The master transit time distribution of variable flow systems

Abstract

[1] The transit time of water is an important indicator of catchment functioning and affects many biological and geochemical processes. Water entering a catchment at one point in time is composed of water molecules that will spend different amounts of time in the catchment before exiting. The next water input pulse can exhibit a totally different distribution of transit times. The distribution of water transit times is thus best characterized by a time-variable probability density function. It is often assumed, however, that the variability of the transit time distribution is negligible and that catchments can be characterized with a unique transit time distribution. In many cases this assumption is not valid because of variations in precipitation, evapotranspiration, and catchment water storage and associated (de)activation of dominant flow paths. This paper presents a general method to estimate the time-variable transit time distribution of catchment waters. Application of the method using several years of rainfall-runoff and stable water isotope data yields an ensemble of transit time distributions with different moments. The combined probability density function represents the master transit time distribution and characterizes the intraannual and interannual variability of catchment storage and flow paths. Comparing the derived master transit time distributions of two research catchments (one humid and one semiarid) reveals differences in dominant hydrologic processes and dynamic water storage behavior, with the semiarid catchment generally reacting slower to precipitation events and containing a lower fraction of preevent water in the immediate hydrologic response.

What can flux tracking teach us about water age distribution patterns and their temporal dynamics?

“…flows from fast and slow model components, resulting in changing TTDs for individual storm events, depending on the contributions from the respective flow components. Recently some studies explicitly addressed the time-invariance topic in detail and allowed for a dynamic representation of flow path distributions (Botter et al, 2010Hrachowitz et al, 2010b;Morgenstern et al, 2010;McGuire and McDonnell, 2010; Van der Velde et al, 2010;Birkel et al, 2012a;Heidbüchel et al, 2012;Cvetkovic et al, 2012).…”

“…Due to the elemental difference between hydrologic response and particle response (e.g. Beven, 1981;Neal et al, 1988;Roa-Garcia and Weiler, 2010;Heidbüchel et al, 2012), standard conceptual models can rarely accommodate stream tracer dynamics. This is partly the result of stream tracer concentrations reflecting the actual particle movement by advective and diffusive processes at specific flow velocities along actual flow lines, potentially routing particles through the passive storage at depths below stream level, depending on the geology (e.g.…”

“…Nippgen et al, 2011) and transit time distribution (TTD), respectively (e.g. Heidbüchel et al, 2012). Barnes and Bonell (1996) suggested that both responses, stream flow and tracer concentration, can be accommodated in a conceptual model by introducing a storage component …”

Constitution of a catchment virtual observatory for sharing flow and transport models outputs

“…Several distribution types have been used in catchment studies, including the dispersion model (Kirchner et al, 2001;McGlynn et al, 8 2003;McGuire et al, 2002), the piston flow model (McGlynn et al, 2003), and exponentialpiston flow (Maloszewski and Zuber, 1996;McGlynn et al, 2003;McGuire et al, 2002;Timbe et al, 2014). The exponential distribution has been the most widely used (more than 60% of the studies in several recent reviews; McGuire and McDonnell, 2006;Mueller et al, 2013;Roa-Garcia and Weiler, 2010;Seeger and Weiler, 2014), though more recently, the gamma function has been recognized as more conceptually and mathematically suitable to represent catchment behaviour and mixing processes due to its short breakthrough time and long tail (Birkel et al, 2012;Dunn et al, 2010;Heidbüchel et al, 2012;Hrachowitz, 2011;Hrachowitz et al, 2010;Kirchner et al, 2001Kirchner et al, , 2000Soulsby et al, 2011).…”

“…Such steady-state systems are described with a single travel time distribution (Heidbüchel et al, 2012). While this simplification may realistically represent some humid catchments, in most environments, seasonally and event driven variations in precipitation and evapotranspiration can violate this assumption, leading to time-variant time distributions (Heidbüchel et al, 2012;Hrachowitz et al, 2010;Rinaldo et al, 2011;Van der Velde et al, 2015). In addition to low-frequency changes such as seasonal or climatic change, antecedent catchment wetness can vary between events, influencing time 10 distributions at a weekly scale (Birkel et al, 2011;Hrachowitz et al, 2009), and variation in the contribution of old and young water to the outlet can occur during a single event (Harman, 2015).…”