非吸收椭球形粒子尺度分布反演的一种新方法

doi:10.7523/j.issn.2095-6134.2010.3.004

摘要/Abstract

摘要：

研究了非吸收椭球形粒子尺度分布的反演问题.对于连续消光谱,得到了尺度分布与消光系数之间一个新的变换关系.对于离散消光谱,给出了基于Gamma分布展开的粒子尺度分布函数的级数表示,其中展开系数可通过求解相应的约束线性方程组来确定.在某种给定的反演精度下,实施积分所需的最短应测量波长与最小可反演粒径成正比.数值试验表明,本文所发展的解析技术是有效的,可容忍消光谱约5%的随机误差.

关键词: 尺度分布函数, 最小可反演粒径, 最短应测量波长

Abstract:

The inversion problem of the nonabsorbing spheroidal particle size distribution has been studied in this paper. For continuous extinction spectrum, a new transform relationship between size distribution and extinction coefficient is derived. For discrete extinction spectrum, a series representation of particle size distribution based on Gamma distribution function is given, in which the unknown expansion coefficients are determined by solving the corresponding constraints linear equations. The shortest wavelength required for the implementation of integral is proportional to the smallest inversible particle size in a given inversion accuracy. Numerical tests have shown that this analytic technique is stable and efficient and it can tolerate about 5% of noise-corruption in extinction spectrum.

Key words: size distribution function, smallest inversible size, shortest measured wavelength

中图分类号:

O439

赵剑琦. 非吸收椭球形粒子尺度分布反演的一种新方法[J]. 中国科学院大学学报, 2010, 27(3): 323-330.

ZHAO Jian-Qi. A new method for the determination of the spheroidal nonabsorbing particle size distribution[J]. , 2010, 27(3): 323-330.

参考文献

[1] IPCC 2007. Climate Change 2007: The Physical Science Basis. Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change
[M]. Solomon S, Qin D, Manning M, et al. Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA.

[2] King MD, Kaufman Y J, Tanre D, et al. Remote sensing of tropospheric aerosols from space: Past, present, and future
[J]. Bulletin of the American Meteorological Society, 1999, 80: 2229-2259.

[3] Kaufamn Y J, Tanre D, Boucher O. A satellite view of aerosols in the climate system
[J]. Nature, 2002, 419: 215-223.

[4] ngstrm A. On the atmospheric transmission of sun radiation and on dust in the air
[J]. Geografiska Annaler, 1929, 11: 156-166.

[5] ngstrm A. On the atmospheric transmission of sun radiation II
[J]. Geografiska Annaler,1930, 12: 130-159.

[6] Mie G. Beitrage zur optik trüber medien speziell kolloidaler metallsungen
[J]. Annalen der Physik, 1908,25: 377- 445.

[7] Waterman P C. Symmetry, unitarity, and geometry in electromagnetic scattering
[J]. Physical Review, 1971, D3: 825-839.

[8] Yee S K. Numerical solution of initial boundary value problems involving Maxwells equation in isotropic media
[J].IEEE Transactions on Antennas and Propagation, 1966, AP-14: 302-307.

[9] Berenger J P. A perfectly matched layer for the absorption of electromagnetic waves
[J]. Journal of Computational Physics, 1994,114:185-200.

[10] van de Hulst H C. Light scattering by small particles
[M]. New York: Wiley, 1957.

[11] Dobbins R A, Jizmagian G S. Optical scattering cross sections for polydispersions of dielectric spheres
[J]. Journal of the Optical Society of America, 1966, 56:1345-1350.

[12] Tarantola A, Valette B. Generalized nonlinear inverse problems solved using the least squares criterion
[J]. Reviews of Geophysics, 1982, 20: 219-232.

[13] Phillips D L. A technique for the numerical solution of certain integral equations of the first kind
[J]. Journal of the Association for Computing Machinery, 1962, 9: 84-97.

[14] Twomey S. Comparison of constrained linear inversion and an iterative non-linear algorithm applied to the indirect estimation of particle size distributions
[J]. Journal of Computational Physics, 1975, 18:188-200.

[15] Bockmann C. Hybrid regularization method for the ill-posed inversion of multiwave-length lidar data in the retrieval of aerosol size distributions . Applied Optics, 2001, 40: 1329-1342.

[16] Platnick S, King M D, Ackerman S K, et al. The MODIS cloud products: algorithms and examples from Terra
[J]. IEEE Transactions on Geoscience and Remote Sensing, 2003, 41: 459-473.

[17] Wang Y, Fan S, Feng X, et al. Regularized inversion method for retrieval of aerosol particle size distribution function in W^1-2 space
[J]. Applied Optics, 2006, 45 (28): 7456-7467.

