Travel time distribution in a hillslope: Insight from numerical simulations

Solute transport in a three-dimensional, heterogeneous hillslope is analyzed through a series of detailed, three-dimensional numerical simulations. The investigation focuses on the transport of a pulse of a passive solute, taking into account realistic features of the relevant flow domain (i.e., the spatial heterogeneity of the soil hydraulic properties and records of the time-dependent meteorological data and evapotranspiration). The scope of the present work is to analyze a few issues regarding the travel time probability density function (pdf) f(tau) of solute, with particular reference to the following: (1) the suitability of the time invariance assumption and the circumstance under which it may represent a valid approximation, (2) the shape of the resulting travel time pdf f(tau), and (3) the difference between f( tau) and the instantaneous unit hydrograph. It is found that in many cases of practical interest the transport of contaminants in catchments can be analyzed by assuming the time-invariant approximation for f(tau), provided that the calendar time is replaced by a flow-corrected time. Here f(tau) is calculated through the analysis of the breakthrough curve represented in terms of flux-averaged concentration versus cumulate discharge. The rescaling of time with respect to the cumulated outflow takes care in an approximate way of the transient processes occurring in the porous medium. The derived f(tau) is weakly dependent on various attributes, like the level of heterogeneity, presence of evaporation or transpiration, and injection period. The main exception regards the cases in which plant transpiration is intense in the vicinity of the channel after relatively long periods of low rain. The impact of the parameters' heterogeneity on f(tau) is generally quite limited, the dispersion being ruled by the distribution of length paths within the hillslope. The derived f(tau) seems compatible with the Gamma distribution, being characterized by both fast and slow responses, with a pronounced power law early peak and an exponential-like tail. Comparison of f(tau) with the often employed Gamma instantaneous unit hydrograph emphasizes the differences between water and solute dynamics after rainfall events.