Vol. 32, issue 07, article # 4

Samoilova S. V. Simultaneous reconstruction of the complex refractive index and the particle size distribution function from the lidar data: examination of the algorithms. // Optika Atmosfery i Okeana. 2019. V. 32. No. 07. P. 525–538. DOI: 10.15372/AOO20190704 [in Russian].
Copy the reference to clipboard

A method is suggested for joint determination of two aerosol microphysical characteristics: the complex refractive index m = mreal + i × mimage and the spherical-particle size distribution function U(r) from the data of the nighttime vertical lidar sensing at the wavelengths 355–1064 nm. During their simultaneous estimation it is useful to minimize the discrepancy functional Ф(m) in the range of the physically justified m. The principal limitations due to a wider region of the global minima of Ф(m) appear at mtrueimage Î [0.01; 0.04] and give rise to a potential shift of the resulting values of mestreal and mestimage. A simultaneous use of several functionals gives a better estimate of m due to different sets of the respective optical characteristics. The problem in retrieving the distribution function is caused by the information content of the coarse particle measurements. The statistical regularization method offers an unambiguous estimation of U(r) for the mean radius up to 3 mm, and gives an admissible estimate for larger radii. The algorithms have been tested using 8 values of absorption, when 50 empirical models of the size distribution function are assigned to one value mtrueimage.


aerosol, lidar, particle size distribution function, complex refractive index


  1. Remer L.A., Kaufman Y.J., Tanré D., Mattoo S., Chu D.A., Martins J.V., Li R.-R., Ichoku C., Levi R.C., Kleidman R.G., Eck T.F., Vermote E., Holben B.N. The MODIS aerosol algorithm, products, and validation // J. Atmos. Sci. 2005. V. 62. P. 947–973.
  2. Tanré D., Bréon F.M., Deusé J.L., Dubovik O., Ducos F., Francois P., Goloub P., Herman M., Lifermann A., Waquet F. Remote sensing of aerosol by using polarized, directional and spectral measurements within the A-Train: The PARASOL mission // Atmos. Meas. Tech. Discuss. 2011. V. 4. P. 2037–2069. DOI: 10.5194/amtd-4-2037-2011.
  3. Winker D.M., Vaughan M.A., Omar A., Hu Y., Powell K.A., Liu Z., Hunt W.H., Young S.A. Overview of the CALIPSO mission and CALIOP data processing algorithms // J. Atmos. Ocean. Technol. 2009. V. 26. P. 2310–2323. DOI: 10.1175/2009JTECHA1281.1.
  4. Holben B.N., Eck T.F., Slutsker I., Tanré D., Buis J.P., Setzer A., Vermote E., Reagan J.A., Kaufman Y., Nakajima T., Lavenu F., Jankowiak I., Smirnov A. AERONET – A federated instrument network and data archive for aerosol characterization // Remote Sens. Environ. 1998. V. 66. P. 1–16.
  5. Dubovik O.V., Lapyonok T.V., Oshchepkov S.L. Improved technique for data inversion: Optical sizing of multicomponent aerosols // Appl. Opt. 1995. V. 34. P. 8422–8436.
  6. Dubovik O.V., King M.D. A flexible inversion algorithm for retrieval of aerosol optical properties from Sun and sky radiance measurements // J. Geophys. Res. 2000. V. 105. P. 20673–20696.
  7. Bösenberg J., Ansmann A., Baldasano J.M., Balis D., Böckmann C., Calpini B., Chaikovsky A., Flamant P., Hågård A., Mitev V., Papayannis A., Pelon J., Resendes D., Schneider J., Spinelli N., Trickl T., Vaughan G., Visconti G., Wiegner M. EARLINET: a European aerosol research lidar network // Advances in Laser Remote Sensing / A. Dabas, C. Loth, J. Pelon (eds.). Editions de L’Ecole Polytechnique, 2000. P. 155–158.
  8. Murayama T., Sugimoto N., Uno I., Kinoshita K., Aoki K., Hagiwara N., Liu Z., Matsui I., Sakai T., Shibata T., Arao K., Sohn B.-J., Won J.-G., Yoon S.-C., Li T., Zhou J., Hu H., Abo M., Iokibe K., Koga R., Iwasaka Y. Ground-based network observation of Asian dust events of April 1998 in east Asia // J. Geophys. Res. 2001. V. 106. P. 18345–18359.
  9. Chaikovsky A.P., Ivanov A.P., Balin Yu.S., Elnikov A.V., Tulinov G.F., Plusnin I.I., Bukin O.A., Chen B.B. CIS-LiNet – Lidar Network for Monitoring Aerosol and Ozone in CIS Regions // Reviewed and Revised Papers Presented at the 23d ILRC / C. Nagasava, N. Sugimoto (eds.). Nara, Japan, 2006. P. 671–672.
