Regularized Solutions to the Aerosol Data Inversion Problem

Regularized solutions to the aerosol data inversion problem are presented. An approximate form of generalized cross validation is developed that is applicable to this linearly constrained inverse problem. The results obtained with this algorithm for choosing the smoothing parameter are compared with those obtained by the method of discrepancy and by minimizing an unbiased estimate of the inverted errors. Examples are presented that demonstrate the importance of using generalized cross validation to choose the smoothing parameter when the magnitude of the errors in the data is difficult to estimate.