Abstract

A backward Monte Carlo computation procedure has been used to simulate the intensity and degree of polarization of the twilight sky during 1977. It was found that the single scattering approximation is applicable for detection of stratospheric aerosols by twilight measurement during background periods. Based on the simulation, a scheme is proposed for retrieving the stratospheric aerosol scattering coefficient utilizing the measured degree of polarization at the 0.7-μm wavelength in the zenith direction of the twilight sky. Compared with the in situ measurement, both the retrieved total optical depth and the retrieved profile of the aerosol scattering coefficient below 30 km agree reasonably well with measurements.

© 1988 Optical Society of America

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References

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  1. K. Labitzke, B. Naujokat, “On the Effect of the Volcanic Eruptions of Mount Agung and El Chichon on the Temperature of the Stratosphere,” Geofiz. Int. 23-2, 223 (1984).
  2. D. G. Collins, W. G. Blattner, M. B. Wells, H. G. Horak, “Backward Monte Carlo Calculations of the Polarization Characteristics of the Radiation Emerging from Spherical-Shell Atmospheres,” Appl. Opt. 11, 2684 (1972).
    [CrossRef] [PubMed]
  3. B. Wu, D. Lu, “Simulating the Characteristics of the Twilight Sky After a Volcanic Eruption by Monte-Carlo Method,” submitted to Atmos. Sci. (in Chinese).
  4. R. C. Whitten, Ed., The Stratospheric Aerosol Layer, Topics in Current Physics, Vol. 28 (Springer-Verlag, New York, 1982), p. 33.
    [CrossRef]
  5. K. L. Coulson, “Characteristics of Skylight at the Zenith During Twilight as Indicators of Atmospheric Turbidity. 1: Degree of Polarization,” Appl. Opt. 19, 3469 (1980).
    [CrossRef] [PubMed]
  6. K. L. Coulson, “Characteristics of Skylight at the Zenith During Twilight as Indicators of Atmospheric Turbidity. 2: Intensity and Color Ratio,” Appl. Opt. 20, 1516 (1981).
    [CrossRef] [PubMed]
  7. U.S. Standard Atmosphere, National Oceanic and Atmospheric Administration, National Aeronautic and Space Administration, U.S. Air Force (1976).
  8. L. Elterman, “UV, Visible and IR Attenuation for Altitude to 50 km,” AFCRL-68-0153 (1968).
  9. D. Deirmendjian, Electromagnetic Scattering on Spherical Polydispersions (Elsevier, New York, 1969), p. 78.
  10. Handbook of Geophysics and Space Environments (1965), AFCRL.
  11. E. K. Bigg, “Size Distributions of Stratospheric Aerosols and Their Variations with Altitude and Time,” J. Atmos. Sci. 33, 1080 (1976).
    [CrossRef]
  12. T. J. Swissler, P. Hamill, M. Osborn, “A Comparison of Lidar and Balloon-Borne Particle Counter Measurements of the Stratospheric Aerosol 1974–1980,” J. Atmos. Sci. 39, 909 (1982).
    [CrossRef]
  13. D. J. Hofmann, J. M. Rosen, “On the Background Stratospheric Aerosol Layer,” J. Atmos. Sci. 38, 168 (1981).
    [CrossRef]
  14. R. W. Fegley, H. T. Ellis, J. L. Heffter, “Volcanic Contributions to the Stratospheric Sulfate Layer,” J. Appl. Meteorol. 19, 683 (1980).
    [CrossRef]
  15. G. Steinhorst, “Stratospheric Aerosol Concentration Determined by an Iterative Method from Twilight Polarization Measurements,” Contrib. Atmos. Phys. 50, 508 (1977).
  16. G. Dietze, “On the Aerosol Factor in the Twilight Method,” Pure Appl. Geophys. 77, 159 (1969).
    [CrossRef]

1984 (1)

K. Labitzke, B. Naujokat, “On the Effect of the Volcanic Eruptions of Mount Agung and El Chichon on the Temperature of the Stratosphere,” Geofiz. Int. 23-2, 223 (1984).