  10. Bösenberg J., Hoff R.M. Plan for the implementation of the GAW Aerosol Lidar Observation Network GALION // WMO. 2007. N 1443. 45 р.
  11. Burton S.P., Chemyakin E., Liu X., Knobelspiesse K., Stamnes S., Sawamura P., Moore R.H., Hostetler C.A., Ferrare R.A. Information content and sensitivity of the 3b + 2a lidar measurement system for aerosol microphysical retrievals // Atmos. Meas. Tech. 2016. V. 9. P. 5555–5574. DOI: 10.5194/amt-9-5555-2016.
  12. Pappalardo G., Amodeo A., Apituley A., Comeron A., Freudenthaler V., Linné H., A. Ansmann A., Bösenberg J., D'Amico G., Mattis I., Mona L., Wandinger U., Amiridis V., Alados-Arboledas L., Nicolae D., Wiegner M. EARLINET: Towards an advanced sustainable European aerosol lidar network // Atmos. Meas. Tech. 2014. V. 7. P. 2389–2409. DOI: 10.5194/amt-7-2389-2014.
  13. Samoilova S.V., Balin Yu.S. Reconstruction of the aerosol optical parameters from the data of sensing with a multifrequency Raman lidar // Appl. Opt. 2008. V. 47. P. 6816–6831.
  14. Willeke K., Whitby K.T. Atmospheric aerosol: size distribution interpretation // J. Air Poll. Control Assoc. 1975. V. 25. P. 529–534.
  15. Twitty J.T. The inversion of aureole measurements to derive aerosol size distributions // J. Atmos. Sci. 1975. V. 32. P. 584–591.
  16. Gorchakov G.I., Gorchakova I.A. Lykosov E.A., Tolstobrov V.G., Turovtseva L.S. Opredelenie koeffitsienta prelomleniya i mikrostruktury tumannoj dymki // Izv. AN SSSR. Fiz. atmosf. i okeana. 1976. V. 12, N 6. P. 612–619.
  17. Veretennikov V.V., Naats I.E., Panchenko M.V., Fadeev V.Ya. K opredeleniyu mikrostruktury i pokazatelya prelomleniya atmosfernykh dymok iz polyarizatsionnykh kharakteristik svetorasseyaniya // Izv. AN SSSR. Fiz. atmosf. i okeana. 1978. V. 14, N 12. P. 1313–1317.
  18. Veretennikov V.V., Kozlov V.S., Naats I.E., Fadeev V.Ya. Optical studies of smoke aerosol: An inversion method and its applications // Opt. Lett. 1979. V. 4. P. 411–413.
  19. Zuev V.E., Naats I.E. Obratnye zadachi lazernogo zondirovaniya. Novosibirsk: Nauka, 1982. 240 p.
  20. Rakhimov R.F., Kozlov V.S., Panchenko M.V., Tumakov A.G., Shmargunov V.P. Svojstva atmosfernogo aerozolya v dymovykh shlejfakh lesnykh pozharov po dannym spektronefelometricheskikh izmerenij // Optika atmosf. i okeana. 2014. V. 27, N 2. P. 126–133.
  21. Makienko E.V., Rakhimov R.F., Pkhalagov Yu.A., Uzhegov V.N. Mikrofizicheskaya interpretatsiya anomal'noj spektral'noj zavisimosti aerozol'nogo oslableniya izlucheniya na prizemnoj trasse // Optika atmosf. i okeana. 2003. V. 16, N 12. P. 1102–1106.
  22. Veretennikov V.V. Sovmestnoe opredelenie mikrostruktury i pokazatelya prelomleniya aerozolya po dannym solnechnoj fotometrii // Optika atmosf. i okeana. 2007. V. 20, N 3. P. 214–221.
  23. Veretennikov V.V. Vosstanovlenie mikrostrukturnykh parametrov grubodispersnogo aerozolya s ispol'zovaniem ikh regressionnykh svyazej so spektral'nym oslableniem sveta v IK-diapazone // Optika atmosf. i okeana. 2017. V. 30, N 8. P. 696–704.
  24. Bedareva T.V., Sviridenkov M.A., Zhuravleva T.B. Vosstanovlenie opticheskikh i mikrofizicheskikh kharakteristik aerozolya po dannym nazemnykh spektral'nykh izmerenij pryamoj i rasseyannoj solnechnoj radiatsii. Part 1. Testirovanie algoritma // Optika atmosf. i okeana. 2012. V. 25, N 7. P. 602–612. DOI: 10.1134/S1024856013010041.
