Comparison of negative skewed space fractional models with time nonlocal approaches for stream solute transport modeling

Abstract

Continuous time random walks (CTRW), multi-rate mass transfer (MRMT), and fractional advection-dispersion equations (FADEs) are three promising models of anomalous transport as commonly found in natural streams. Although these paradigms are mathematically related, understanding their advantages and limitations poses a challenge for model selection. In this paper, we quantitatively evaluate the advection-dispersion equation (ADE), fractional-mobile-immobile (FMIM), fractional-in-space ADE (sFADE), fractional in space transient storage (FSTS), truncated time-fractional model (TTFM), and CTRW models with truncated power-law waiting time distribution (CTRW-TPL) by fitting them first to synthetic data. We then applied these models to observations from tracer experiments conducted in several rivers. Based on the extensive analysis, we conclude that the performance of the FSTS model (in particular, the model with negative skewness β=-1) is comparable or superior to the other nonlocal models evaluated in the paper; therefore, the model represents an alternative to existing models for simulating stream solute transport for spatially-homogeneous flows.