Quantifying the influence of matrix diffusion on transit time distributions (TTDs) in mountain catchments

Abstract

Solute transit or travel time distributions (TTDs) are relevant to both hydrochemical response and inference of hydrologic mechanisms in catchments.  A significant fraction of streamflow in mountain catchments is derived from groundwater flow through fractured bedrock.  It is well established that matrix diffusion significantly influences the travel time of tracers in fractured rock.  However, few models of catchment TTDs explicitly incorporate the influence of matrix diffusion.  I present theoretical analyses of the combined influence of matrix diffusion and variable advective travel times along streamlines, on the total TTD in a catchment hillslope flow system in both the frequency and time domains.  The frequency domain analyses reveal that matrix diffusion inherently leads to 1/frequency or “fractal scaling” behavior, which has been widely documented.  Application to the Lower Hafren experimental watershed at Plynlimon, Wales, shows that theoretical stream concentration power spectra match observations very well.  Time-domain analyses reveal that matrix diffusion leads to TTDs that decline steeply at early times and also exhibit long tails, consistent with gamma distributions with shape parameter α = 0.5 (or more generally < 1).  I present illustrative applications of the time-domain analysis to interpret environmental tracer observations (tritium-helium, 3H-3He; and sulfur hexafluoride, SF6) from two mountain catchments in Colorado, USA.  Both catchments are underlain by fractured bedrock and environmental tracer transport is likely influenced strongly by matrix diffusion. The time-domain model employs a fitted advective travel time distribution and involves two additional dimensionless parameters: the first is a measure of the strength of matrix diffusion and the second represents the influence of the accessible matrix diffusion thickness.  These parameters were assigned based on field information, with minor adjustments. Results illustrate the significant influence of matrix diffusion on TTDs in mountain catchments with fractured bedrock, and parsimonious approaches to representing this influence.