Matrix Diffusion as a Mechanism Contributing to Fractal Stream Chemistry and Long‐Tailed Transit Time Distributions

Abstract

AbstractSolute transit or travel time distributions (TTDs) in catchments are relevant to both hydrochemical response and inference of hydrologic mechanisms. Long‐tailed TTDs and fractal scaling behavior of stream concentration power spectra (∼1/frequency, or 1/frequency to a power <2) are widely observed in catchment studies. In several catchments, a significant fraction of streamflow is derived from groundwater in shallow fractured bedrock, where matrix diffusion significantly influences solute transport. I present frequency and time domain theoretical analyses of solute transport to quantify the influence of matrix diffusion on fractal scaling and long‐tailed TTDs. The theoretical concentration power spectra exhibit fractal scaling, and the corresponding TTDs resemble a gamma distribution. The tails of the TTDs are influenced by accessible matrix width, exhibiting a sustained power‐law (rather than exponential) decline for large matrix widths. Application to an experimental catchment shows that theoretical spectra match previously reported power spectral estimates derived from concentration measurements.