Intercomparing the Twomey method with a multimodal lognormal approach to retrieve the aerosol size distribution

This paper concentrates on intercomparing an objective algorithm to estimate the columnar aerosol size distribution from aerosol spectral extinction and a widespread robust nonparametric inversion approach. The nonparametric approach which has been considered is the Phillips-Twomey second-derivative regularization method. The parametric approach assumes that the size distribution is the linear combination of a set of lognormal functions (typically, from 10 to 30 distributions are considered) which have suitable mode radii and standard deviations. Intercomparisons have been performed on the basis of aerosol optical thicknesses derived by high-resolution solar radiation absorption spectra in the spectral region 0.40 − 1.1 μm. Absorption spectra were recorded by a grating spectrometer with a resolution of 0.5 nm. Each inversion, either parametric or nonparametric, was obtained by using more than 450 data points at a time which, from a statistical point of view, allowed us to obtain high-quality results. For the cases presented here, we found that the two approaches agree fairly well in indicating the most significant characteristics of the aerosol size distribution.

[1]  M F Carfora,et al.  Objective algorithms for the aerosol problem. , 1995, Applied optics.

[2]  Constrained eigenfunction method for the inversion of remote sensing data: application to particle size determination from light scattering measurements. , 1989, Applied optics.

[3]  S. Twomey Introduction to the Mathematics of Inversion in Remote Sensing and Indirect Measurements , 1997 .

[4]  F. Kasten,et al.  A new table and approximation formula for the relative optial air mass , 1964 .

[5]  H. V. Hulst Light Scattering by Small Particles , 1957 .

[6]  Michael D. King,et al.  Sensitivity of constrained linear inversions to the selection of the Lagrange multiplier. [for inferring columnar aerosol size distribution from spectral aerosol optical depth measurements] , 1982 .

[7]  G. Shaw Error analysis of multi-wavelength sun photometry , 1976 .

[8]  Hwa-Chi Wang,et al.  Adaptation of the Twomey Algorithm to the Inversion of Cascade Impactor Data , 1990 .

[9]  David L. Phillips,et al.  A Technique for the Numerical Solution of Certain Integral Equations of the First Kind , 1962, JACM.

[10]  Bo G Leckner,et al.  The spectral distribution of solar radiation at the earth's surface—elements of a model , 1978 .

[11]  H. Hasan,et al.  Fitting Multimodal Lognormal Size Distributions to Cascade Impactor Data , 1990 .

[12]  H Quenzel,et al.  Information content of optical data with respect to aerosol properties: numerical studies with a randomized minimization-search-technique inversion algorithm. , 1981, Applied optics.

[13]  S. Twomey,et al.  On the Numerical Solution of Fredholm Integral Equations of the First Kind by the Inversion of the Linear System Produced by Quadrature , 1963, JACM.

[14]  Anders Ångström,et al.  On the Atmospheric Transmission of Sun Radiation and on Dust in the Air , 1929 .

[15]  Thomas Kaijser,et al.  A simple inversion method for determining aerosol size distributions , 1983 .

[16]  Ernest Vigroux,et al.  Contribution à l'étude expérimentale de l'absorption de l'ozone , 1953 .

[17]  J A Reagan,et al.  Inverse problem and the pseudoempirical orthogonal function method of solution. 1: Theory. , 1988, Applied optics.

[18]  W. John,et al.  Modes in the size distributions of atmospheric inorganic aerosol , 1990 .

[19]  Michael D. King,et al.  A Method for Inferring Total Ozone Content from the Spectral Variation of Total Optical Depth Obtained with a Solar Radiometer , 1976 .