Streambed

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Christian Schmidt - One of the best experts on this subject based on the ideXlab platform.

  • estimating time variable aerobic respiration in the Streambed by combining electrical conductivity and dissolved oxygen time series
    2016
    Co-Authors: Marie J. Kurz, Nico Trauth, M. Vieweg, Jan H. Fleckenstein, Andreas Musolff, Christian Schmidt
    Abstract:

    Aerobic respiration is an important component of in-stream metabolism. The larger part occurs in the Streambed, where it is difficult to directly determine actual respiration rates. Existing methods for determining respiration are based on indirect estimates from whole-stream metabolism or provide time invariant results estimated from oxygen consumption measurements in enclosed chambers that do not account for the influence of hydrological changes. In this study we demonstrate a simple method for determining time-variable hyporheic respiration. We use a windowed cross-correlation approach for deriving time-variable travel times from the naturally changing electrical conductivity signal that is transferred into the sediment. By combining the results with continuous in situ dissolved oxygen measurements, variable oxygen consumption rate coefficients in the Streambed are obtained. An empirical temperature relationship is derived and used for standardizing the respiration rate coefficients to isothermal conditions. For demonstrating the method, we compare two independent measurement spots in the Streambed, which were located upstream and downstream of an in-stream gravel bar and thus exposed strongly diverse travel times. The derived respiration rate results are in accordance with findings of other stream studies. By comparing the travel time and respiration rate coefficient (i.e., Damkohler number) we estimate the contribution of each to the oxygen consumption in the Streambed.

  • influence of water flux and redox conditions on chlorobenzene concentrations in a contaminated Streambed
    2011
    Co-Authors: Christian Schmidt, Marion Martienssen, E Kalbus
    Abstract:

    Significant natural attenuation may occur on the passage of groundwater plumes through Streambed sediments because of the transition from anaerobic to aerobic conditions and an increased microbial activity. Varying directions and magnitudes of water flow in the Streambed may enhance or inhibit the supply of oxygen to the Streambed and thus influence the redox zoning. In a field study at a small stream in the industrial area of Bitterfeld-Wolfen, we observed the variability of hydraulic gradients, Streambed temperatures, redox conditions and monochlorobenzene (MCB) concentrations in the Streambed over the course of 5 months. During the observation period, the hydrologic conditions changed from losing to gaining. Accordingly, the temperature-derived water fluxes changed from recharge to discharge. Redox conditions were highly variable between -170 and 368 mV in the shallow Streambed at a depth of 0.1 m below the Streambed surface. Deeper in the Streambed, at depths of 0.3 m and 0.5 m, the redox conditions were more stable between -198 and -81 mV and comparable to those typically found in the aquifer. MCB concentrations in the Streambed at 0.3 and 0.5 m depth increased with increasing upward water flux. The MCB concentrations in the shallow Streambed at 0.1 m depth appeared to be independent of the hydrologic conditions suggesting that degradation of MCB may have occured. Copyright (C) 2010 John Wiley & Sons, Ltd.

  • influence of aquifer and Streambed heterogeneity on the distribution of groundwater discharge
    2009
    Co-Authors: Christian Schmidt, E Kalbus, John Molson, Frido Reinstorf, Mario Schirmer
    Abstract:

    Abstract. The spatial distribution of groundwater fluxes through a Streambed can be highly variable, most often resulting from a heterogeneous distribution of aquifer and Streambed permeabilities along the flow pathways. Using a groundwater flow and heat transport model, we defined four scenarios of aquifer and Streambed permeability distributions to simulate and assess the impact of subsurface heterogeneity on the distribution of groundwater fluxes through the Streambed: (a) a homogeneous low-K Streambed within a heterogeneous aquifer; (b) a heterogeneous Streambed within a homogeneous aquifer; (c) a well connected heterogeneous low-K Streambed within a heterogeneous aquifer; and (d) a poorly connected heterogeneous low-K Streambed within a heterogeneous aquifer. The simulation results were compared with a base case scenario, in which the Streambed had the same properties as the aquifer, and with observed data. The results indicated that the aquifer has a stronger influence on the distribution of groundwater fluxes through the Streambed than the Streambed itself. However, a homogeneous low-K Streambed, a case often implemented in regional-scale groundwater flow models, resulted in a strong homogenization of fluxes, which may have important implications for the estimation of peak mass flows. The flux distributions simulated with heterogeneous low-K Streambeds were similar to the flux distributions of the base case scenario, despite the lower permeability. The representation of heterogeneous distributions of aquifer and Streambed properties in the model has been proven to be beneficial for the accuracy of flow simulations.

