Inversion algorithm for non-spherical dust particle size distributions

  • Siyu Cai
  • Jiandong MaoEmail author
  • Hu Zhao
  • Chunyan Zhou
  • Xin Gong
  • Hongjiang Sheng
Regular Paper


Dust particles are the main aerosol component of the atmosphere, and can influence human, environmental, and ecological health. Particle size distribution is an important aerosol micro-physical parameter that denotes the concentration distribution of particles of different radii and can determine the extinction characteristics of these particles. In traditional inversion algorithms, the aerosol is generally assumed to be spherical according to Mie theory, and the relationship between aerosol optical thickness and particle size distribution is described by the Fredholm integral equation of the first kind. For non-spherical dust particles, this spherical assumption is obviously unreasonable and yields unreliable results. Therefore, we developed an algorithm assuming non-spherical particles for inversion of dust particle size distributions. In the case of non-spherical particles, the extinction efficiency factor kernel functions of the ellipsoid were calculated using the anomalous diffraction approximation method, and the kernel function of Mie scattering theory was substituted with these new kernel functions. Moreover, the Phillips–Twomey method was employed to solve the Fredholm integral equation of the first kind using aerosol optical thickness data from a CE-318 sun photometer. To verify the feasibility of the anomalous diffraction approximation method, experiments were carried out under sunny, dusty, windy and hazy weather conditions. These experiments showed that the extinction kernel function for non-spherical particles obtained using the anomalous diffraction approximation method is suitable for inversion of non-spherical dust particle size distributions under different weather conditions in the Yinchuan area.


Dust aerosol Non-spherical particle Anomalous diffraction approximation Particle size distribution 



This work was supported by the National Natural Science Foundation of China (No. 61765001 and 61565001), Leading Talents of Scientific and Technological Innovation of Ningxia, Plan for Leading Talents of the State Ethnic Affairs Commission of the People’s Republic of China, Scientific Research Project of North Minzu University (No. 2016GQR07) and the Innovation Team of Lidar Atmosphere Remote Sensing of Ningxia.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflicts of interest.


