Abstract

A single-parameter statistical model of directed light-scattering coefficients of coastal haze is suggested. The scattering coefficient for λ = 0.55 μm is the input parameter of the model. The accuracy of restoration of directed light-scattering coefficients for the scattering angles of 15–160° has been determined to be no worse than 20–25%. The increase in values of the restoration errors for the scattering angles for the near-forward and -backward directions is mentioned. The physical reasons for the observed statistical relationships are briefly discussed.

© 1985 Optical Society of America

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References

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  1. V. E. Zuev, Propagation of Visible and Infrared Radiation in the Atmosphere (Sov. Radio, Moscow, 1970).
  2. Yu. S. Georgievskii, G. V. Rozenberg, “Humidity as a factor of aerosol variability,” Izv. Akad. Nauk SSSR Ser. Fiz. Atm. Okeana 9, 126–138 (1973).
  3. Yu. S. Georgievskii, G. V. Rozenberg, X. X. Lyubovtseva, G. I. Gorchakov, “The model of optical and microphysical characteristics of haze,” in Physics of Atmosphere and Problems of Climate (Nauka, Moscow, 1980), pp. 216–257.
  4. C. Butcher, Introduction to Chemistry of the Atmosphere (Mir, Moscow, 1977).
  5. G. I. Gorchakov, “Scattering matrices and the types of optical weather,” Izv. Akad. Nauk SSSR, Ser. Fiz. Atm. Okeana 9, 204–209 (1973).
  6. A. M. Obukhov, “On orthogonal disintegrations of empirical functions,” Izv. Akad. Nauk SSSR Ser. Geofiz. No. 3, 432–439 (1960).
  7. G. I. Gorchakov, G. V. Rozenberg, “Correlation couplings between optical characteristics of finely divided hazes,” Izv. Akad. Nauk SSSR Ser. Fiz. Atm. Okeana 3, 611–620 (1967).
  8. G. I. Gorchakov, N. A. Sviridenkov, “Statistical model of optical characteristics of atmospheric haze,” Izv. Akad. Nauk SSSR Ser. Fiz. Atm. Okeana 15, 53–60 (1979).
  9. A. L. Irisov, M. V. Panchenko, V. G. Oshlakov, A. G. Tumakov, V. Ya. Fadeev, “Equipment and methods of studying angular characteristics of atmospheric air,” in Scattering and Refraction of Optical Radiation in the Atmosphere, M. V. Kabanov, ed. (Izdat. Institute of Atmospheric Optics SB, USSR Academy of Science, Tomsk, 1976), pp. 129–141.
  10. A. K. Mitropol’skii, Procedure of Statistical Calculations (Nauka, Moscow, 1971).
  11. D. Deirmendjian, Electromagnetic Scattering on Spherical Polydispersions (American Elsevier, New York, 1969).

1979

G. I. Gorchakov, N. A. Sviridenkov, “Statistical model of optical characteristics of atmospheric haze,” Izv. Akad. Nauk SSSR Ser. Fiz. Atm. Okeana 15, 53–60 (1979).

1973

Yu. S. Georgievskii, G. V. Rozenberg, “Humidity as a factor of aerosol variability,” Izv. Akad. Nauk SSSR Ser. Fiz. Atm. Okeana 9, 126–138 (1973).

G. I. Gorchakov, “Scattering matrices and the types of optical weather,” Izv. Akad. Nauk SSSR, Ser. Fiz. Atm. Okeana 9, 204–209 (1973).

1967

G. I. Gorchakov, G. V. Rozenberg, “Correlation couplings between optical characteristics of finely divided hazes,” Izv. Akad. Nauk SSSR Ser. Fiz. Atm. Okeana 3, 611–620 (1967).

1960

A. M. Obukhov, “On orthogonal disintegrations of empirical functions,” Izv. Akad. Nauk SSSR Ser. Geofiz. No. 3, 432–439 (1960).

Butcher, C.

C. Butcher, Introduction to Chemistry of the Atmosphere (Mir, Moscow, 1977).

Deirmendjian, D.

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

Fadeev, V. Ya.

A. L. Irisov, M. V. Panchenko, V. G. Oshlakov, A. G. Tumakov, V. Ya. Fadeev, “Equipment and methods of studying angular characteristics of atmospheric air,” in Scattering and Refraction of Optical Radiation in the Atmosphere, M. V. Kabanov, ed. (Izdat. Institute of Atmospheric Optics SB, USSR Academy of Science, Tomsk, 1976), pp. 129–141.