  • evaluation and field scale application of an analytical method to quantify groundwater discharge using mapped Streambed temperatures
    2007
    Co-Authors: Christian Schmidt, Brewster Conant, Marti Bayerraich, Mario Schirmer
    Abstract:

    Summary A method for calculating groundwater discharge through a Streambed on a sub-reach to a reach scale has been developed using data from plan-view mapping of Streambed temperatures at a uniform depth along a reach of a river or stream. An analytical solution of the one-dimensional steady-state heat-diffusion–advection equation was used to determine fluxes from observed temperature data. The method was applied to point measurements of Streambed temperatures used to map a 60 m long reach of a river by Conant Jr. [Conant Jr. B., 2004. Delineating and quantifying ground water discharge zones using Streambed temperatures. Ground Water 42(2), 243–257] and relies on the underlying assumption that Streambed temperatures are in a quasi-steady-state during the period of mapping. The analytical method was able to match the values and pattern of flux previously obtained using an empirical relationship that related Streambed temperatures to fluxes obtained from piezometers and using Darcy’s law. A second independent test of the analytical method using temperature mapping and seepage meter fluxes along a first-order stream confirmed the validity of the approach. The USGS numerical heat transport model VS2DH was also used to evaluate the thermal response of the Streambed sediments to transient variations in surface water temperatures and showed that quasi-steady-state conditions occurred for most, but not all, conditions. During mapping events in the winter, quasi-steady-state conditions were typically observed for both high and low groundwater discharge conditions, but during summer mapping events quasi-steady-state conditions were typically not achieved at low flux areas or where measurements were made at shallow depths. Major advantages of using this analytical method include: it can be implemented using a spreadsheet; it does not require the installation or testing of piezometers or seepage meters (although they would help to confirm the results); and it needs only a minimal amount of input data related to water temperatures and the thermal properties of water and the sediments. The field results showed the analytical solution tends to underestimate high fluxes. However, a sensitivity analysis of possible model inputs shows the solution is relatively robust and not particularly sensitive to small uncertainties in input data and can produce reasonable flux estimates without the need for calibration.

  • characterization of spatial heterogeneity of groundwater stream water interactions using multiple depth Streambed temperature measurements at the reach scale
    2006
    Co-Authors: Christian Schmidt, Marti Bayerraich, Mario Schirmer
    Abstract:

    Abstract. Streambed temperatures can be easily, accurately and inexpensively measured at many locations. To characterize patterns of groundwater-stream water interaction with a high spatial resolution, we measured 140 vertical Streambed temperature profiles along a 220 m section of a small man-made stream. Groundwater temperature at a sufficient depth remains nearly constant while stream water temperatures vary seasonally and diurnally. In summer, Streambed temperatures of groundwater discharge zones are relatively colder than downwelling zones of stream water. Assuming vertical flow in the Streambed, the observed temperatures are correlated to the magnitude of water fluxes. The water fluxes are then estimated by applying a simple analytical solution of the heat conduction-advection equation to the observed vertical temperature profiles. The calculated water fluxes through the Streambed ranged between 455 Lm−2 d−1 of groundwater discharging to the stream and approximately 10 Lm−2 d−1 of stream water entering the Streambed. The investigated reach was dominated by groundwater discharge with two distinct high discharge locations accounting for 50% of the total flux on 20% of the reach length.

