On the interplay between hillslope and drainage network flow dynamics in the catchment travel time distribution

Travel time is a robust measure of water transport dynamics in catchments. At a given control section along a drainage network, travel time distribution results from an interplay between two main processes: (i) the transport through the hillslopes and (ii) transport through the drainage network. The main scope of this work is to quantify this interplay, specifically we aim to identify the relative impact of hillslopes and channels on the travel time at the catchment scale. A theoretical framework is developed following a bottom-up modelling approach that combines a Boussinesq model for water flow and water travel time in hillslopes, with a geomorphological model for water transport in drainage network. Simple semi-analytical solutions are derived for the first two moments of the travel time distribution within a flow section. We provide some relevant examples based on synthetic rainfall data, exploring the relative impacts of hillslope and channel properties. As expected, the dynamics of the hillslopes control the travel time distribution at the catchment scale. The drainage network typically introduces a lag in the average travel time exiting the hillslopes and reduces the temporal fluctuations of the mean travel time and its variance. Our theoretical model provides meaningful insights on the investigation of the dominant dynamics taking place in catchments: results suggest that hillslopes and their features are the main driver of travel time in catchments. The temporal fluctuations of the travel time moments show a non-linear dependence with the recharge time-series and need to be considered as time-variant. Variability of water ages collected in a single water sample can be very large, the latter feature may have a significant effect on the water quality and on the tracer data analysis, largely governed by the contact times between water and catchment material.