Parameter estimation for fractional transport: A particle-tracking approach

Space-fractional advection-dispersion models provide attractive alternatives to the classical advection-dispersion equation for model applications that exhibit early arrivals and plume skewness. This paper develops a flexible method for estimating the parameters of the fractional transport model on the basis of spatial plume snapshots or temporal breakthrough curve data. A particle-tracking approach provides error bars for the parameter estimates and a general method for model fitting and comparison via optimal weighted least squares. A simple model of concentration variance, based on the particle-tracking approach, identifies the optimal weights.