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Retrieval of aerosol scattering phase function and single scattering albedo according to data of radiation measurements in solar almucantar: Numerical simulation


The paper considers two iteration methods for retrieving the aerosol scattering phase function and single scattering albedo, referenced to the total atmospheric column, from clear-sky radiance measurements in the solar almucantar. Numerical simulation (visible spectral range) is used to study the convergence of the methods and the sensitivity of the retrieved parameters to the aerosol optical depth and surface albedo and to the accuracy of their specification, as well as to errors of measurements of scattered solar radiation. It is shown that the optical situations with high to moderate atmospheric transparency are most favorable for solution of the inverse problem.

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  1. 1.

    K. Ya. Kondrat’ev, “Aerosol as a Climate-Forming Component of the Atmosphere. 2. Direct and Indirect Impact on Climate,” Opt. Atmos. Okeana 15, 301–320 (2002).

    Google Scholar 

  2. 2.

    K. Ya. Kondrat’ev, “Aerosol and Climate: Current State and Prospects for Developments. 3. Aerosol Radiation Perturbing Action”, Opt. Atmos. Okeana 19, 565–575 (2006).

    Google Scholar 

  3. 3.

    S. Solomon, D. Qin, M. Manning, Z. Chen, M. Marquis, K. B. Averyt, M. Tignor, and H. L. Miller, Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change (Cambridge Univ., Cambridge, 2007), Ch. 2.

    Google Scholar 

  4. 4.

    H. Yu, Y. Kaufman, M. Chin, G. Feingold, L. Remer, T. Anderson, Y. Balkanski, N. Bellouin, O. Boucher, S. Christopher, P. DeCola, R. Kahn, D. Koch, N. Loeb, M. Reddy, M. Schulz, T. Takemura, and M. Zhou, “A Review of Measurement-Based Assessments of the Aerosol Direct Radiative Effect and Forcing,” Atmos. Chem. Phys. 6, 613–666 (2006).

    ADS  Article  Google Scholar 

  5. 5.

    M. Zhou, H. Yu, R. Dickinson, O. Dubovik, and B. Holben, “A Normalized Description of the Direct Effect of Key Aerosol Types on Solar Radiation as Estimated from AERONET Aerosols and MODIS Albedo,” J. Geophys. Res. 110, D19202 (2005), doi: 10.1029/2005JD005909.

    ADS  Article  Google Scholar 

  6. 6.

    V. S. Antyufeev, A. I. Ivanov, G. Sh. Livshits, and G. A. Mikhailov, “Determination of Aerosol Indicatrix of Scattering of Cloudless Atmosphere in 0.55–2.4 μm Spectral Region,” Izv. AN SSSR, Fiz. Atmos. Okeana 16, 146–155 (1980).

    Google Scholar 

  7. 7.

    V. S. Antyufeev and M. A. Nazaraliev, Inverse Problems in Atmospheric Optis (VTs AN SSSR, Novosibirsk, 1988) [in Russian].

    Google Scholar 

  8. 8.

    M. Wang and H. Gordon, “Retrieval of the Columnar Aerosol Phase Function and Single-Scattering Albedo from Sky Radiance over the Ocean: Simulation,” Appl. Opt. 32, 4598–4609 (1993).

    ADS  Article  Google Scholar 

  9. 9.

    H. Yang and H. R. Gordon, “Retrieval of the Columnar Aerosol Phase Function and Single-Scattering Albedo from Sky Radiance over Land: Simulations,” Appl. Opt. 37, 978–997 (1998).

    ADS  Article  Google Scholar 

  10. 10.

    C. Devaux, A. Vermeulen, J. L. Deuze, P. Dubuisson, M. Herman, and R. Senter, “Retrieval of Aerosol Single-Scattering Albedo from Ground-Based Measurements: Application to Observational Data,” J. Gephys. Res. D 103, 8753–8761 (1998).

    ADS  Article  Google Scholar 

  11. 11.

    H. R. Gordon and T. Zhang, “Columnar Aerosol Properties over Oceans by Combining Surface and Aircraft Measurements: Simulations,” Appl. Opt. 34, 5552–5555 (1995).

    ADS  Article  Google Scholar 

  12. 12.

    T. Zhang and H. R. Gordon, “Columnar Aerosol Properties over Oceans by Combining Surface and Aircraft Measurements: Sensitivity Analysis,” Appl. Opt. 36, 2650–2662 (1997).

    ADS  Article  Google Scholar 

  13. 13.

