Influence of distributed flow losses and gains on the estimation of transient storage parameters from stream tracer experiments
Research highlights
► Specification of spatially distributed lateral fluxes affects solute transport parameter estimates. ► Information contained on the breakthrough curve alone is insufficient to select the appropriate model structure. ► Implementation of qLatOut, the lateral ouflow, in OTIS leads to solute mass to groundwater. ► The absence of implementation of qLatOut in OTIS promotes the storage of solute mass in the transient storage zone.
Introduction
Transient storage plays a key role in the transport and fate of solutes in streams. It encompasses hyporheic exchange and in-stream storage in pools or other regions of slow-moving water. Solute transport dynamics have often been characterized using tracer experiments at the reach scale. This technique involves the estimation of parameters in a transient storage model (TSM) to provide an optimal fit between the simulated tracer breakthrough curve and an experimental tracer breakthrough curve resulting from a controlled injection of dissolved tracer. Fitted model parameters reflect reach-integrated solute transport dynamics and are typically interpreted in relation to the magnitude of transient storage and its variation among streams and with stream discharge (Worman, 1998, Wondzell, 2006, Lautz and Siegel, 2007). Exchange between the stream water and the different transient storage zones has been modelled with a first-order mass transfer (Bencala and Walters, 1983), a one-dimensional diffusive flux (Jackman et al., 1984, Worman, 2000) or various probability density functions for residence time distribution such as power law or gamma distributions (Haggerty et al., 2000). All models show similar results for shorter time scales, but power law or gamma residence time distributions perform better for longer time periods (Haggerty et al., 2000). In recent years, many studies have modelled transient storage effects via the One-dimensional Transport with Inflow and Storage model structure (OTIS) (Runkel, 1998).
Due to their spatially integrated nature, reach-scale tracer experiments do not provide information on the sub-reach scale variability of solute transport dynamics. For instance, it is difficult to separate the effects of the hyporheic zone from that of in-stream pools on solute retention. Recent studies have attempted to differentiate the magnitude and timing of exchange with in-stream pools versus the hyporheic zone using one or more of the following approaches: tracer experiments on bedrock reaches, where hyporheic exchange can be assumed to be negligible; tracer experiments at the scale of individual channel units; and by using hydrometric measurements to provide an independent estimate hyporheic exchange via Darcy’s law (Gooseff et al., 2005, Gooseff et al., 2008, Hall et al., 2002, Scordo and Moore, 2009, Stofleth et al., 2008).
In addition to the processes of advection, dispersion and transient storage, TSMs have to account for lateral inflow and outflow, especially for simulating nutrient transport. Water flow and solute mobilization usually originate on hillslopes with downslope flow and solute transport by surface and/or subsurface flow paths. Water and solutes then enter the stream directly or via the hyporheic zone, ultimately to be transported in the advective part of the stream. We define lateral inflow as the discharge from the hillslope (or deeper groundwater) to the stream and lateral outflow as the flow from the stream to deep infiltration into the groundwater and substratum or the flow through hyporheic flow paths that extend beyond the (spatial or temporal) domain of study. Mechanisms driving water delivery from or to the stream are highly variable in time and space across a broad range of landscapes and land uses (Genereux et al., 1993, Huff et al., 1982, Kuraś et al., 2008, Shaman et al., 2004).
The extent to which lateral inflow and outflow affect TSM parameterization has been widely overlooked. OTIS is most suited to the present study because its structure accounts for both lateral inflow and lateral outflow. A standard parameterization of lateral fluxes in OTIS first involves the computation of the reach water balance from the difference in measured discharge between the downstream and upstream boundaries of the experimental reach. Either lateral inflow or later outflow is then applied to the reach depending on whether it is net gaining or losing water, respectively. However, it is possible for a stream reach to alternate between gaining and losing segments over distances of tens to hundreds of meters (e.g., Story et al., 2003, Ruehl et al., 2006). In this situation, the standard approach would not provide an accurate representation of the solute mass balance, potentially distorting the parameters representing downstream transport and transient storage.
In the present study, we assess the sensitivity of a TSM parameterization to the specified spatial pattern of lateral fluxes from and to the stream using tracer experiments at the reach scale. Solute transport dynamics were simulated under three contrasting spatial configurations of lateral fluxes:
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The reach is concurrently gaining and losing water over its whole length.
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The upstream half of the reach is gaining water while its downstream half is losing water.
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The upstream half of the reach is losing water while its downstream half is gaining water.
Simulation results were compared to those from the standard application of the TSM. From the comparison of transient storage model simulations specific to each spatial configuration of lateral fluxes, we address the following questions: (1) Do fitted transient storage model parameters depend on the specification of the spatial configuration of lateral fluxes? (2) How large is the uncertainty caused by lack of knowledge of the spatial organization of lateral fluxes relative to the variability in fitted model parameters among reaches?
Section snippets
Study site description
Investigations were carried out in the 17.4 km2 Cotton Creek Experimental Watershed (CCEW) located in the Kootenay Mountains in south-eastern British Columbia, Canada (Fig. 1). This study is part of a larger research project investigating snowmelt, runoff and sediment transport processes and their response to forest disturbances including logging practices and the ongoing mountain pine beetle epidemic. Mean annual precipitation in the area is 650 mm, with snow accumulation and melt being the
Solute transport modelling
We applied OTIS, a one-dimensional finite-difference solute transport model that solves for solute concentrations in the stream and transient storage zone (Runkel, 1998). OTIS accounts for advection, dispersion, lateral fluxes and first-order mass transfer between stream and transient storage domains, as represented by the following equations:where C, CS and CL are the solute concentrations in the stream, transient storage zone and
Assessment of goodness-of-fit
For each of the 32 simulations (four configurations of lateral fluxes for each of eight reaches), the non-linear optimization algorithm implemented in UCODE_2005 successfully converged toward a solution (best estimate for Θ). Two reaches have been selected in Fig. 5 to illustrate the goodness-of-fit of the simulated BTCs from all four configurations to the experimental BTC. Semi-log plots of the same BTCs highlight the departure of simulated BTCs from the experimental ones at the tail of the
Patterns of parameter estimates among configurations InBh–InDn–InUp
It remains unclear why estimates of D and α did not show strong contrasts among configurations, although we suspect the lack of contrast resulted from tradeoffs between parameter values during the optimization process to accommodate the shape of the observed BTC. In the following, we focus on interpreting the patterns of A, qLatOut and AS, for which strong contrasts exist among configurations. The systematic variations in the parameter estimates among configurations can be interpreted in
Conclusion
This study has shown that comparisons of transient storage model parameters among reaches or as a function of time at a single reach may be confounded not only by the currently recognized sources of uncertainty in analysing BTCs, but also by incorrect specification of the spatial patterns of inflow and outflows. Model parameterization is thus highly dependent on the model structure. Moreover, the stream BTC alone does not provide enough information to select the appropriate model structure and
Acknowledgements
This study has been supported financially by grants Y073294 and Y092214 from the Forest Science Program of the Forest Investment Initiative of British Columbia. The authors are indebted to Rob Runkel for his extensive comments about the structure and interpretation of output from OTIS. We thank two anonymous reviewers whose comments greatly improved an earlier version of this manuscript, Michael Gooseff and Eileen Poeter for their advices regarding the implementation of OTIS within UCODE_2005,
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