Using SAS functions and high‐resolution isotope data to unravel travel time distributions in headwater catchments

Abstract

We use high‐resolution tracer data from an experimental site to test theoretical approaches that integrate catchment‐scale flow and transport processes in a unified framework centered on selective age sampling by streamflow and evapotranspiration fluxes. Transport processes operating at the catchment scale are reflected in the evolving residence time distribution of the catchment water storage and in the age selection operated by out‐fluxes. Such processes are described here through StorAge Selection (SAS) functions parameterized as power laws of the normalized rank storage. Such functions are computed through appropriate solution of the master equation defining formally the evolution of residence and travel times. By representing the way in which catchment storage generates outflows composed by water of different ages, the main mechanism regulating the tracer composition of runoff is clearly identified and detailed comparison with empirical data sets are possible. Properly calibrated numerical tools provide simulations that convincingly reproduce complex measured signals of daily deuterium content in stream waters during wet and dry periods. Results for the catchment under consideration are consistent with other recent studies indicating a tendency for natural catchments to preferentially release younger available water. The study shows that power law SAS functions prove a powerful tool to explain catchment‐scale transport processes that also has potential in less intensively monitored sites.

Using StorAge Selection functions to quantify ecohydrological controls on the time-variant age of evapotranspiration, soil water, and recharge

“…However, during dry conditions there is likely a much larger shift towards older waters. During wet conditions this is similar to the shape of SAS function used in previous studies (Harman, 2015;Queloz et al, 2015;Rinaldo et al, 2015;Benettin et al, 2017), while during dry 10 conditions a beta or gamma distribution may be more representative.…”

“…Higher uncertainty during dry conditions is not an anomaly with SAS functions (e.g. Benettin et al, 2017), but exemplifies a general concern for both wet and dry periods regarding the number of data points required to best characterize the SAS function under extreme conditions. 15…”

Understanding snow hydrological processes through the lens of stable water isotopes

“…Stable isotope compositions of oxygen and hydrogen in water (subsequently referred to as stable isotopes of water) have a long-standing tradition as tracers in hydrology , which among many applications have been widely used to separate different sources of streamflow (Klaus & McDonnell, 2013), to understand hillslope-scale hydrologic processes (Tetzlaff, Birkel, Dick, Geris, & Soulsby, 2014) and to estimate the residence time of water at various catchment scales (Benettin et al, 2017;Birkel & Soulsby, 2015;Tetzlaff et al, 2015). For snow hydrology, such measurements are particularly promising because winter precipitation falling as snow generally has distinct isotopic compositions compared to summer precipitation, meaning it may be used to trace the evolution and contribution of snow to hydrological pathways within catchments.…”

<i>tran</i>-SAS v1.0: a numerical model to compute catchment-scale hydrologic <i>tran</i>sport using StorAge Selection functions

“…This notably reduces the number of involved parameters and it simplifies the applicability of the model to different datasets and contexts. Although more research is needed to classify the expected shapes of the SAS functions based , 2015;Harman, 2015;Queloz et al, 2015b;Benettin et al, 2017;Wilusz et al, 2017) and a reasonable choice of the initial storage S 0 .…”

“…A simple class of probability distributions that is suitable to serve as SAS function is the power-law distribution (Queloz et al, 2015b;Benettin et al, 2017), which takes the form:…”