Kenneth H Williams - One of the best experts on this subject based on the ideXlab platform.

  • seasonal manganese transport in the hyporheic zone of a snowmelt dominated river east river colorado usa
    2020
    Co-Authors: Savannah R Bryant, Cm Saup, Amelia R Nelson, Audrey H Sawyer, John N Christensen, Kenneth H Williams, Martin A Briggs, Michael J Wilkins
    Abstract:

    Manganese (Mn) plays a critical role in river-water quality because Mn-oxides serve as sorption sites for contaminant metals. The aim of this study is to understand the seasonal cycling of Mn in an alpine Streambed that experiences large spring snowmelt events and the potential responses to changes in snowmelt timing and magnitude. To address this goal, annual variations in river-water/groundwater interaction and Mn(aq) transport were measured and modeled in the bed of East River, Colorado, USA. In observations and numerical models, oxygenated river water containing dissolved organic carbon (DOC) mixes with groundwater rich in Mn(aq) in the Streambed. The mixing depth increases during spring snowmelt when river discharge increases, leading to a greater DOC supply to the hyporheic zone and net respiration of Mn-oxides, despite an enhanced supply of oxygen. As groundwater upwelling resumes during the subsequent baseflow period, Mn(aq)-rich groundwater mixes with oxygenated river water, resulting in net accumulation of Mn-oxides until the bed freezes in winter. To explore potential responses of Mn transport to different climate-induced hydrological regimes, three hydrograph scenarios were numerically modeled (historic, low-snow, and storm) for the Rocky Mountain region. In a warming climate, Mn(aq) export to the river decreases, and Mn(aq) oxidation is favored in the upper Streambed sediments over more of the year. One important implication is that the Streambed may have an increased sorption capacity for metals over more of the year, leading to potential changes in river-water quality.

  • hyporheic zone microbiome assembly is linked to dynamic water mixing patterns in snowmelt dominated headwater catchments
    2019
    Co-Authors: Cm Saup, Mm Tfaily, Savannah R Bryant, Amelia R Nelson, Kira Harris, Audrey H Sawyer, John N Christensen, Kenneth H Williams
    Abstract:

    Author(s): Saup, CM; Bryant, SR; Nelson, AR; Harris, KD; Sawyer, AH; Christensen, JN; Tfaily, MM; Williams, KH; Wilkins, MJ | Abstract: ©2019. American Geophysical Union. All Rights Reserved. Terrestrial and aquatic elemental cycles are tightly linked in upland fluvial networks. Biotic and abiotic mineral weathering, microbially mediated degradation of organic matter, and anthropogenic influences all result in the movement of solutes (e.g., carbon, metals, and nutrients) through these catchments, with implications for downstream water quality. Within the river channel, the region of hyporheic mixing represents a hot spot of microbial activity, exerting significant control over solute cycling. To investigate how snowmelt-driven seasonal changes in river discharge affect microbial community assembly and carbon biogeochemistry, depth-resolved pore water samples were recovered from multiple locations around a representative meander on the East River near Crested Butte, CO, USA. Vertical temperature sensor arrays were also installed in the Streambed to enable seepage flux estimates. Snowmelt-driven high river discharge led to an expanding zone of vertical hyporheic mixing and introduced dissolved oxygen into the Streambed that stimulated aerobic microbial respiration. These physicochemical processes contributed to microbial communities undergoing homogenizing selection, in contrast to other ecosystems where lower permeability may limit the extent of mixing. Conversely, lower river discharge conditions led to a greater influence of upwelling groundwater within the Streambed and a decrease in microbial respiration rates. Associated with these processes, microbial communities throughout the Streambed exhibited increasing dissimilarity between each other, suggesting that the earlier onset of snowmelt and longer periods of base flow may lead to changes in the composition (and associated function) of Streambed microbiomes, with consequent implications for the processing and export of solutes from upland catchments.

E Kalbus - One of the best experts on this subject based on the ideXlab platform.