Georgievskii, Yu. S.

Yu. S. Georgievskii, G. V. Rozenberg, “Humidity as a factor of aerosol variability,” Izv. Akad. Nauk SSSR Ser. Fiz. Atm. Okeana 9, 126–138 (1973).

Yu. S. Georgievskii, G. V. Rozenberg, X. X. Lyubovtseva, G. I. Gorchakov, “The model of optical and microphysical characteristics of haze,” in Physics of Atmosphere and Problems of Climate (Nauka, Moscow, 1980), pp. 216–257.

Gorchakov, G. I.

G. I. Gorchakov, N. A. Sviridenkov, “Statistical model of optical characteristics of atmospheric haze,” Izv. Akad. Nauk SSSR Ser. Fiz. Atm. Okeana 15, 53–60 (1979).

G. I. Gorchakov, “Scattering matrices and the types of optical weather,” Izv. Akad. Nauk SSSR, Ser. Fiz. Atm. Okeana 9, 204–209 (1973).

G. I. Gorchakov, G. V. Rozenberg, “Correlation couplings between optical characteristics of finely divided hazes,” Izv. Akad. Nauk SSSR Ser. Fiz. Atm. Okeana 3, 611–620 (1967).

Yu. S. Georgievskii, G. V. Rozenberg, X. X. Lyubovtseva, G. I. Gorchakov, “The model of optical and microphysical characteristics of haze,” in Physics of Atmosphere and Problems of Climate (Nauka, Moscow, 1980), pp. 216–257.

Irisov, A. L.

A. L. Irisov, M. V. Panchenko, V. G. Oshlakov, A. G. Tumakov, V. Ya. Fadeev, “Equipment and methods of studying angular characteristics of atmospheric air,” in Scattering and Refraction of Optical Radiation in the Atmosphere, M. V. Kabanov, ed. (Izdat. Institute of Atmospheric Optics SB, USSR Academy of Science, Tomsk, 1976), pp. 129–141.

Lyubovtseva, X. X.

Yu. S. Georgievskii, G. V. Rozenberg, X. X. Lyubovtseva, G. I. Gorchakov, “The model of optical and microphysical characteristics of haze,” in Physics of Atmosphere and Problems of Climate (Nauka, Moscow, 1980), pp. 216–257.

Mitropol’skii, A. K.

A. K. Mitropol’skii, Procedure of Statistical Calculations (Nauka, Moscow, 1971).

Obukhov, A. M.

A. M. Obukhov, “On orthogonal disintegrations of empirical functions,” Izv. Akad. Nauk SSSR Ser. Geofiz. No. 3, 432–439 (1960).

Oshlakov, V. G.

A. L. Irisov, M. V. Panchenko, V. G. Oshlakov, A. G. Tumakov, V. Ya. Fadeev, “Equipment and methods of studying angular characteristics of atmospheric air,” in Scattering and Refraction of Optical Radiation in the Atmosphere, M. V. Kabanov, ed. (Izdat. Institute of Atmospheric Optics SB, USSR Academy of Science, Tomsk, 1976), pp. 129–141.

Panchenko, M. V.

A. L. Irisov, M. V. Panchenko, V. G. Oshlakov, A. G. Tumakov, V. Ya. Fadeev, “Equipment and methods of studying angular characteristics of atmospheric air,” in Scattering and Refraction of Optical Radiation in the Atmosphere, M. V. Kabanov, ed. (Izdat. Institute of Atmospheric Optics SB, USSR Academy of Science, Tomsk, 1976), pp. 129–141.

Rozenberg, G. V.

Yu. S. Georgievskii, G. V. Rozenberg, “Humidity as a factor of aerosol variability,” Izv. Akad. Nauk SSSR Ser. Fiz. Atm. Okeana 9, 126–138 (1973).

G. I. Gorchakov, G. V. Rozenberg, “Correlation couplings between optical characteristics of finely divided hazes,” Izv. Akad. Nauk SSSR Ser. Fiz. Atm. Okeana 3, 611–620 (1967).

Yu. S. Georgievskii, G. V. Rozenberg, X. X. Lyubovtseva, G. I. Gorchakov, “The model of optical and microphysical characteristics of haze,” in Physics of Atmosphere and Problems of Climate (Nauka, Moscow, 1980), pp. 216–257.

