skip to main content

Title: Solute Transport Through Unsteady Hydrologic Systems Along a Plug Flow‐To‐Uniform Sampling Continuum

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.

more » « less
Award ID(s):
Author(s) / Creator(s):
Publisher / Repository:
DOI PREFIX: 10.1029
Date Published:
Journal Name:
Water Resources Research
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. Abstract

    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
  2. Abstract

    Understanding transit times (TT) and residence times (RT) distributions of water in catchments has recently received a great deal of attention in hydrologic research since it can inform about important processes relevant to the quality of water delivered by streams and landscape resilience to anthropogenic inputs. The theory of transit time distributions (TTD) is a practical framework for understanding TT of water in natural landscapes but, due to its lumped nature, it can only hint at the possible internal processes taking place in the subsurface. While allowing for the direct observation of water movement, Electrical Resistivity Imaging (ERI) can be leveraged to better understand the internal variability of water ages within the subsurface, thus enabling the investigation of the physical processes controlling the time‐variability of TTD. In this study, we estimated time‐variable TTD of a bench‐scale bare‐soil sloping soil lysimeter through the StorAge Selection (SAS) framework, a traditional lumped‐systems method, based on sampling of output tracer concentrations, as well as through an ERI SAS one, based on spatially distributed images of water ages. We compared the ERI‐based SAS results with the output‐based estimates to discuss the viability of ERI at laboratory experiments for understanding TTD. The ERI‐derived images of the internal evolution of water ages were able to elucidate the internal mechanisms driving the time‐variability of ages of water being discharged by the system, which was characterized by a delayed discharge of younger water starting at the highest storage level and continuing throughout the water table recession.

    more » « less
  3. Abstract

    Spatially integrated transport models have been applied widely to model hydrologic transport. However, we lack simple and process‐based theoretical tools to predict the transport closures—transit time distributions (TTDs) and StorAge Selection (SAS) functions. This limits our ability to infer characteristics of hydrologic systems from tracer observations and to make first‐order estimates of SAS functions in catchments where no tracer data is available. Here we present a theoretical framework linking TTDs and SAS functions to hydraulic groundwater theory at the hillslope scale. For hillslopes where the saturated hydraulic conductivity declines exponentially with depth, analytical solutions for the closures are derived that can be used as hypotheses to test against data. In the simplest form, the hillslope SAS function resembles a uniform or exponential distribution (corresponding to flow pathways in the saturated zone) offset from zero by the storage in the unsaturated zone that does not contribute to discharge. The framework is validated against nine idealized virtual hillslopes constructed using a 2‐D Richards equation‐based model, and against data from tracer experiments in two artificial hillslopes. Modeled internal age, life expectancy, and transit time structures reproduce theoretical predictions. The experimental data also support the theory, though further work is needed to account for the effects of time‐variability. The shape and tailing of TTDs and their power spectra are discussed. The theoretical framework yields several dimensionless numbers that can be used to classify hillslope scale flow and transport dynamics and suggests distinct water age structures for high or low Hillslope number.

    more » « less
  4. Abstract

    Accurately quantifying and predicting the reactive transport of nitrate () in hydrologic systems continues to be a challenge, due to the complex hydrological and biogeochemical interactions that underlie this transport. Recent advances related to time‐variant water age have led to a new method that probes water mixing and selection behaviors using StorAge Selection (SAS) functions. In this study, SAS functions were applied to investigate storage, water selection behaviors, and export regimes in a tile‐drained corn‐soybean field. The natural abundance stable nitrogen and oxygen isotopes of tile drainage were also measured to provide constraints on biogeochemical transformations. The SAS functions, calibrated using chloride measurements at tile drain outlets, revealed a strong young water preference during tile discharge generation. The use of a time‐variant SAS function for tile discharge generated unique water age dynamics that reveal an inverse storage effect driven by the activation of preferential flow paths and mechanically explain the observed variations in isotopes. Combining the water age estimates with isotope fingerprinting shed new light on export dynamics at the tile‐drain scale, where a large mixing volume and the lack of a strong vertical contrast in concentration resulted in chemostatic export regimes. For the first time, isotopes were embedded into a water age‐based transport model to model reactive transport under transient conditions. The results of this modeling study provided a proof‐of‐concept for the potential of coupling water age modeling with isotope analysis to elucidate the mechanisms driving reactive transport.

    more » « less
  5. Abstract

    Spatially integrated water transport dynamics at the hillslope scale have rarely been observed directly, and underlying physical mechanisms of those dynamics are poorly understood. We present time‐variable transit time distributions and StorAge Selection (SAS) functions for a 28 days tracer experiment conducted at the Landscape Evolution Observatory, Biosphere 2, the University of Arizona, AZ, USA. The observed form of the SAS functions is concave, meaning that older water in the hillslope was preferentially discharged than younger water. The concavity is, in part, explained by the relative importance of advective and diffusive water dynamics and by the geomorphologic structure of the hillslopes. A simple numerical examination illustrates that, for straight plan‐shaped hillslopes, the saturated zone SAS function is concave when the hillslope Péclet (Pe) number is large (and thus when the advective water dynamics are more pronounced). We also investigated the effect of hillslope planform geometry on the saturated zone SAS function using a model and found that the more convergent the plan shape is, the more concave the SAS function is. A numerical examination indicates that the unsaturated zone SAS function is concave for straight and convergent hillslopes when the soil thickness is uniform. The concavity of those subcomponent SAS functions signifies that the hillslope scale SAS function is concave for straight or convergent plan shape hillslopes when the hillslope Pe number is high.

    more » « less