[18] Pahlow M, Müller D, Tesche M, et al. Retrieval of aerosol properties from combined multiwavelength lidar and sunphotometer measurements
[J]. Applied Optics, 2006, 45 (28): 7429-7442.

[19] Shifrin K S, Perelman A Y. The determination of the spectrum of particles in a dispersed system from data on its transparency. I. The fundamental equation for the determination of the spectrum of the particles
[J]. Optics and Spectroscopy (USSR), 1963, 15: 285-289.

[20] Box M A, McKellar B H. Analytic inversion of multispectral extinction data in the anomalous diffraction approximation
[J]. Optics Letters, 1978, 3: 91-93.

[21] Shifrin K S, Perelman A Y, Volgin V M. Calculations of particle-radius distribution density from the integral characteristics of the spectral attenuation coefficient
[J]. Optics and Spectroscopy (USSR), 1981, 51: 534-538.

[22] Fymat A L. Analytical inversions in remote sensing of particle size distributions. 1. Multispectral extinctions in the anomalous diffraction approximation
[J]. Applied Optics, 1978, 17:1675-1676.

[23] Fymat A L, Mease K D. Reconstructing the size distribution of spherical particles from angular forward scattering data // Fymat A L, Zuev V E. Remote Sensing of the Atmosphere: Inversion Methods and Applications. New York: Elsevier,1978.

[24] Fymat A L, Smith C B. Analytical inversions in remote sensing of particle size distributions. 4. Comparison of Fymat and Box-McKellar solutions in the anomalous diffraction approximation
[J]. Applied Optics, 1979, 18:3595-3598.

[25] Box M A, McKellar B H. Relationship between two analytic inversion formulae for multispectral extinction data
[J]. Applied Optics, 1979, 18: 3599-3601.

[26] Smith C B. Inversion of the anomalous diffraction approximation for variable complex index of refraction near unity
[J]. Applied Optics, 1982, 21: 3363-3366.

[27] Klett D J. Anomalous diffraction model for inversion of multispectral extinction data including absorption effects
[J]. Applied Optics, 1984, 23: 4499-4508.

[28] Wang J, Hallett F R. Spherical particle size determination by analytical inversion of the UV-visible-NIR extinction spectrum
[J]. Applied Optics, 1996, 35: 193-197.

[29] Franssens G, Mazière M D, Fonteyn D. Determination of the aerosol size distribution by analytic inversion of the extinction spectrum in the complex anomalous diffraction approximation
[J]. Applied Optics, 2000, 39: 4214-4236.

[30] Liou K N, TakanoY. Light scattering by nonspherical particles: Remote sensing and climatic implications
[J]. Atmospheric Research, 1994, 31:271-298.

[31] Nakajima T, Tanaka M, Yamano M,et al. Aerosol optical characteristics in the yellow sand events observed in May, 1982 at Nagasaki—Part Ⅱ Models . Journal of the Meteorological Society of Japan, 1989, 67: 279-291.

[32] Heintzenberg J. Particle size distributions from scattering measurements of nonspherical particles via Mie-theory
[J]. Beitraege zur Physik der Atmosphaere, 1998,51: 91- 99.

[33] Gobbi G P, Barnaba F, Blumthaler M, et al. Observed effects of particles nonsphericity on the retrieval of marine and desert dust aerosol optical depth by lidar
[J]. Atmospheric Research, 2002, 61:1- 14. Doi: 10.1016/S0169-8095(01)00104-1.

[34] Dubovik O, Holben B N, Lapyonok T, et al, Nonspherical aerosol retrieval method employing light scattering by spheroids
[J]. Geophysical Research Letters, 2002, 29. 10.1029/2001GL014506.

[35] Zhao T X, Laszlo I, Dubovik O, et al. A study of the effect of non-spherical dust particles on the AVHRR aerosol optical thickness retrievals
[J]. Geophysical Research Letters, 2003, 30(6): 1317. doi: 10.1029/2002GL016379.

[36] Wenzel K,Von Hoyningen-Huene W, Schienbein S. Effects of nonsphericity on Saharan dust optical properties
[J]. Journal of Aerosol Science, 1996, 27(Suppl 1):565-566.

[37] Mishchenko M I, Lacis A A, Carlson B E, et al. Nonsphericity of dust-like tropospheric aerosols: Implications for aerosol remote sensing and climate modeling
[J]. Geophysical Research Letters, 1995, 22: 1077-1080.

[38] Asano S, Yamaoto G. Light scattering by a spheroidal particles
[J]. Applied Optics, 1975, 14: 29-49.

[39] Shankar R. Principles of quantum mechanics
[M]. New York: Plenum, 1994.