Sviridenkov, N. A.

G. I. Gorchakov, N. A. Sviridenkov, “Statistical model of optical characteristics of atmospheric haze,” Izv. Akad. Nauk SSSR Ser. Fiz. Atm. Okeana 15, 53–60 (1979).

Tumakov, A. G.

A. L. Irisov, M. V. Panchenko, V. G. Oshlakov, A. G. Tumakov, V. Ya. Fadeev, “Equipment and methods of studying angular characteristics of atmospheric air,” in Scattering and Refraction of Optical Radiation in the Atmosphere, M. V. Kabanov, ed. (Izdat. Institute of Atmospheric Optics SB, USSR Academy of Science, Tomsk, 1976), pp. 129–141.

Zuev, V. E.

V. E. Zuev, Propagation of Visible and Infrared Radiation in the Atmosphere (Sov. Radio, Moscow, 1970).

Izv. Akad. Nauk SSSR Ser. Fiz. Atm. Okeana

Yu. S. Georgievskii, G. V. Rozenberg, “Humidity as a factor of aerosol variability,” Izv. Akad. Nauk SSSR Ser. Fiz. Atm. Okeana 9, 126–138 (1973).

G. I. Gorchakov, G. V. Rozenberg, “Correlation couplings between optical characteristics of finely divided hazes,” Izv. Akad. Nauk SSSR Ser. Fiz. Atm. Okeana 3, 611–620 (1967).

G. I. Gorchakov, N. A. Sviridenkov, “Statistical model of optical characteristics of atmospheric haze,” Izv. Akad. Nauk SSSR Ser. Fiz. Atm. Okeana 15, 53–60 (1979).

Izv. Akad. Nauk SSSR Ser. Geofiz. No.

A. M. Obukhov, “On orthogonal disintegrations of empirical functions,” Izv. Akad. Nauk SSSR Ser. Geofiz. No. 3, 432–439 (1960).

Izv. Akad. Nauk SSSR, Ser. Fiz. Atm. Okeana

G. I. Gorchakov, “Scattering matrices and the types of optical weather,” Izv. Akad. Nauk SSSR, Ser. Fiz. Atm. Okeana 9, 204–209 (1973).

Other

V. E. Zuev, Propagation of Visible and Infrared Radiation in the Atmosphere (Sov. Radio, Moscow, 1970).

Yu. S. Georgievskii, G. V. Rozenberg, X. X. Lyubovtseva, G. I. Gorchakov, “The model of optical and microphysical characteristics of haze,” in Physics of Atmosphere and Problems of Climate (Nauka, Moscow, 1980), pp. 216–257.

C. Butcher, Introduction to Chemistry of the Atmosphere (Mir, Moscow, 1977).

A. L. Irisov, M. V. Panchenko, V. G. Oshlakov, A. G. Tumakov, V. Ya. Fadeev, “Equipment and methods of studying angular characteristics of atmospheric air,” in Scattering and Refraction of Optical Radiation in the Atmosphere, M. V. Kabanov, ed. (Izdat. Institute of Atmospheric Optics SB, USSR Academy of Science, Tomsk, 1976), pp. 129–141.

A. K. Mitropol’skii, Procedure of Statistical Calculations (Nauka, Moscow, 1971).

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

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Figures (2)

Fig. 1
Fig. 1

Angular dependence of the first eigenvector π1 of the autocorrelation matrix BL of directed light-scattering coefficients for the three seasonal ensembles (I, 1975; II, 1976; III, 1977).

Fig. 2
Fig. 2

Normalized aerosol-scattering phase functions restored within the framework of the single-parameter model for two values of meteorological visibility Sm = 50 km and Sm = 5 km.

Tables (2)

Tables Icon

Table 1 Correlation Coefficients C1i with log Ci and with ri

Tables Icon

Table 2 Empirical Coefficients for Single- Parameter Model

Equations (5)

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B L ( φ k , φ l ) = 1 N 1 i = 1 N Δ L i ( φ k ) Δ L i ( φ l ) ,
log μ i ( φ k ) = log μ φ k ) ¯ + j = 1 n C j i π j ( φ k ) ,
log μ i ( φ k ) = log μ ( φ k ) ¯ + C 1 i π 1 ( φ k ) .
log μ ( φ ) = K ( φ ) log σ + log C ( φ ) ,
f ( φ ) = C ( φ ) σ K ( φ ) 1 .

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