1982 (1)

T. J. Swissler, P. Hamill, M. Osborn, “A Comparison of Lidar and Balloon-Borne Particle Counter Measurements of the Stratospheric Aerosol 1974–1980,” J. Atmos. Sci. 39, 909 (1982).
[CrossRef]

1981 (2)

1980 (2)

R. W. Fegley, H. T. Ellis, J. L. Heffter, “Volcanic Contributions to the Stratospheric Sulfate Layer,” J. Appl. Meteorol. 19, 683 (1980).
[CrossRef]

K. L. Coulson, “Characteristics of Skylight at the Zenith During Twilight as Indicators of Atmospheric Turbidity. 1: Degree of Polarization,” Appl. Opt. 19, 3469 (1980).
[CrossRef] [PubMed]

1977 (1)

G. Steinhorst, “Stratospheric Aerosol Concentration Determined by an Iterative Method from Twilight Polarization Measurements,” Contrib. Atmos. Phys. 50, 508 (1977).

1976 (1)

E. K. Bigg, “Size Distributions of Stratospheric Aerosols and Their Variations with Altitude and Time,” J. Atmos. Sci. 33, 1080 (1976).
[CrossRef]

1972 (1)

1969 (1)

G. Dietze, “On the Aerosol Factor in the Twilight Method,” Pure Appl. Geophys. 77, 159 (1969).
[CrossRef]

1968 (1)

L. Elterman, “UV, Visible and IR Attenuation for Altitude to 50 km,” AFCRL-68-0153 (1968).

Bigg, E. K.

E. K. Bigg, “Size Distributions of Stratospheric Aerosols and Their Variations with Altitude and Time,” J. Atmos. Sci. 33, 1080 (1976).
[CrossRef]

Blattner, W. G.

Collins, D. G.

Coulson, K. L.

Deirmendjian, D.

D. Deirmendjian, Electromagnetic Scattering on Spherical Polydispersions (Elsevier, New York, 1969), p. 78.

Dietze, G.

G. Dietze, “On the Aerosol Factor in the Twilight Method,” Pure Appl. Geophys. 77, 159 (1969).
[CrossRef]

Ellis, H. T.

R. W. Fegley, H. T. Ellis, J. L. Heffter, “Volcanic Contributions to the Stratospheric Sulfate Layer,” J. Appl. Meteorol. 19, 683 (1980).
[CrossRef]

Elterman, L.

L. Elterman, “UV, Visible and IR Attenuation for Altitude to 50 km,” AFCRL-68-0153 (1968).

Fegley, R. W.

R. W. Fegley, H. T. Ellis, J. L. Heffter, “Volcanic Contributions to the Stratospheric Sulfate Layer,” J. Appl. Meteorol. 19, 683 (1980).
[CrossRef]

Hamill, P.

T. J. Swissler, P. Hamill, M. Osborn, “A Comparison of Lidar and Balloon-Borne Particle Counter Measurements of the Stratospheric Aerosol 1974–1980,” J. Atmos. Sci. 39, 909 (1982).
[CrossRef]

Heffter, J. L.

R. W. Fegley, H. T. Ellis, J. L. Heffter, “Volcanic Contributions to the Stratospheric Sulfate Layer,” J. Appl. Meteorol. 19, 683 (1980).
[CrossRef]

Hofmann, D. J.

D. J. Hofmann, J. M. Rosen, “On the Background Stratospheric Aerosol Layer,” J. Atmos. Sci. 38, 168 (1981).
[CrossRef]

Horak, H. G.

Labitzke, K.

K. Labitzke, B. Naujokat, “On the Effect of the Volcanic Eruptions of Mount Agung and El Chichon on the Temperature of the Stratosphere,” Geofiz. Int. 23-2, 223 (1984).

Lu, D.

B. Wu, D. Lu, “Simulating the Characteristics of the Twilight Sky After a Volcanic Eruption by Monte-Carlo Method,” submitted to Atmos. Sci. (in Chinese).

Naujokat, B.

