Aerosol Data Inversion: Optimal Solutions and Information Content

Citation

Wolfenbarger, J. Kenneth (1990) Aerosol Data Inversion: Optimal Solutions and Information Content. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/efdm-c587. https://resolver.caltech.edu/CaltechETD:etd-11092007-094509

Abstract

The determination of an aerosol size distribution is presently difficult because current aerosol instruments cannot perfectly discriminate aerosols based on size and because a only limited number of data can be obtained. As a result, for a given set of data the relationship between the unknown distribution and the data is a finite Fredholm integral equation. If the size distribution is desired, then one should answer the following
• What measurements should be taken?
• How should the measurements be used to determine a size distribution?

In this thesis, we shed some light on the answers to these questions by finding optimal solutions to the Fredholm integral equation, and by characterizing the size of the solution set.

The questions of existence and uniqueness of solutions subject to linear inequality constraints are examined. Optimal solutions based on regularization are developed, and numerical methods for finding these solutions are described. Numerical experiments are presented that demonstrate the importance of
• describing dependent error sources.
• considering the magnitude of the errors in the data when there are few data.
• using generalized cross validation when there are many data and the magnitude of the errors is unknown.

An analysis that uses some simple information concepts is presented for examining the size of the solution set. An example is presented that demonstrates the effect of dependent errors on the information provided by the data, and some illustrative experiment design studies are presented.

Thesis Files