Elsevier

Journal of Hydrology

Volume 396, Issues 3–4, 13 January 2011, Pages 277-291
Journal of Hydrology

Influence of distributed flow losses and gains on the estimation of transient storage parameters from stream tracer experiments

https://doi.org/10.1016/j.jhydrol.2010.11.018Get rights and content

Abstract

Interactions between mobile stream water and transient storage zones have been the subject of careful attention for decades. However, few studies have considered explicitly the influence of water exchange between the channel and neighbouring hydrological units when modelling transient storage processes, especially the lateral inflow coming from hillslope contributions and outflow to a deep aquifer or to hyporheic flow paths extending beyond the study reach. The objective of this study was to explore the influence of different conceptualizations of these hydrologic exchanges on the estimation of transient storage parameters. Slug injections of sodium chloride (NaCl) were carried out in eight contiguous reaches in the Cotton Creek Experimental Watershed (CCEW), located in south-east British Columbia. Resulting breakthrough curves were subsequently analysed using a Transient Storage Model (TSM) in an inverse modelling framework. We estimated solute transport parameters using three distinct, hypothetical spatial patterns of lateral inflow and outflow, all based on variations of the same five-parameter model structure. We compared optimized parameter values to those resulting from a distinct four-parameter model structure meant to represent the standard application of the TSM, in which only lateral inflow was implemented for net gaining reaches or only lateral outflow for net losing reaches. In the five-parameter model, solute mass was stored predominantly in the transient storage zone and slowly released back to the stream. Conversely, solute mass was predominantly removed from the stream via flow losses in the four-parameter model structure. This led to contrasting estimates of solute transport parameters and subsequent interpretation of solute transport dynamics. Differences in parameter estimates across variations of the five-parameter model structure were small yet statistically significant, except for the transient storage exchange rate coefficient α, for which unique determination was problematic. We also based our analysis on Fmed200, the fraction of median transport time due to transient storage. Differences across configurations in Fmed200 estimates were consistent but small when compared to the variability of Fmed200 among reaches. Optimized parameter values were influenced dominantly by the model structure (four versus five parameters) and then by the conceptualization of spatial arrangement of lateral fluxes along the reach for a set model structure. When boundary conditions are poorly defined, the information contained in the stream tracer breakthrough curve is insufficient to identify a single, unambiguous model structure representing solute transport simulations. Investigating lateral fluxes prior to conducting a study on transient storage processes is necessary, as assuming a certain spatial organization of these fluxes might set ill-defined bases for inter-reach comparisons. Given the difficulty in quantifying the spatial patterns and magnitudes of lateral inputs and outputs, we recommend small-scale laboratory tracer experiments with well-defined and variable boundary conditions as a complement to field studies to provide new insights into stream solute dynamics.

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:

  • The reach is concurrently gaining and losing water over its whole length.

  • The upstream half of the reach is gaining water while its downstream half is losing water.

  • 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:Ct=-QACx+1AxADCx+qLatInA(CL-C)+α(CS-C)dCSdt=αAAS(C-CS)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,

References (37)

  • S.H. Ensign et al.

    In-channel transient storage and associated nutrient retention: evidence from experimental manipulations

    Limnology and Oceanography

    (2005)
  • M.N. Gooseff et al.

    Determining in-channel (dead zone) transient storage by comparing solute transport in a bedrock channel-alluvial channel sequence, Oregon

    Water Resources Research

    (2005)
  • R. Haggerty et al.

    On the late-time behavior of tracer test breakthrough curves

    Water Resources Research

    (2000)
  • R. Haggerty et al.

    Power-law residence time distribution in the hyporheic zone of a 2nd-order mountain stream

    Geophysical Research Letters

    (2002)
  • R.O. Hall et al.

    Relating nutrient uptake with transient storage in forested mountain streams

    Limnology and Oceanography

    (2002)
  • J.W. Harvey et al.

    Evaluating the reliability of the stream tracer approach to characterize stream-subsurface water exchange

    Water Resources Research

    (1996)
  • M.C. Hill et al.

    Effective groundwater model calibration: with analysis of data, sensitivities, predictions, and uncertainty

    (2007)
  • D.D. Huff et al.

    Flow variability and hillslope hydrology

    Earth Surface Processes and Landforms

    (1982)
  • Cited by (22)

    • Calibrating pollutant dispersion in 1-D hydraulic models of river networks

      2015, Journal of Hydro-Environment Research
      Citation Excerpt :

      Hence, Bencala and Walters (1983) introduced the effect of the transient storage in the right-hand side of Eq. (1). Such model has been widely used to better understand physical processes in experimental results (Cheong and Seo (2003); Gooseff et al. (2005); Wörman and Wachniew (2007); Bottacin-Busolin et al. (2011); Szeftel et al. (2011) among others). However, it remains difficult to be applied in predictive models since it introduces two additional variables (solute concentration and cross-section area of the storage zone) and one additional parameter (stream storage exchange coefficient), which may be difficult to evaluate.

    • Estimating instream constituent loads using replicate synoptic sampling, Peru Creek, Colorado

      2013, Journal of Hydrology
      Citation Excerpt :

      Due to this possibility, tracer-based estimates of streamflow must be checked for mass conservation, an exercise that requires a secondary, independent estimate of streamflow. Possible techniques that provide this secondary estimate include traditional streamflow measurements (by current meters or ADV), slug tracer injections (Covino et al., 2010; Szeftel et al., 2011), and/or flume measurements. Experimental results (Schmadel et al., 2010) indicate that incomplete lateral mixing leads to considerable uncertainty in slug-based estimates of streamflow, and this issue is pertinent to the present application due to wide cross-sections (Section 2).

    • Do transient storage parameters directly scale in longer, combined stream reaches? Reach length dependence of transient storage interpretations

      2013, Journal of Hydrology
      Citation Excerpt :

      Recent work on stream flow mass balances (Covino and McGlynn, 2007; Payn et al., 2009) suggest that the conceptual model of only net gains influencing stream tracer concentrations is naïve. Furthermore, it has been shown that ignoring these stream water (and solute) exchanges influences transient storage modeling results (Szeftel et al., 2011). However, there is not enough additional information to constrain gross gains and losses of stream flow for sub-reaches or the entire experimental reach at this site.

    View all citing articles on Scopus
    View full text