K. Labitzke, B. Naujokat, “On the Effect of the Volcanic Eruptions of Mount Agung and El Chichon on the Temperature of the Stratosphere,” Geofiz. Int. 23-2, 223 (1984).

Osborn, M.

T. J. Swissler, P. Hamill, M. Osborn, “A Comparison of Lidar and Balloon-Borne Particle Counter Measurements of the Stratospheric Aerosol 1974–1980,” J. Atmos. Sci. 39, 909 (1982).
[CrossRef]

Rosen, J. M.

D. J. Hofmann, J. M. Rosen, “On the Background Stratospheric Aerosol Layer,” J. Atmos. Sci. 38, 168 (1981).
[CrossRef]

Steinhorst, G.

G. Steinhorst, “Stratospheric Aerosol Concentration Determined by an Iterative Method from Twilight Polarization Measurements,” Contrib. Atmos. Phys. 50, 508 (1977).

Swissler, T. J.

T. J. Swissler, P. Hamill, M. Osborn, “A Comparison of Lidar and Balloon-Borne Particle Counter Measurements of the Stratospheric Aerosol 1974–1980,” J. Atmos. Sci. 39, 909 (1982).
[CrossRef]

Wells, M. B.

Wu, B.

B. Wu, D. Lu, “Simulating the Characteristics of the Twilight Sky After a Volcanic Eruption by Monte-Carlo Method,” submitted to Atmos. Sci. (in Chinese).

AFCRL-68-0153 (1)

L. Elterman, “UV, Visible and IR Attenuation for Altitude to 50 km,” AFCRL-68-0153 (1968).

Appl. Opt. (3)

Contrib. Atmos. Phys. (1)

G. Steinhorst, “Stratospheric Aerosol Concentration Determined by an Iterative Method from Twilight Polarization Measurements,” Contrib. Atmos. Phys. 50, 508 (1977).

Geofiz. Int. (1)

K. Labitzke, B. Naujokat, “On the Effect of the Volcanic Eruptions of Mount Agung and El Chichon on the Temperature of the Stratosphere,” Geofiz. Int. 23-2, 223 (1984).

J. Appl. Meteorol. (1)

R. W. Fegley, H. T. Ellis, J. L. Heffter, “Volcanic Contributions to the Stratospheric Sulfate Layer,” J. Appl. Meteorol. 19, 683 (1980).
[CrossRef]

J. Atmos. Sci. (3)

E. K. Bigg, “Size Distributions of Stratospheric Aerosols and Their Variations with Altitude and Time,” J. Atmos. Sci. 33, 1080 (1976).
[CrossRef]

T. J. Swissler, P. Hamill, M. Osborn, “A Comparison of Lidar and Balloon-Borne Particle Counter Measurements of the Stratospheric Aerosol 1974–1980,” J. Atmos. Sci. 39, 909 (1982).
[CrossRef]

D. J. Hofmann, J. M. Rosen, “On the Background Stratospheric Aerosol Layer,” J. Atmos. Sci. 38, 168 (1981).
[CrossRef]

Pure Appl. Geophys. (1)

G. Dietze, “On the Aerosol Factor in the Twilight Method,” Pure Appl. Geophys. 77, 159 (1969).
[CrossRef]

Other (5)

D. Deirmendjian, Electromagnetic Scattering on Spherical Polydispersions (Elsevier, New York, 1969), p. 78.

Handbook of Geophysics and Space Environments (1965), AFCRL.

U.S. Standard Atmosphere, National Oceanic and Atmospheric Administration, National Aeronautic and Space Administration, U.S. Air Force (1976).

B. Wu, D. Lu, “Simulating the Characteristics of the Twilight Sky After a Volcanic Eruption by Monte-Carlo Method,” submitted to Atmos. Sci. (in Chinese).

R. C. Whitten, Ed., The Stratospheric Aerosol Layer, Topics in Current Physics, Vol. 28 (Springer-Verlag, New York, 1982), p. 33.
[CrossRef]

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Figures (9)

Fig. 1
Fig. 1

Zenith polarization. Solid line, observation; ○, simulation for profile A; ×, for profile B.