    M. Sviridenkov, “Simplified Techniques for Retrieving Aerosol Characteristics from Extinction and Sky Radiance Measurements,” in Proceedings of the Conference on Visibility, Aerosols, and Atmospheric Optics, Vienna, Sept. 2006, pp. 85–86.

  14. 14.

    G. A. Mikhailov, S. A. Ukhinov, and A. S. Chimaeva, “Monte Carlo Algorithms for Reconstructing the Scattering Phase Function with Allowance for Polarization,” Dokl. Akad. Nauk 423, 161–164 (2008) [Dokl. Math. 78, 839 (2008)].

    MathSciNet  Google Scholar 

  15. 15.

    O. Dubovik and M. King, “A Flexible Inversion Algorithm for Retrieval Aerosol Optical Properties from Sun and Sky Radiance Measurements,” J. Gephys. Res. D 105, 20673–20696 (2000).

    ADS  Article  Google Scholar 

  16. 16.

    S. M. Sakerin, S. A. Beresnev, S. Yu. Gorda, D. M. Kabanov, G. I. Kornienko, Yu. I. Markelov, A. V. Mikhalev, S. V. Nikolashkin, M. V. Panchenko, V. A. Poddubny, V. V. Pol’kin, A. Smirnov, M. A. Tashchilin, S. A. Turchinovich, Yu. S. Turchinovich, B. Kholben, and T. A. Eremina, “Characteristics of Year Trend of Spectral Aerosol Optic Thickness of Atmosphere in Siberia Conditions,” Opt. Atmos. Okeana 22, 566–574 (2009).

    Google Scholar 

  17. 17.

    Monte-Carlo Method in Atmospheric Optics, Ed. by G. I. Marchuk (Nauka, Novosibirsk, 1976) [in Russian].

    Google Scholar 

  18. 18.

    G. I. Marchuk, Methods of Numerical Mathematics, 2nd ed. (Springer, New York, 1982; Nauka, Moscow, 1989).

    MATH  Google Scholar 

  19. 19.

    V. A. Smerkalov, “Mean-Weighted Indicatrix of Aerosol Light Scattering,” Opt. Atmos. Okeana 13, 323–328 (2000).

    Google Scholar 

  20. 20.

    O. Dubovik, B. N. Holben, Y. J. Kaufman, M. Yamasoe, A. Smirnov, D. Tanre, and I. Slutsker, “Single-Scattering Albedo of Smoke Retrieved from the Sky Radiance and Solar Transmittance Measured from Ground,” J. Gephys. Res. D 103, 31903–31923 (1998).

    ADS  Article  Google Scholar 

  21. 21.

    M. A. Nazaraliev, Statistical Simulation of Radiation Processes in Atmosphere (Nauka, Novosibirsk, 1990) [in Russian].

    Google Scholar 

  22. 22.

    G. Sh. Livshits, Scattering of Light in Atmosphere (Nauka, Alma-Ata, 1965) [in Russian].

    Google Scholar 

  23. 23.

    M. Hess, P. Koepke, and I. Schult, “Optical Properties of Aerosols and Clouds: the Software Package OPAC,” Bull. Amer. Meteorol. Soc. 79, 831–844 (1998).

    ADS  Article  Google Scholar 

  24. 24.

    S. M. Sakerin and D. M. Kabanov, “Spectral Dependences of the Atmospheric Aerosol Optical Depth in Spectral Region 0.34–4 μm,” Opt. Atmos. Okeana 20, 156–164 (2007).

    Google Scholar 

  25. 25.

    V. A. Smerkalov, Applied Optics of Atmosphere (Gidrometeoizdat, St.-Petersburg, 1997) [in Russian].

    Google Scholar 

  26. 26.

    D. Deirmendjian, Electromagnetic Scattering on Spherical Polydispersions (Amer. Elsevier, New York, 1969; Mir, Moscow, 1971).

    Google Scholar 

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Correspondence to T. V. Bedareva.

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Original Russian Text © T.V. Bedareva, T.B. Zhuravleva, 2011, published in Optica Atmosfery i Okeana.

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Bedareva, T.V., Zhuravleva, T.B. Retrieval of aerosol scattering phase function and single scattering albedo according to data of radiation measurements in solar almucantar: Numerical simulation. Atmos Ocean Opt 24, 373 (2011).

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  • Aerosol Particle
  • Phase Function
  • Aerosol Optical Depth
  • Surface Albedo
  • Single Scattering Albedo