Abstract

An IR transmission model for thin and subvisual cirrus clouds composed of hexagonal ice crystals with a specific use for target detection has been developed. The present model includes parameterizations of the ice crystal size distribution and the position of cirrus clouds in terms of ambient temperature. To facilitate the scattering and absorption calculations for hexagonal column and plate crystals in connection with transmission calculations, we have developed parameterized equations for their single scattering properties by using the results computed from a geometric ray-tracing program. The successive order-of-scattering approach has been used to account for multiple scattering of ice crystals associated with a target–detector system. The direct radiance, path radiance, and radiances produced by multiple scattering and background radiation involving cirrus clouds have been computed for 3.7- and 10-μm wavelengths. We show that the background radiance at the 3.7-μm wavelength is relatively small so that a high contrast may be obtained using this wavelength for the detection of airborne and ground-based objects in the presence of thin cirrus clouds. Finally, using the present model, including a simple prediction scheme for the ice crystal size distribution and cloud position, the transmission of infrared radiation through cirrus clouds can be efficiently evaluated if the target–detector geometry is defined.

© 1990 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. K. N. Liou, “Influence of Cirrus Clouds on Weather and Climate Processes: A Global Perspective,” Mon. Weather Rev. 114, 1167–1199 (1986).
    [CrossRef]
  2. A. J. Heymsfield, C. M. R. Platt, “A Parameterization of the Particle Size Spectrum of Ice Clouds in Terms of the Ambient Temperature and the Ice Water Content,” J. Atmos. Sci. 41, 846–855 (1984).
    [CrossRef]
  3. Y. Takano, K. N. Liou, “Solar Radiative Transfer in Cirrus Clouds. Part I: Single-scattering and Optical Properties of Hexagonal Ice Crystals,” J. Atmos. Sci. 46, 3–19 (1989).
    [CrossRef]
  4. A. J. Heymsfield, “Cirrus Uncinus Generating Cells and the Evolution of Cirriform Clouds. Part I. Aircraft Observations of the Growth of the Ice Phase,” J. Atmos. Sci. 32, 799–808 (1975).
    [CrossRef]
  5. A. J. Heymsfield, “Precipitation Development in Stratiform Ice Clouds: A Microphysical and Dynamical Study,” J. Atmos. Sci. 34, 367–381 (1977).
    [CrossRef]
  6. S. Warren, “Optical Constants of Ice from the Ultraviolet to the Microwave,” Appl. Opt. 23, 1206–1225 (1984).
    [CrossRef] [PubMed]
  7. A. H. Auer, D. L. Veal, “The Dimension of Ice Crystals in Natural Clouds,” J. Atmos. Sci. 27, 919–926 (1970).
    [CrossRef]
  8. C. M. R. Platt Harshvardhan, “Temperature Dependence of Cirrus Extinction: Implication for Climate Feedback,” J. Geophys. Res. 93, 11051–11058 (1988).
    [CrossRef]
  9. Y. Takano, K. N. Liou, “Solar Radiative Transfer in Cirrus Clouds. Part II: Theory and Computation of Multiple Scattering in an Anisotropic Medium,” J. Atmos. Sci. 46, 20–36 (1989).
    [CrossRef]
  10. R. W. Pratt, “Review of Radiosonde Humidity and Temperature Errors,” J. Atmos. Ocean. Tech., 2, 404–407 (1985).
    [CrossRef]
  11. F. J. Kneizys et al., “Atmospheric Transmittance/Radiance: Computer Code <sc>lowtran</sc>5,” Scientific Report, AFGL-TR-80-0067, Air Force Geophysics Laboratory (1980).

