A systematic examination of a random sampling strategy for source apportionment calculations.

Estimating the relative contributions from multiple potential sources of a specific component in a mixed environmental matrix is a general challenge in diverse fields such as atmospheric, environmental and earth sciences. Perhaps the most common strategy for tackling such problems is by setting up a system of linear equations for the fractional influence of different sources. Even though an algebraic solution of this approach is possible for the common situation with N+1 sources and N source markers, such methodology introduces a bias, since it is implicitly assumed that the calculated fractions and the corresponding uncertainties are independent of the variability of the source distributions. Here, a random sampling (RS) strategy for accounting for such statistical bias is examined by investigating rationally designed synthetic data sets. This random sampling methodology is found to be robust and accurate with respect to reproducibility and predictability. This method is also compared to a numerical integration solution for a two-source situation where source variability also is included. A general observation from this examination is that the variability of the source profiles not only affects the calculated precision but also the mean/median source contributions.