Adaptation of the Twomey Algorithm to the Inversion of Cascade Impactor Data

The Twomey nonlinear iterative algorithm for inverting aerosol size distribution data has been adapted for use with the Berner cascade impactor. Key factors affecting the performance of the algorithm have been identified. A procedure producing accurate inversions without artifacts includes establishing a set of continuous and smooth kernel functions based on measurements of the impactor cutoff characteristics, using modified weighting functions, placing constraints on the first-guess distribution, treating zero values and the ends of the distribution, and setting stopping criteria based on experimental errors. This general approach should be useful in solving inversion problems for other cascade impactors. The routine was extensively tested with numerically created test distributions and a large data base of ambient aerosol samples. An extended version of the program separates the inverted size distribution into a spectrum of lognormal distributions. Lognormal parameters from 44 ambient nitrate size distributions have been compared to the results of the inversion program of Dzubay and Hasan.