained by measurements of the distances between corresponding points of the cloud and shadow and by radiation measurements.

Tables (1)

Tables Icon

Table I Comparison of Reflectivities at 0.75 and 0.55 μm

Equations (18)

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I λ d λ = 1 4 μ 0 F λ d λ exp ( τ / μ 0 ) R λ exp ( τ ) + I λ d λ, 
I = λ 1 λ 2 I λ d λ = λ 1 λ 2 ( 1 4 μ 0 F λ R λ exp [ τ ( 1 + 1 / μ 0 ) ] + I λ ) d λ ,
I λ = ω F λ 4 P ( ϕ ) { 1 exp [ τ ( 1 + 1 / μ 0 ) ] } ,
P ( ϕ ) = 3 4 ( 1 + cos 2 ϕ ) = 3 4 ( 1 + μ 0 2 ) .
I = λ 1 λ 2 { [ 1 4 μ 0 F λ R λ 3 ω 16 F λ ( 1 + μ 0 2 ) ] exp [ τ ( 1 + 1 / μ 0 ) ] + 3 ω 16 F λ ( 1 + μ 0 2 ) } d λ .
τ = λ 4 h α d z ,
I = λ 1 λ 2 { [ 1 4 μ 0 F λ R λ 3 ω 16 F λ ( 1 + μ 0 2 ) ] × [ 1 h α d z ( 1 + 1 / μ 0 ) / λ 4 ] + 3 ω 16 F λ ( 1 + μ 0 2 ) } d λ .
I 0 . 5 0 . 6 = R λ [ 1 4 μ 0 F λ ( λ 2 λ 1 ) 1 12 μ 0 F λ ( 1 + 1 / μ 0 ) h α d z ( λ 1 3 λ 2 3 ) ] + 1 16 ( 1 + 1 / μ 0 ) ( 1 + μ 0 2 ) F λ h α d z ( λ 1 3 λ 2 3 ) .
I 0 . 7 0 . 8 = 1 4 μ 0 R λ [ a ( λ 4 λ 3 ) b 2 ( λ 4 2 λ 3 2 ) ] + h α d z ( 1 + 1 / μ 0 ) [ a 3 ( λ 4 3 λ 3 3 ) b 2 ( λ 4 2 λ 3 2 ) ] × [ 1 4 μ 0 R λ 3 16 ( 1 + μ 0 2 ) ] .
β = a 3 ( 1 / λ 4 3 1 / λ 3 3 ) b 2 ( 1 / λ 4 2 1 / λ 3 2 ) , γ = a ( λ 4 λ 3 ) b 2 ( λ 4 2 λ 3 2 ) , δ = F λ ( λ 2 λ 1 ) , η = F λ ( 1 / λ 1 3 1 / λ 2 3 ) ,
A = γ I 0 . 5 0 . 6 δ I 0 . 7 0 . 8 , 1 16 ( 1 + 1 μ 0 ) ( 1 + μ 0 2 ) ( 3 β δ + γ η ) ( 1 + 1 μ 0 ) ( I 0 . 7 0 . 8 η / 3 + I 0 . 5 0 . 6 β ) ,
α = 32 π 3 c 1 2 M 3 N 0 ρ ,
A = 8 . 36 × 10 22 h ρ d z ,
P δ ( μ ) 2 f δ ( 1 μ ) + ( 1 f ) ( 1 + 3 g μ ) ,
P δ ( μ ) d Ω 4 π = 1 , μ P δ ( μ ) d Ω 4 π = μ P ( μ ) d Ω 4 π = g , μ 2 P δ ( μ ) d Ω 4 π = μ 2 P ( μ ) d Ω 4 π = f .
g = g f 1 f
τ = ( 1 ω f ) τ c l ,
n ( r ) = r a exp [ a b ( r r c ) a ] ,

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