1989 (2)

Y. Takano, K. N. Liou, “Solar Radiative Transfer in Cirrus Clouds. Part I: Single-scattering and Optical Properties of Hexagonal Ice Crystals,” J. Atmos. Sci. 46, 3–19 (1989).
[CrossRef]

Y. Takano, K. N. Liou, “Solar Radiative Transfer in Cirrus Clouds. Part II: Theory and Computation of Multiple Scattering in an Anisotropic Medium,” J. Atmos. Sci. 46, 20–36 (1989).
[CrossRef]

1988 (1)

C. M. R. Platt Harshvardhan, “Temperature Dependence of Cirrus Extinction: Implication for Climate Feedback,” J. Geophys. Res. 93, 11051–11058 (1988).
[CrossRef]

1986 (1)

K. N. Liou, “Influence of Cirrus Clouds on Weather and Climate Processes: A Global Perspective,” Mon. Weather Rev. 114, 1167–1199 (1986).
[CrossRef]

1985 (1)

R. W. Pratt, “Review of Radiosonde Humidity and Temperature Errors,” J. Atmos. Ocean. Tech., 2, 404–407 (1985).
[CrossRef]

1984 (2)

A. J. Heymsfield, C. M. R. Platt, “A Parameterization of the Particle Size Spectrum of Ice Clouds in Terms of the Ambient Temperature and the Ice Water Content,” J. Atmos. Sci. 41, 846–855 (1984).
[CrossRef]

S. Warren, “Optical Constants of Ice from the Ultraviolet to the Microwave,” Appl. Opt. 23, 1206–1225 (1984).
[CrossRef] [PubMed]

1977 (1)

A. J. Heymsfield, “Precipitation Development in Stratiform Ice Clouds: A Microphysical and Dynamical Study,” J. Atmos. Sci. 34, 367–381 (1977).
[CrossRef]

1975 (1)

A. J. Heymsfield, “Cirrus Uncinus Generating Cells and the Evolution of Cirriform Clouds. Part I. Aircraft Observations of the Growth of the Ice Phase,” J. Atmos. Sci. 32, 799–808 (1975).
[CrossRef]

1970 (1)

A. H. Auer, D. L. Veal, “The Dimension of Ice Crystals in Natural Clouds,” J. Atmos. Sci. 27, 919–926 (1970).
[CrossRef]

Auer, A. H.

A. H. Auer, D. L. Veal, “The Dimension of Ice Crystals in Natural Clouds,” J. Atmos. Sci. 27, 919–926 (1970).
[CrossRef]

Heymsfield, A. J.

A. J. Heymsfield, C. M. R. Platt, “A Parameterization of the Particle Size Spectrum of Ice Clouds in Terms of the Ambient Temperature and the Ice Water Content,” J. Atmos. Sci. 41, 846–855 (1984).
[CrossRef]

A. J. Heymsfield, “Precipitation Development in Stratiform Ice Clouds: A Microphysical and Dynamical Study,” J. Atmos. Sci. 34, 367–381 (1977).
[CrossRef]

A. J. Heymsfield, “Cirrus Uncinus Generating Cells and the Evolution of Cirriform Clouds. Part I. Aircraft Observations of the Growth of the Ice Phase,” J. Atmos. Sci. 32, 799–808 (1975).
[CrossRef]

Kneizys, F. J.

F. J. Kneizys et al., “Atmospheric Transmittance/Radiance: Computer Code <sc>lowtran</sc>5,” Scientific Report, AFGL-TR-80-0067, Air Force Geophysics Laboratory (1980).

Liou, K. N.

Y. Takano, K. N. Liou, “Solar Radiative Transfer in Cirrus Clouds. Part II: Theory and Computation of Multiple Scattering in an Anisotropic Medium,” J. Atmos. Sci. 46, 20–36 (1989).
[CrossRef]

Y. Takano, K. N. Liou, “Solar Radiative Transfer in Cirrus Clouds. Part I: Single-scattering and Optical Properties of Hexagonal Ice Crystals,” J. Atmos. Sci. 46, 3–19 (1989).
[CrossRef]

K. N. Liou, “Influence of Cirrus Clouds on Weather and Climate Processes: A Global Perspective,” Mon. Weather Rev. 114, 1167–1199 (1986).
[CrossRef]

Platt, C. M. R.

A. J. Heymsfield, C. M. R. Platt, “A Parameterization of the Particle Size Spectrum of Ice Clouds in Terms of the Ambient Temperature and the Ice Water Content,” J. Atmos. Sci. 41, 846–855 (1984).
[CrossRef]

Platt Harshvardhan, C. M. R.

