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Particle size distribution retrieval from multispectral optical depth: Influences of particle nonsphericity and refractive index

Retrieval of size distributions from multispectral optical depth measurements requires solution of an ill-posed inverse problem. The ill-posedness causes problems such as solution ambiguity. Size distribution retrieval becomes more complicated in the presence of nonspherical particles and/or refractive index errors. A new retrieval algorithm is first developed which allows for both smoothing and nonnegativity constraint along with the L-curve method for choosing the Lagrange multiplier that controls the degree of the imposed smoothing. This new algorithm is compared to an iterative algorithm and the method of truncated singular value decomposition, demonstrating that the new algorithm outperforms the other two. With the new algorithm to perform the size distribution retrieval and with the T-matrix method to calculate optical depth for a given cloud consisting of randomly oriented finite circular cylinders, the influence of particle nonsphericity on the size distribution retrieval is investigated by use of the Mie theory for spheres as well as the anomalous diffraction theory for cylinders. The results show that spurious particles and even spurious particle modes occur for both approximations. The effect of refractive index errors are also investigated, showing that even a small perturbation of refractive indices can cause serious distortions of retrieved size distributions. A further examination reveals that either applying an approximate light-scattering theory (Mie theory or anomalous diffraction theory) to nonspherical particles or using incorrect refractive indices results in systematic errors in the model which in turn conspire with the ill-posedness inherent in the retrieval to cause the distortions of retrieved size distributions. The retrieval process essentially transforms the model error into the error in retrieved size distribution, yet improves the agreement between true and retrieved optical depth.