  • influence of water flux and redox conditions on chlorobenzene concentrations in a contaminated Streambed
    2011
    Co-Authors: Christian Schmidt, Marion Martienssen, E Kalbus
    Abstract:

    Significant natural attenuation may occur on the passage of groundwater plumes through Streambed sediments because of the transition from anaerobic to aerobic conditions and an increased microbial activity. Varying directions and magnitudes of water flow in the Streambed may enhance or inhibit the supply of oxygen to the Streambed and thus influence the redox zoning. In a field study at a small stream in the industrial area of Bitterfeld-Wolfen, we observed the variability of hydraulic gradients, Streambed temperatures, redox conditions and monochlorobenzene (MCB) concentrations in the Streambed over the course of 5 months. During the observation period, the hydrologic conditions changed from losing to gaining. Accordingly, the temperature-derived water fluxes changed from recharge to discharge. Redox conditions were highly variable between -170 and 368 mV in the shallow Streambed at a depth of 0.1 m below the Streambed surface. Deeper in the Streambed, at depths of 0.3 m and 0.5 m, the redox conditions were more stable between -198 and -81 mV and comparable to those typically found in the aquifer. MCB concentrations in the Streambed at 0.3 and 0.5 m depth increased with increasing upward water flux. The MCB concentrations in the shallow Streambed at 0.1 m depth appeared to be independent of the hydrologic conditions suggesting that degradation of MCB may have occured. Copyright (C) 2010 John Wiley & Sons, Ltd.

  • influence of aquifer and Streambed heterogeneity on the distribution of groundwater discharge
    2009
    Co-Authors: Christian Schmidt, E Kalbus, John Molson, Frido Reinstorf, Mario Schirmer
    Abstract:

    Abstract. The spatial distribution of groundwater fluxes through a Streambed can be highly variable, most often resulting from a heterogeneous distribution of aquifer and Streambed permeabilities along the flow pathways. Using a groundwater flow and heat transport model, we defined four scenarios of aquifer and Streambed permeability distributions to simulate and assess the impact of subsurface heterogeneity on the distribution of groundwater fluxes through the Streambed: (a) a homogeneous low-K Streambed within a heterogeneous aquifer; (b) a heterogeneous Streambed within a homogeneous aquifer; (c) a well connected heterogeneous low-K Streambed within a heterogeneous aquifer; and (d) a poorly connected heterogeneous low-K Streambed within a heterogeneous aquifer. The simulation results were compared with a base case scenario, in which the Streambed had the same properties as the aquifer, and with observed data. The results indicated that the aquifer has a stronger influence on the distribution of groundwater fluxes through the Streambed than the Streambed itself. However, a homogeneous low-K Streambed, a case often implemented in regional-scale groundwater flow models, resulted in a strong homogenization of fluxes, which may have important implications for the estimation of peak mass flows. The flux distributions simulated with heterogeneous low-K Streambeds were similar to the flux distributions of the base case scenario, despite the lower permeability. The representation of heterogeneous distributions of aquifer and Streambed properties in the model has been proven to be beneficial for the accuracy of flow simulations.

Daniele Tonina - One of the best experts on this subject based on the ideXlab platform.

  • does Streambed heterogeneity matter for hyporheic residence time distribution in sand bedded streams
    2016
    Co-Authors: Daniele Tonina, Felipe P J De Barros, Alessandra Marzadri, Alberto Bellin
    Abstract:

    Abstract Stream water residence times within Streambed sediments are key values to quantify hyporheic processes including sediment thermal regime, solute transient storage, dilution rates and biogeochemical transformations, such as those controlling degassing nitrous oxide. Heterogeneity of the Streambed sediment hydraulic properties has been shown to be potentially an important factor to characterize hyporheic processes. Here, we quantify the importance of Streambed heterogeneity on residence times of dune-like bedform induced hyporheic fluxes at the bedform and reach scales. We show that heterogeneity has a net effect of compression of the hyporheic zone (HZ) toward the Streambed, changing HZ volume from the homogenous case and thus inducing remarkable differences in the flow field with respect to the homogeneous case. We unravel the physical conditions for which the commonly used homogenous field assumption is applicable for quantifying hyporheic processes thus explaining why predictive measures based on a characteristic residence time, like the Damkohler number, are robust in heterogeneous sand bedded streams.