  25. Bohren F.C., Huffman D.R. Absorption and scattering of light by small particles. New York: John Wiley & Sons, Inc., 1983. 530 p.
  26. Müller D., Wandinger U., Ansmann A. Microphysical particle parameters from extinction and backscatter lidar data by inversion with regularization: Theory // Appl. Opt. 1999. V. 38. P. 2346–2357.
  27. Böckmann C. Hybrid regularization method for the ill-posed inversion of multiwavelength lidar data in the retrieval of aerosol size distribution // Appl. Opt. 2001. V. 40. P. 1329–1342.
  28. Böckmann C., Mironova I., Müller D., Schneidenbach L., Nessler R. Microphysical aerosol parameters from multiwavelength lidar // J. Opt. Soc. Am. 2005. V. A22(3). P. 518–528.
  29. Veselovskii I., Kolgotin A., Griaznov V., Müller D., Franke K., Whiteman D.M. Inversion of multiwavelength Raman lidar data for retrieval of bimodal aerosol size distribution // Appl. Opt. 2004. V. 43. P. 1180–1195.
  30. Veselovski I., Kolgotin A., Müller D., Whiteman D.M. Information content of multiwavelength lidar data with respect to microphysical particle properties derived from eigenvalue analysis // Appl. Opt. 2005. V. 44. P. 5292–5303.
  31. Kolgotin A., Müller D. Theory of inversion with two-dimensional regularization: profiles of microphysical particle properties derived from multiwavelength lidar measurements // Appl. Opt. 2008. V. 47. P. 4472–4490.
  32. Omar A.H., Winker D.M., Vaughan M.A., Hu Y., Trepte Ch.H., Ferrare R.A., Lee K.-P., Hostetler Ch.A., Kittaka Ch., Rogers R.R., Kuehn R.E., Lie Zh. The CALIPSO automated aerosol classification and lidar ratio selection algorithm // J. Atmos. Ocean. Technol. 2009. V. 26, N 10. P. 1994–2014.
  33. Veselovskii I., Dubovik O., Kolgotin A., Lapyonok T., Di Girolamo P., Summa D., Whiteman D.M., Mishchenko M., Tanre D. Application of randomly oriented spheroids for retrieval of dust particle parameters from multiwavelength lidar measurements // J. Geophys. Res. 2010. V. 115. P. D21203. DOI: 10.1029/2010D014139.
  34. Veselovskii I., Dubovik O., Kolgotin A., Korenskiy M., Whiteman D.N., Allakhverdiev K., Huseyinoglu F. Linear estimation of particle bulk parameters from multi-wavelength lidar measurements // Atmos. Meas. Tech. 2012. V. 5. P. 1135–1145. DOI: 10.5194/amt-5-1135-2012.
  35. Müller D., Veselovskii I., Kolgotin A., Tesche M., Ansmann A., Dubovik O. Vertical profiles of pure dust and mixed smoke-dust plumes inferred from inversion of multiwavelength Raman/polarization lidar data and comparison to AERONET retrievals and in situ observa- tions // Appl. Opt. 2013. V. 52. P. 3178–3202.
  36. Wagner J., Ansmann A., Wandinger U., Seifert P., Chwarz A., Tesche M., Chaikovsky A., Dubovik O. Evaluation of the Lidar/Radiometer Inversion Code (LIRIC) to determinate microphysical properties of volcanic and desert dust // Atmos. Meas. Tech. 2013. V. 6. P. 1707–1724. DOI: 10.5194/amt-6-1707-2013.
  37. Chemyakin E., Müller D., Burton Sh., Kolgotin A., Hostetler Ch., Ferrare R. Arrange and average algorithm for the retrieval of aerosol parameters from multiwavelength high-spectral-resolution lidar/Raman lidar data // Appl. Opt. 2014. V. 53. P. 7252–7266.
  38. Chemyakin E., Burton S., Kolgotin A., Müller D., Hostetler C., Ferrare R. Retrieval of aerosol parameters from multiwavelength lidar: Investigation of the underlying inverse mathematical problem // Appl. Opt. 2016. V. 5. P. 2188–2202.
  39. Kahnert M., Andersson E. How much information do extinction and backscattering measurements contain about the chemical composition of atmospheric aerosol? // Atmos. Chem. Phys. 2017. V. 17. P. 3423–3444. DOI: 10.5194/acp-17-3423-2017.
  40. Alexandrov M.D., Mishchenko M.I. Information content of bistatic lidar observations of aerosols from space // Opt. Express. 2017. V. 25, N 4. P. A134–A150.
  41. Mishchenko M.I., Hovenier J.W., Travis L.D. Light Scattering by Nonspherical Particles. San Diego, CA, USA: Academic Press, 2000. 690 pp.