  1. 1.
    Toledo, F., Garrido, C., Díaz, M., Rondanelli, R., Jorquera, S., Valdivieso, P.: AOT retrieval procedure for distributed measurements with low-cost sun photometers. J. Geophys. Res. 123(2), 1113–1131 (2018)Google Scholar
  2. 2.
    Zhang, X., Mao, M.: Orientation-averaged optical properties of nonspherical dust aerosols. J. Light Scatt. 29(1), 16–20 (2017)MathSciNetGoogle Scholar
  3. 3.
    Shi, G.Y., Wang, H., Wang, B.: Sensitivity experiments on the effects of optical properties of dust aerosol on their radiative forcing under clear sky condition. J. Meteorol. Soc. Jpn 83, 333–346 (2005)CrossRefGoogle Scholar
  4. 4.
    Jia, X., Wang, W., Chen, Y., Huang, J., Chen, J., Zhang, H., Bai, H., Zhang, P.: Influence of dust aerosols on cloud radiative over Northern China. China Environ. Sci. 30(8), 1009–1014 (2010)Google Scholar
  5. 5.
    Watson, A.J., Bakker, D.C.E., Ridgwell, A.J., et al.: Effect of iron supply on southern ocean CO2 uptake and implications for glacial atmospheric CO2. Nature 407(6805), 730–733 (2005)ADSCrossRefGoogle Scholar
  6. 6.
    Holben, B.N., Eck, T.F., Slutsker, I., Tanre, D., Buis, J.P., Setzer, A., Vermote, E., Reagan, J.A., Kaufman, Y.J., Nakajima, T., Lavenu, F., Jankowiak, I., Smirnov, A.: AERONET-A federated instrument network and data archive for aerosol characterization. Rem. Sens. Environ. 66(1), 1–16 (1998)ADSCrossRefGoogle Scholar
  7. 7.
    Kim, D.H., Sohn, B.J., Nakajima, T., Takamura, T., Takemura, T., Choi, B.C., Yoon, S.C.: Aerosol optical properties over east Asia determined from ground-based sky radiation measurements. J. Geophy. Res. 109(2), D02209 (2004)ADSGoogle Scholar
  8. 8.
    Uchiyama, A., Yamazaki, A., Togawa, H., Asano, J.: Characteristics of aeolian dust observed by sky-radiometer in the Intensive observation period 1 (IOP1). J. Meteor. Soc. Jpn. 83A(3), 91–305 (2005)Google Scholar
  9. 9.
    Wehrli, C., Calibration of filter radiometers for the GAW Aerosol Optical Depth network at Jungfraujoch and Mauna Loa. In: Proceedings of ARJ workshop, SANW congress, Davos, Switzerland, 70–71: (2002)Google Scholar
  10. 10.
    Che, H., Zhang, X., Chen, H., Damiri, B., Goloub, P., Li, Z., Zhang, X., Wei, Y., Zhou, H., Dong, F., Li, D., Zhou, T.: Instrument calibration and aerosol optical depth (AOD) validation of the China aerosol remote sensing network (CARSNET). J. Geophys. Res. 114, (D3 (2009)CrossRefGoogle Scholar
  11. 11.
    Song, Y., Lu, L., Li, S., Xin, W., Yan, Q., Hua, D.: Analysis of light scattering properties of non-spherical aerosol particles. J. Xi’an Univ. Technol. 33(2), 233–239 (2017)Google Scholar
  12. 12.
    Zhang, H., Zhao, W., Ren, D., Qu, Y., Song, B.: Improved algorithm of Mie scattering parameter based on matlab. J. Light Scatt., 20 (2), 102–110 (2008)Google Scholar
  13. 13.
    Olmo, F.J., Quirantes, A., Alcántara, A., Lyamani, H., Alados-Arboledas, L.: Preliminary results of a non-spherical aerosol method for the retrieval of the atmospheric aerosol optical properties. J. Quant. Spectrosc. Radiat. Transf. 100(1), 305–314 (2006)ADSCrossRefGoogle Scholar
  14. 14.
    Kobayashi, E., Uchiyama, A., Yamazaki, A., Kudo, R.: Retrieval of aerosol optical properties based on the spheroid model. J. Meteorol. Soc. Jpn. 88(5), 847–856 (2010)CrossRefGoogle Scholar
  15. 15.
    Dubovik, O., King, M.D.: A flexible inversion algorithm for retrieval of aerosol optical properties from sun and sky radiance measurements. J. Geophys. Res. 105(D16), 20673–20696 (2000)ADSCrossRefGoogle Scholar
  16. 16.
    Van de Hulst, H.C.: Light Scattering by Small Particles. Dover, New York (1981)Google Scholar
  17. 17.
    Ghislan, R.F.: A new method for aerosol size distribution retrieval based on the anomalous diffraction approximation. In: Proc. SPIE, 4168, pp. 243–248: (2000)Google Scholar
  18. 18.
