Quantifying catchment-scale mixing and its effect on time-varying travel time distributions

Travel time distributions are often used to characterize catchment discharge behavior, catchment vulnerability to pollution and pollutant loads from catchments to downstream waters. However, these distributions vary with time because they are a function of rainfall and evapotranspiration. It is important to account for these variations when the time scale of interest is smaller than the typical time-scale over which average travel time distributions can be derived. Recent studies have suggested that subsurface mixing controls how rainfall and evapotranspiration affect the variability in travel time distributions of discharge. To quantify this relation between subsurface mixing and dynamics of travel time distributions, we propose a new transformation of travel time that yields transformed travel time distributions, which we call Storage Outflow Probability (STOP) functions. STOP functions quantify the probability for water parcels in storage to leave a catchment via discharge or evapotranspiration. We show that this is equal to quantifying mixing within a catchment. Compared to the similar Age function introduced by Botter et al. (2011), we show that STOP functions are more constant in time, have a clearer physical meaning and are easier to parameterize. Catchment-scale STOP functions can be approximated by a two-parameter beta distribution. One parameter quantifies the catchment preference for discharging young water; the other parameter quantifies the preference for discharging old water from storage. Because of this simple parameterization, the STOP function is an innovative tool to explore the effects of catchment mixing behavior, seasonality and climate change on travel time distributions and the related catchment vulnerability to pollution spreading