Table of Contents
ISRN Applied Mathematics
Volume 2012, Article ID 465320, 20 pages
Research Article

Inverse Dispersion for an Unknown Number of Sources: Model Selection and Uncertainty Analysis

Defence R&D Canada – Suffield, P.O. Box 4000 Stn Main, Medicine Hat, AB, Canada T1A 8K6

Received 20 June 2012; Accepted 10 July 2012

Academic Editors: Y. Dimakopoulos, J. R. Fernandez, and T. Y. Kam

Copyright © 2012 Her Majesty the Queen in Right of Canada. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A simple recursive method is presented for performing the inverse dispersion modeling of an unknown number of (localized) sources, given a finite number of noisy concentration data acquired by an array of detectors. Bayesian probability theory is used to address the problem of selecting the source model which is most plausible in view of the given concentration dataset and all the available prior information. The recursive algorithm involves subtracting a predicted concentration signal arising from a source model consisting of 𝑁 localized sources from the measured concentration data for increasing values of 𝑁 and examining the resulting residual data to determine if the residuals are consistent with the estimated noise level in the concentration data. The method is illustrated by application to a real concentration dataset obtained from an atmospheric dispersion experiment involving the simultaneous release of a tracer from four sources.