Inference of Particle Size Distribution Function of Aerosol Clouds from Light Scattering Measurements

摘要

Perhaps the most versatile and efficient method for inferring the particle size distribution function (PSDF) of aerosol clouds from remote light scattering measurements is the constrained linear inversion procedure. However, conventional numerical implementations of this procedure are subject to the following two problems: (1) an appropriate discrete approximation must be chosen for the PSDF which adequately achieves the correct balance between the conflicting requirements of resolution of detail in the PSDF and of efficiency in the computation of the solution and (2) a proper value must be selected that adequately reflects the tradeoff between the fidelity to the observed optical data and the smoothness of the solution. Consequently, an adequate recovery of the PSDF, based on the constrained linear inversion procedure, is usually achieved only after a certain amount of tedious preliminary exploratory analysis. An alternative implementation is presented which overcomes the problems associated with the conventional implementation. Firstly, an explicit analytical (continuous) representation for the solution of the constrained linear inversion procedure is developed which obviates the need to obtain a discrete approximation for the PSDF. Secondly, an objective procedure, based on the principle of generalized cross-validation, is utilized for the selection of the proper value for the Lagrange multiplier. These two developments provide the basis for an objective, fully automated implementation of the constrained linear inversion technique. Numerical examples of PSDF inversions, are presented for synthetic aerosol optical extinction and scattering data.