    Sun, W.B., Fu, Q.: Anomalous diffraction theory for randomly oriented nonspherical particle: a comparison between original and simplified solutions. J. Quant. Spectrosc. Radiat. Transf. 70(4–6), 737–747 (2001)ADSCrossRefGoogle Scholar
  19. 19.
    Xu, M., Lax, M.: Anomalous diffraction of light with geometrical path statistics of rays and a Gaussian ray approximation. Opt. lett. 28(3), 179–181 (2003)ADSCrossRefGoogle Scholar
  20. 20.
    Tang, H., Sun, X., Yuan, G.: Application on circular cylinder particle size distribution based on anomalous diffraction approximation. Chin. J. Lasers 34(3), 411–416 (2007)Google Scholar
  21. 21.
    Tang, H.: Study of inversion algorithm of particle size distribution using total light scattering method. PhD thesis, Harbin: Harbin Institute of Technology. 2008.10Google Scholar
  22. 22.
    Paramonov, L.E.: Optical equivalence of isotropic ensembles of ellipsoidal particles in the Rayleigh-Gans-Debye and anomalous diffraction approximations and its consequences. Opt. Spectrosc. 112(5), 787–795 (2012)ADSCrossRefGoogle Scholar
  23. 23.
    Gong, C., Wei, H., Li, X., Shao, S., Xu, Q., Chen, X.: The influence of the aspect ratio to the light scattering properties of cylinder ice particles. Acta Opt. Sin. 29(5), 1155–1159 (2009)CrossRefGoogle Scholar
  24. 24.
    Yamamoto, G., Tanaka, M.: Increasing of global albedo due to air pollution. J. Atos. Sci. 29(8), 1405–1412 (1972)ADSCrossRefGoogle Scholar
  25. 25.
    Whitby, K.T., Husar, R.B., Liu, B.Y.H.: The aerosol distribution of Los Angeles Smog. J. Celluloid Interface Sci. 39(1), 177–204 (1973)ADSCrossRefGoogle Scholar
  26. 26.
    Zhao, J., Hu, Y.: Bridging technique for calculating the extinction efficiency of arbitrary shaped particles. Appl. Opt. 42(24), 4937–4945 (2003)ADSCrossRefGoogle Scholar
  27. 27.
    King, M.D., Byrne, D.M., Herman, B.M., Reagan, J.A.: Aerosol size distribution obtained by inversion of spectral optical depth measurement. J. Atmos. Sci. 35(11), 2153–2167 (1978)ADSCrossRefGoogle Scholar
  28. 28.
    Twomey, S.: Introduction to the Mathematics of inversion in Remote Sensing and Indirect Measurements. Dover publication Inc., New York (1977)Google Scholar
  29. 29.
    Qiu, J., Wang, H., Zhou, X., lv, D.: Experimental study of remote sensing atmospheric aerosol size distribution by combined solar extinction and forward scattering method. Adv. Atmos. Sci. 7(1), 33–41 (1983)Google Scholar
  30. 30.
    Li, F., Liu, J., Lv, D.: Analyses of composite observation of optical properties of atmospheric aerosols in the late summer over some areas of North China. Sci. Atmospherica Sin. 19(2), 235–242 (1995)Google Scholar
  31. 31.
    Mao, J., Sheng, H., Zhao, H., Zhou, C.: Observation study on the size distribution of sand dust aerosol particles over Yinchuan, China. Adv. Meteorol. 2014, 1–7 (2014)CrossRefGoogle Scholar
  32. 32.
    Vitale, V., Tomasi, C., Lupi, A., Cacciari, A., Marani, S.: Retrieval of columnar aerosol size distributions and radiative forcing evaluations from sun photo metric measurements taken during the CLEARCOLUMN (ACE2) experiment. Atoms. Environ. 34(29–30), 5095–5105 (2000)Google Scholar
  33. 33.
    Heintzenberg, J., Muller, H., Quenzel, H., Thomalla, E.: Information content of optical data with respect to aerosol properties: numerical studies with a randomized minimization search technique inversion algorithm. Appl. Opt. 20(8), 1308–1315 (1981)ADSCrossRefGoogle Scholar
  34. 34.
    Herman, B.M., Browing, S.R., Reagan, J.A.: Determination of aerosol size distributions from lidar measurements. J. Atmos. Sci. 28(5), 763–771 (1971)ADSCrossRefGoogle Scholar
  35. 35.
    Ren, Y., Li, X., Lu, M., Hu, X.: Application prospect measurement by sun photometer CE318 and retrieval methodology. Meteorol. Sci. Technol. 34(3), 349–352 (2006)Google Scholar

Copyright information

© The Optical Society of Japan 2019

Authors and Affiliations

  1. 1.School of Electrical and Information EngineeringNorth Minu UniversityYinchuanChina

Personalised recommendations