C. M. R. Platt Harshvardhan, “Temperature Dependence of Cirrus Extinction: Implication for Climate Feedback,” J. Geophys. Res. 93, 11051–11058 (1988).
[CrossRef]

Pratt, R. W.

R. W. Pratt, “Review of Radiosonde Humidity and Temperature Errors,” J. Atmos. Ocean. Tech., 2, 404–407 (1985).
[CrossRef]

Takano, Y.

Y. Takano, K. N. Liou, “Solar Radiative Transfer in Cirrus Clouds. Part II: Theory and Computation of Multiple Scattering in an Anisotropic Medium,” J. Atmos. Sci. 46, 20–36 (1989).
[CrossRef]

Y. Takano, K. N. Liou, “Solar Radiative Transfer in Cirrus Clouds. Part I: Single-scattering and Optical Properties of Hexagonal Ice Crystals,” J. Atmos. Sci. 46, 3–19 (1989).
[CrossRef]

Veal, D. L.

A. H. Auer, D. L. Veal, “The Dimension of Ice Crystals in Natural Clouds,” J. Atmos. Sci. 27, 919–926 (1970).
[CrossRef]

Warren, S.

Appl. Opt. (1)

J. Atmos. Ocean. Tech. (1)

R. W. Pratt, “Review of Radiosonde Humidity and Temperature Errors,” J. Atmos. Ocean. Tech., 2, 404–407 (1985).
[CrossRef]

J. Atmos. Sci. (6)

A. H. Auer, D. L. Veal, “The Dimension of Ice Crystals in Natural Clouds,” J. Atmos. Sci. 27, 919–926 (1970).
[CrossRef]

Y. Takano, K. N. Liou, “Solar Radiative Transfer in Cirrus Clouds. Part II: Theory and Computation of Multiple Scattering in an Anisotropic Medium,” J. Atmos. Sci. 46, 20–36 (1989).
[CrossRef]

A. J. Heymsfield, C. M. R. Platt, “A Parameterization of the Particle Size Spectrum of Ice Clouds in Terms of the Ambient Temperature and the Ice Water Content,” J. Atmos. Sci. 41, 846–855 (1984).
[CrossRef]

Y. Takano, K. N. Liou, “Solar Radiative Transfer in Cirrus Clouds. Part I: Single-scattering and Optical Properties of Hexagonal Ice Crystals,” J. Atmos. Sci. 46, 3–19 (1989).
[CrossRef]

A. J. Heymsfield, “Cirrus Uncinus Generating Cells and the Evolution of Cirriform Clouds. Part I. Aircraft Observations of the Growth of the Ice Phase,” J. Atmos. Sci. 32, 799–808 (1975).
[CrossRef]

A. J. Heymsfield, “Precipitation Development in Stratiform Ice Clouds: A Microphysical and Dynamical Study,” J. Atmos. Sci. 34, 367–381 (1977).
[CrossRef]

J. Geophys. Res. (1)

C. M. R. Platt Harshvardhan, “Temperature Dependence of Cirrus Extinction: Implication for Climate Feedback,” J. Geophys. Res. 93, 11051–11058 (1988).
[CrossRef]

Mon. Weather Rev. (1)

K. N. Liou, “Influence of Cirrus Clouds on Weather and Climate Processes: A Global Perspective,” Mon. Weather Rev. 114, 1167–1199 (1986).
[CrossRef]

Other (1)

F. J. Kneizys et al., “Atmospheric Transmittance/Radiance: Computer Code <sc>lowtran</sc>5,” Scientific Report, AFGL-TR-80-0067, Air Force Geophysics Laboratory (1980).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (9)

Fig. 1
Fig. 1

Computed single-scattering coalbedo, 1 − ω ˜, denoted by crosses and the fitted curve as a function of the physical parameter z defined in Eq. (5). There is a slight discontinuity at z = 0.4 that defines strong and weak absorption.

Fig. 2
Fig. 2

(a) First-order scattering contribution and definitions of the nadir angle, θ, half beamwidth of the detector ψ, and path length s, in a target–detector system. In this diagram, s′ = DE, and ss′ = ET. (b) Contribution of order of scattering higher than the first in a target–detector system. In this diagram, s′ = DE, s″ = EF, s1 = TG, and s2 = GE. Other notations are defined in the text.