  42. Mishchenko M.I., Travis L.D., Lacis A.A. Scattering, Absorption, and Emission of Light by Small Particles. Cambridge, United Kingdom: Cambridge University Press, 2002. 450 pp.
  43. Dubovik O., Sinyuk A., Lapyonok T., Holben B.N., Mishchenko M., Yang P., Eck T.F., Volten H., Munoz O., Veihelmann B., van der Zande W.J., Leon J.-F., Sorikin M., Slutsker I. Application of spheroid momels to account for aerosol particle nonsphericity in remote sensing of desert dust // J. Geophys. Res. 2006. V. 111. P. D11208. DOI: 10.1029/2005D006619.
  44. Samoilova S.V., Sviridenkov M.A., Penner I.E. Retrieval of the particle size distribution funcion from the data of lidar sensing under the assumption of known refractive index // Appl. Opt. 2016. V. 55. P. 8022–8029. https://doi.org/10.1364/AO.55.008022.
  45. Samojlova S.V. Vosstanovlenie kompleksnogo pokazatelya prelomleniya po lidarnym izmereniyam: vozmozhnosti i ogranicheniya // Optika atmosf. i okeana. 2014. V. 27, N 3. P. 197–206.
  46. Samoilova S.V., Penner I.E., Kokhanenko G.P., Balin Yu.S. Simultaneous reconstruction of two microphysical aerosol characteristics from the lidar data // J. Quant. Spectrosc. Radiat. Transfer. 2019. V. 222–223. P. 35–44. https://doi.org/10.1016/ j.jqsrt.2018.10.014.
  47. Verhaege Ch., Shcherbakov V., Personne P. Limitations on retrieval of complex refractive index of spherical particles from scattering measurements // J. Quant. Spectrosc. Radiat. Transfer. 2008. V. 109. P. 2338–2348. DOI: 10.1016/j.jqsrt.2008.05.009.
  48. Verhaege Ch., Shcherbakov V., Personne P. Retrieval of complex refractive index and size distribution of spherical particles from Dual-Polarization Polar Nephelometer data // J. Quant. Spectrosc. Radiat. Transfer. 2009. V. 110, P. 1690–1697. DOI: 10.1016/j.jqsrt.2009.01.004.
  49. Lopatin A., Dubovik O., Chaikovsky A., Goloub P., Lapyonok T., Tanré D., Litvinov P. Enhancement of aerosol characterization using synergy of lidar and sun-photometer coincident observations: The GARRLiC algorithm // Atmos. Meas. Tech. 2013. V. 6. P. 2065–2088. DOI: 10.5194/amt-6-2065-2013.
  50. Chaikovsky A., Dubovik O., Holben B., Bril A., Goloub Ph., Tanré D., Pappalardo G., Wandinger U., Chaikovskaya L., Denisov S., Grudo J., Lopatin A., Karol Ya., Lapyonok T., Amiridis V., Ansmann A., Apituley A., Allados-Arboledas L., Binietoglou I., Boselli A., D’Amico G., Freudenthaler V., Giles D., Granados-Muñoz M.J., Kokkalis P., Nicolae D., Oshchepkov S., Papayannis A., Perrone M.R., Pietruczuk A., Rocadenbosch F., Sicard M., Slutsker I., Talianu C., De Tomasi F., Tsekeri A., Wagner J., Wang X. Lidar-Radiometer Inversion Code (LIRIC) for the retrieval of vertical aerosol properties from combined lidar/radiometer data: Development and distribution in EARLINET // Atmos. Meas. Tech. 2016. V. 9. P. 1181–1205. DOI: 10.5194/amt-9-1181-2016.
  51. Tikhonov A.N., Arsenin V.Ya. Metody resheniya nekorrektnykh zadach. M.: Nauka, 1986. 285 p.
  52. Vasilenko G.I. Teoriya vosstanovleniya signalov. M.: Sovetskoe radio, 1979. 272 p.
  53. Samoilova S., Sviridenkov M., Penner I., Kokhanenko G., Balin Yu. Retrieval of the tropospheric aerosol microphysical characteristics from the data of multifrequency lidar sensing // EPJ Web Conf. 2018. 28th Laser Radar Conf. V. 176. URL: https://doi.org/10.1051/epjconf/201817605055 (last access: 28.06.2019).
  54. Bedareva T.V., Sviridenkov M.A., Zhuravleva T.B. Vosstanovlenie opticheskikh i mikrofizicheskikh kharakteristik aerozolya po dannym nazemnykh spektral'nykh izmerenij pryamoj i rasseyannoj solnechnoj radiatsii. Part 2. Aprobatsiya algoritma // Optika atmosf. i okeana. 2012. V. 25, N 9. P. 768–777. DOI: 10.1134/S102485601302005X.