Fig. 2
Fig. 2

Zenith intensity; see Fig. 1 caption.

Fig. 3
Fig. 3

Integrands ΔI of Eq. (1) corresponding to a set of solar zenith angles.

Fig. 4
Fig. 4

Profiles of the aerosol scattering coefficient. Curve 0 is the first guess; curves 1 and 2 are the tenth and sixtieth iterated results with the Haze H phase function, respectively.

Fig. 5
Fig. 5

Profiles of the aerosol scattering coefficient derived from aerosol measurements. Curve 1, measurements by Junge et al. in 1959–1960; curves 2 and 3, minimal and maximal values in measurements by Hofmann and Rosen in 1978–1979, respectively.

Fig. 6
Fig. 6

Degree of polarization for Haze H. Curves 0, 1, and 2 correspond to the profiles shown in Fig. 4, respectively; curve 3 is the measurement.

Fig. 7
Fig. 7

Aerosol scattering phase functions corresponding to two different size distributions.

Fig. 8
Fig. 8

Aerosol scattering coefficient profile used in the test of effects of the phase function on the calculated degree of polarization.

Fig. 9
Fig. 9

Degree of polarization calculated by the single scattering model using the aerosol scattering coefficient profile shown in Fig. 8. Curves 0 and 1 correspond to Haze H and Haze M phase functions, respectively; curve 2 is the measurement.

Tables (7)

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Table I Ratio of the Scattered Intensities of Various Orders to First-Order Scattering for Profile A

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Table II Ratio of the Scattered Intensities of Various Orders to First-Order Scattering for Profile Ba

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Table III Comparison of Calculated Intensity I and Polarization δ for Single Scattering Model with those for Monte Carlo Simulation Using the Iterated Aerosol Profile; Optical Depth τ′ = 0.0513

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Table IV Relationship of Solar Zenith Angle with Height of the Contributing Region for the Degree of Polarization

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Table V Iterated Results and Errors

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Table VI Results by Using Single Scattering Model

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Table VII Effect of Upper and Lower Atmosphere on Intensity I and Polarization δ; Subscript a refers to Case (a) etc.

Equations (9)

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I 1 , 2 ( θ ) = h 1 h 2 [ k m ( h ) P m 1 , m 2 ( θ , h ) + k a ( h ) P a 1 , a 2 ( θ , h ) ] × exp { - 0 h [ k m ( h ) + k a ( h ) + k o z ( h ) ] d h } × exp { - r ( h ) r b [ k m ( r ) + k a ( r ) + k o z ( r ) ] d r } I o d h ,
δ = ( I 2 - I 1 ) / ( I 1 + I 2 ) .
δ ( θ ) = h 1 h 2 { k m ( h ) [ P m 2 ( θ , h ) - P m 1 ( θ , h ) ] + k a ( h ) [ P a 2 ( θ , h ) - P a 1 ( θ , h ) ] } E o z E m E a d h h 1 h 2 { k m ( h ) [ P m 2 ( θ , h ) + P m 1 ( θ , h ) ] + k a ( h ) [ P a 2 ( θ , h ) + P a 1 ( θ , h ) ] } E o z E m E a d h ,
E = exp ( - 0 h k d h ) exp ( - r ( h ) r b k d r ) ,
k m [ P m 2 ( θ ) - P m 1 ( θ ) ] ,
δ ( θ ) ~ 1 / [ 1 + k a ( h * ) / k m ( h * ) ] ~ k m ( h * ) / k a ( h * ) ,
k m ( h * ) = h 1 h 2 k m ( h ) [ P m 2 ( θ , h ) + P m 1 ( θ , h ) ] E o z E m E a d h ,
k a ( h * ) = h 1 h 2 k a ( h ) [ P a 2 ( θ , h ) + P a 1 ( θ , h ) ] E o z E m E a d h ,
δ ( r ) ( θ ) / δ 0 ( θ ) = k a ( r + 1 ) ( h * ) / k a ( r ) ( h * )

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