Fig. 3
Fig. 3

Block diagram for the IR transmission model for cirrus cloud developed in the present study.

Fig. 4
Fig. 4

Scattering phase functions for randomly oriented hexagonal ice crystals at the wavelengths of 3.7 and 10 μm. The ice crystal size distribution used in the calculations corresponds to a temperature of −40°C.

Fig. 5
Fig. 5

Background, path, and direct radiances as functions of the nadir angle θ at the cirrus cloud top for a model midlatitude winter atmosphere. The upper scale is the path length defined as s = Δz/cosθ, where Δz is the cloud thickness.

Fig. 6
Fig. 6

Ratios of scattered radiances to the direct radiance, I(1)/Id and I(2)/Id as functions of the nadir angle or path length.

Fig. 7
Fig. 7

Multiple scattering adjustment factor k defined in Eq. (46) as a function of the nadir angle or path length.

Fig. 8
Fig. 8

Contrast as a function of the nadir angle or path length for 3.7- and 10-μm wavelengths. The parameters used in the calculations are as follows: target equivalent radius rt = 1 m, target equivalent temperature Tt = 873.2 K, half beamwidth of the detector ψ = 1°, cloud base height zb = 8 km, and cloud thickness Δz = 0.5 km.

Fig. 9
Fig. 9

Sensitivity of the contrast at λ = 3.7 μm to (a) the cloud base height (7, 8, and 9 km), (b) the cloud thickness (0.25, 0.5, and 0.75 km), (c) the target equivalent temperature (1073.2, 873.2, and 673.2 K), and (d) the equivalent radius (2, 1, and 0.5 m). See the text for the parameters used in each case.

Tables (2)

Tables Icon

Table I Multiple Scattering Adjustment Factor k

Tables Icon

Table II Single-Scattering Properties of Cirrus Clouds Corresponding to the Results Presented In Fig. 9(a).

Equations (54)

