Unsteady transit time distribution (TTD) theory is a promising new approach for merging hydrologic and water quality models at the catchment scale. A major obstacle to widespread adoption of the theory, however, has been the specification of the StorAge Selection (SAS) function, which describes how the selection of water for outflow is biased by age. In this paper we hypothesize that some unsteady hydrologic systems of practical interest can be described, to first‐order, by a “shifted‐uniform” SAS that falls along a continuum between plug flow sampling (for which only the oldest water in storage is sampled for outflow) and uniform sampling (for which water in storage is sampled randomly for outflow). For this choice of SAS function, explicit formulae are derived for the evolving: (a) age distribution of water in storage; (b) age distribution of water in outflow; and (c) breakthrough concentration of a conservative solute under either continuous or impulsive addition. Model predictions conform closely to chloride and deuterium breakthrough curves measured previously in a sloping lysimeter subject to periodic wetting, although refinements of the model are needed to account for the reconfiguration of flow paths at high storage levels (the so‐called inverse storage effect). The analytical results derived in this paper should lower the barrier to applying TTD theory in practice, ease the computational demands associated with simulating solute transport through complex hydrologic systems, and provide physical insights that might not be apparent from traditional numerical solutions of the governing equations.
In this study, we explore the use of unsteady transit time distribution (TTD) theory to model solute transport in biofilters, a popular form of nature‐based or “green” storm water infrastructure (GSI). TTD theory has the potential to address many unresolved challenges associated with predicting pollutant fate and transport through these systems, including unsteadiness in the water balance (time‐varying inflows, outflows, and storage), unsteadiness in pollutant loading, time‐dependent reactions, and scale‐up to GSI networks and urban catchments. From a solution to the unsteady age conservation equation under uniform sampling, we derive an explicit expression for solute breakthrough during and after one or more storm events. The solution is calibrated and validated with breakthrough data from 17 simulated storms at a field‐scale biofilter test facility in Southern California, using bromide as a conservative tracer. TTD theory closely reproduces bromide breakthrough concentrations, provided that lateral exchange with the surrounding soil is accounted for. At any given time, according to theory, more than half of the water in storage is from the most recent storm, while the rest is a mixture of penultimate and earlier storms. Thus, key management endpoints, such as the pollutant treatment credit attributable to GSI, are likely to depend on the evolving age distribution of water stored and released by these systems.
more » « less- Award ID(s):
- 2021015
- NSF-PAR ID:
- 10449759
- Publisher / Repository:
- DOI PREFIX: 10.1029
- Date Published:
- Journal Name:
- Water Resources Research
- Volume:
- 57
- Issue:
- 2
- ISSN:
- 0043-1397
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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