Time-variable transit time distributions and transport: Theory and application to storage-dependent transport of chloride in a watershed

Abstract

Transport processes and pathways through many hydrodynamic systems vary over time, often driven by variations in total water storage. This paper develops a very general approach to modeling unsteady transport through an arbitrary control volume (such as a watershed) that accounts for temporal variability in the underlying transport dynamics. Controls on the selection of discharge from stored water are encapsulated in probability distributions X Q ðS T ; tÞ of age-ranked storage S T (the volume of water in storage ranked from youngest to oldest). This framework is applied to a long-term record of rainfall and streamflow chloride in a small, humid watershed at Plynlimon, UK. While a time-invariant gamma distribution for X Q produced a good fit to data, the fit was significantly improved when the distribution was allowed to vary with catchment storage. However, the variation was inverse to that of a ''well-mixed'' system where storage has a pure dilution effect. Discharge at high storage was predicted to contain a larger fraction of recent event water than at low storage. The effective volume of storage involved in transport was 3411 mm at mean catchment wetness, but declined by 71 mm per 1 mm of additional catchment storage, while the fraction of event water in discharge increased by 1.4%. This ''inverse storage effect'' is sufficient to reproduce the observed long-memory 1=f fractal spectral structure of stream chloride. Metrics quantifying the strength and direction of storage effects are proposed as useful signatures, and point toward a unified framework for observing and modeling coupled watershed flow and transport.

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

“…The SAS function approach tracks water ages in storage using "age-ranked" storage ( ), which is the cumulative sum of water in storage since the time of rainfall ( , absolute age of water) van der Velde et al, 2012;Harman, 2015). Values of represent the youngest cumulative sum of water in storage (e.g.…”

Residence time distributions for hydrologic systems: Mechanistic foundations and steady-state analytical solutions

“…Its analog, noted in this framework, has been successively called "Age function", "Storage Outflow Probability", and lately, the cumulative of the StorAge Selection (SAS) function (Harman, 2015;Queloz et al, 2015;van der Velde et al, 2012). It is defined by: constitutes an appealing alternative for preliminary study of systems in which none of the physically-based RTDs can be clearly preferred.…”

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

“…Most studies assume that travel time distributions are time invariant, with no seasonal or interannual changes in the overall volume of stored water (Harman, 2015) and relatively short residence times (Van der Velde et al, 2012). Such steady-state systems are described with a single travel time distribution (Heidbüchel et al, 2012).…”

“…Observatory for sharing models outputs Thomas et al 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). In summary, travel time distributions characterize multi-scale and multi-process transport mechanisms in surface and subsurface systems, which vary in time and space (Eberts 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 timeObservatory for sharing models outputs Thomas et al 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). In summary, travel time distributions characterize multi-scale and multi-process transport mechanisms in surface and subsurface systems, which vary in time and space (Eberts et al, 2012).…”