Relative controls of external and internal variability on time-variable transit time distributions, and the importance of StorAge Selection function approaches

Transit time distributions (TTDs) are an efficient way of characterizing complex transport dynamics of a hydrologic system. Time-invariant TTD has been studied extensively, but TTDs are time-varying under unsteady hydrologic systems due to both external variability (e.g., time-variability in fluxes), and internal variability (e.g., time-varying flow pathways). The use of "flow-weighted time" has been suggested to account for the effect of external variability on TTDs, but neglects the role of internal variability. Recently, to account both types of variability, StorAge Selection (SAS) function approaches were developed. One of these approaches enables the transport characteristics of a system - how the different aged water in the storage is sampled by the outflow - to be parameterized by time-variable probability distribution called the rank SAS (rSAS) function, and uses it directly to determine the time-variable TTDs resulting from a given timeseries of fluxes in and out of a system. Unlike TTDs, the form of the rSAS function varies only due to changes in flow pathways, but is not affected by the timing of fluxes alone. However, the relation between physical mechanisms and the time-varying rSAS functions are not well understood. In this study, relative effects of internal and external variability on the TTDs are examined using observations from a homogeneously packed 1 m3 sloping soil lysimeter. The observations suggest the importance of internal variability on TTDs, and reinforce the need to account for this variability using time-variable rSAS functions. Furthermore, the relative usefulness of two other formulations of SAS functions and the mortality rate (which plays a similar role to SAS functions in the McKendrick-von Foerster model of age-structured population dynamics) are also discussed. Finally, numerical modeling is used to explore the role of internal and external variability for hydrologic systems with diverse geomorphic and climate characteristics. This works will give an insight that which approach (or SAS function) is preferable under different conditions.