Parameter estimation for fractional dispersion model for rivers

The fractional dispersion model for natural rivers, extended by including a first order reaction term, contains four parameters. In order to estimate these parameters a fractional Laplace transform-based method is developed in this paper. Based on 76 dye test data measured in natural streams, the new parameter estimation method shows that the fractional dispersion operator parameter F is the controlling parameter causing the non-Fickian dispersion and F does not take on an integer constant of 2 but instead varies in the range of 1.4–2.0. The adequacy of the fractional Laplace transform-based parameter estimation method is determined by computing dispersion characteristics of the extended fractional dispersion model and these characteristics are compared with those observed from 12 dye tests conducted on the US rivers, including Mississippi, Red, and Monocacy. The agreement between computed and observed dispersion characteristics is found to be good. When combined with the fractional Laplace transform-based parameter estimation method, the extended fractional dispersion model is capable of accurately simulating the non-Fickian dispersion process in natural streams.