The quantitative analysis of remote sensing observations of atmospheric aerosols inevitably involves simplified aerosol models.  The most popular and simple spectral model, the spherical approximation (Mie theory) for light scattering combined with single scattering and the assumptions of homogeneous particles has enjoyed great success at exploring the properties of atmospheric aerosol.  In reality, however, we deal with integral spectral responses of very large and generally heterogeneous systems of aerosol particles.  These aerosols exist in a wide variety of forms. As a result, observed spectra may be somewhat different from this simplified specification.  The extinction efficiency can be computed by the following three most popular approaches:  Bohren and Huffman code, T-matrix, (various codes can be downloaded from: http://diogenes.iwt.uni-bremen.de/~wriedt/New/new.php3 ) and Discrete Dipole (DD) techniques ( http://www.astro.princeton.edu/~draine/DDSCAT.html )  ; with frequency dependent refractive indices n*(n)  taken from laboratory measurements.

The extinction spectra of pure components form a basis for the minimization (inversion) procedure

 , subject to ,

where  is the aerosol extinction cross section; Q[..] is the extinction efficiency; n*(n) is the refractive index; r is the particle radius;  is the frequency, and t(n) is the extinction spectrum (observed in remote sensing).  After appropriate normalization by the volume, area or particle number density,  the solution vector P gives the particle size distribution (PDF) and the norm gives the total number, area, or volume density of the aerosol, consequently, if the ray path length is known. 

The term g×S×P is added to deal with a rank deficiency of the matrix K.  The matrix S is designed to minimize the third derivatives of P thus introducing a “smoothness constraint” on the solution vector P.  The parameter g controls the degree of smoothness and, as a rule, is very small.  The non-negativity constraint 1×P³0, where 1 is the identity matrix, is apparent and assures that all spectral intensities are positive or zero (the basic computer code can be obtained from the author by request)

The figure (on the right) illustrates  the IR spectra recorded by the ATMOS instrument carried by the Space Shuttle (http://remus.jpl.nasa.gov/atmos/atmos.html) during three missions in 1992, 1993 and 1994 .  Using these observations, we were able to obtaine the volume density and particle size distribution for sulphate aerosol as a function of altitude.  The density and size distribution of ice particles in several cirrus clouds were also identified.

Another retrieval algorithm in case of --->

The algorithm for retrieving the aerosol parameters from relatively low resolution (or low accuracy)  measurements, which imposes additional difficulties on the inversion, was proposed. It exacerbates the problem of finding the global minimum in a multidimensional space. This problem is not too severe for “good” objective functions with prominent global minima, which can be exactly (or almost exactly) solved. We proposed the retrieval algorithm for the case of nearly equivalent solutions (--->) 

The method combines a linear least squares procedure with a Monte-Carlo-like (random walk) technique.  The Monte Carlo like approach allows an extended range of parameters to be sampled. The procedure visits the vicinities of many local minima rapidly, thus reducing the consequences of the problem’s “ill-posed” nature, or at least identifying different solutions that are equally good. In summary, the techniques proposed here ameliorate the deficiencies introduced by the low resolution data, allowing the important aerosol characteristics (size, composition and phase) to be determined quantitatively.

The figure below shows the results obtained using the IR spectra recorded by the low resolution spectrometer (ILAS instrument on the ADEOS-I satellite in 1997, see http://www-ilas2.nies.go.jp/en/top.html for details).  The characteristics of polar stratospheric clouds such as the volume densities and size of the aerosol particles can be estimated