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

n ( D ) = { A 1 × D B 1 × IWC for D D 0 , A 2 × D B 2 × IWC for D > D 0 ,
D 0 = ( A 2 A 1 ) 1 / ( B 1 - B 2 ) .
C e = 3 2 ( w / 2 ) 2 ( 3 + 4 D / w ) ,
ω ˜ = C s C e = 1 - C a C e .
z = k i ( w / 2 ) 3 3 ( D / w ) 3 + 4 ( D / w ) .
ω ˜ = 1 - n = 1 4 f n z n             for             z < 0.4 ,
ω ˜ = 1 - 0.47 [ 1 - exp ( a z b ) ] ,             z 0.4 ,
C ^ e = 1 N 0 C e ( D ) n ( D ) d D ,
N = 0 n ( D ) d D .
C ^ s ( λ ) = 1 N 0 ω ˜ ( D , λ ) C e ( D ) n ( D ) d D .
β e ( λ ) = N C ^ e ( λ ) β s ( λ ) = N C ^ s ( λ ) β a ( λ ) = β e ( λ ) - β s ( λ ) } .
- d I ( s , Ω ) β e d s = I ( s , Ω ) - J ( s , Ω ) ,
J ( s , Ω ) = ω ˜ 4 π 4 π I ( s , Ω ) P ( Ω , Ω ) d Ω + ( 1 - ω ˜ ) B ( T ) .
I ( 0 , Ω ) = I ( s , Ω ) exp ( - β e s ) + 0 s J ( s , Ω ) exp ( - β e s ) β e d s .
Δ Ω t = π r t 2 / s 2 ,
Δ Ω = π ψ 2 ,
I d ( 0 , Ω ) = ( r t s ψ ) 2 B ( T t ) exp ( - β e s ) .
I ( n ) ( 0 , Ω ) = 0 s J ( n ) ( s , Ω ) exp ( - β e s ) β e d s ,             n = 1 , 2 ,
J ( n ) ( s , Ω ) = ω ˜ 4 π Δ Ω I ( n - 1 ) ( s , Ω ) P ( Ω , Ω ) d Ω .
I ( 0 ) ( s , Ω ) = ( r t s ψ ) 2 B ( T t ) exp [ - β e ( s - s ) ] ,
J ( 1 ) ( s , Ω ) = ω ˜ 4 π I ( 0 ) ( s , Ω ) Δ Ω ( 1 ) P ( Ω , Ω ) d Ω .
Δ Ω ( 1 ) = 2 π ψ .
ψ = ψ + tan - 1 [ s tan ψ / ( s - s ) ] .
I ( 1 ) ( 0 , Ω ) = 0 s J ( 1 ) ( s , Ω ) exp ( - β e s ) β e d s .
I ( 0 ) ( s ) = ( r t s ψ ) 2 B ( T t ) exp ( - β e s 1 ) ,
s 1 = ( s - s ) / cos X .
tan X = - ( s - s ) + [ ( s - s ) + 4 ( s - s ) ( s - s ) tan 2 Θ ] 1 / 2 2 ( s - s ) tan Θ .
J ( 1 ) ( s , Ω ) = ω ˜ 4 π I ( 0 ) ( s ) Δ Ω ( 1 ) ( 2 ) P ( Ω , Ω ) d Ω ,
Δ Ω ( 1 ) ( 2 ) = 2 π ( ψ 2 - ψ 1 ) ,
ψ 1 = 0 , ψ 2 = min ( ξ 1 , ξ 2 ) for s > s ,
ψ 1 = max ( ξ 1 , ξ 2 ) , ψ 2 = π for s < s ,
ξ 1 = π - θ + tan - 1 [ ( s - s ) / ( s - s ) cot θ ] ,
ξ 2 = π - tan - 1 [ ( s - s ) / s cot θ ] + tan - 1 [ ( s - s ) / s cot θ ] ,
θ = cos - 1 μ .
I ( 1 ) ( s , Ω ) = 0 s J ( 1 ) ( s , Ω ) exp ( - β e s 2 ) β e d s .
s 2 = ( s - s ) / cos Θ 1 ,
Θ 1 = Θ - X ,
J ( 2 ) ( s , Ω ) = ω ˜ 4 π Δ Ω ( 2 ) I ( 1 ) ( s , Ω ) P ( Ω , Ω ) d Ω .
Δ Ω ( 2 ) = 2 π [ ( Θ 1 + ψ ) - ( Θ 1 - ψ ) ] ,
I ( 2 ) ( 0 , Ω ) = 0 s J ( 2 ) ( s , Ω ) exp ( - β e s ) β e d s .
J ( n ) ( s , Ω ) = ω ˜ 4 π Δ Ω ( n ) I ( n - 1 ) ( s , Ω ) P ( Ω , Ω ) d Ω ,
I ( n ) ( 0 , Ω ) = 0 s J ( n ) ( s , Ω ) exp ( - β e s ) β e d s , n 3 ,
I t ( 0 , Ω ) = I d ( 0 , Ω ) + n = 1 N I ( n ) ( 0 , Ω ) ,
I t ( 0 , Ω ) ( r t s ψ ) 2 B ( T t ) exp ( - β e * s ) .
I t ( 0 , Ω ) I d ( 0 , Ω ) = exp [ - β e s ( k - 1 ) ] ,
k = β e * / β e 1.
I p ( 0 , Ω ) = 0 s J ( s , Ω ) exp ( - β e s ) β e d s .
I 0 = [ 1 - ( r t / s ψ ) 2 ] I b + ( r t / s ψ ) 2 I p + I t ,
C = ( I 0 - I b ) / I b .
RH = e e i ( e i e s ) = ( 1 + S i ) exp [ 1 R v ( 1 T o - 1 T ) ( L s - L ) ] ,
RH c 0.9 exp [ c ( T - 273 ) ] .
β ¯ e = 1 ( z t - z b ) z b z t β e [ λ , T ( z ) ] d z ,
k ( λ , ψ ) 1 - ω ˜ ( λ ) 2 0 ψ ¯ P ( Θ ) sin Θ d Θ ,
ψ ¯ = { 1.621 ψ + 0.558 for λ = 3.7 μ m 2.089 ψ + 0.895 for λ = 10 μ m .

Metrics