  • Spatiotemporal variability of hyporheic exchange through a pool-riffle-pool sequence
    2013
    Co-Authors: Frank P. Gariglio, Daniele Tonina, Charles H Luce
    Abstract:

    tream water enters and exits the Streambed sediment due to hyporheic fluxes, which stem primarily from the interaction between surface water hydraulics and Streambed morphology. These fluxes sustain a rich ecotone, whose habitat quality depends on their direction and magnitude. The spatiotemporal variability of hyporheic fluxes is not well understood over several temporal scales and consequently, we studied their spatial and temporal variation over a pool-riffle-pool sequence at multiple locations from winter to summer. We instrumented a pool-riffle-pool sequence of Bear Valley Creek, an important salmonid spawning gravel-bed stream in central Idaho, with temperature monitoring probes recording at high temporal resolution (12 minute intervals). Using the thermal time series, weekly winter season seepage fluxes were calculated with a steady-state analytical solution and spring-summer fluxes with a new analytical solution that can also quantify the Streambed thermal properties. Longitudinal pool-riffle-pool conceptualizations of downwelling and upwelling behavior were generally observed, except during the winter season when seepage fluxes tended toward downwelling conditions. Seepage fluxes near the edges of the channel were typically greater than fluxes near the center of the channel, and demonstrated greater seasonal variability. Results show that the interaction between streamflow and Streambed topography has a primary control near the center of the channel, whereas the interaction between stream water and groundwater table has a primary control on seepage fluxes near the banks of the stream.

  • solutions for the diurnally forced advection diffusion equation to estimate bulk fluid velocity and diffusivity in Streambeds from temperature time series
    2013
    Co-Authors: Charles H Luce, Frank P. Gariglio, Daniele Tonina, Ralph Applebee
    Abstract:

    [1] Work over the last decade has documented methods for estimating fluxes between streams and Streambeds from time series of temperature at two depths in the Streambed. We present substantial extension to the existing theory and practice of using temperature time series to estimate Streambed water fluxes and thermal properties, including (1) a new explicit analytical solution to predict one-dimensional fluid velocity from amplitude and phase information; (2) an inverse function, also with explicit formulation; (3) methods to estimate fluid velocity from temperature measurements with unknown depths; (4) methods to estimate thermal diffusivity from the temperature time series when measurement depths are known; (5) methods to track Streambed elevation between two sensors, given knowledge of the thermal diffusivity from (4) above; (6) methods to directly calculate the potential error in velocity estimates based on the measurement error characteristics ; and (7) methods for validation of parameter estimates. We also provide discussion and theoretical insights developed from the solutions to better understand the physics and scaling of the propagation of the diurnal temperature variation through the Streambed. In particular, we note that the equations developed do not replace existing equations applied to the analysis, rather they are new equations representing new aspects of the process, and, as a consequence, they increase the amount of information that can be derived from a particular set of thermal measurements.

  • morphodynamic controls on redox conditions and on nitrogen dynamics within the hyporheic zone application to gravel bed rivers with alternate bar morphology
    2012
    Co-Authors: Alessandra Marzadri, Daniele Tonina, Alberto Bellin
    Abstract:

    [1] Hyporheic flows, which stem from the interaction between stream flow and bedform, transport solute-laden surface waters into the Streambed sediments, where reactive solutes undergo biogeochemical transformations. Despite the importance of hyporheic exchange on riverine ecosystem and biogeochemical cycles, research is limited on the effects of hyporheic fluxes on the fate of reactive solutes within the hyporheic zone. Consequently, we investigate the controls of hyporheic flowpaths, which we link to stream morphology and streamflow, on prevailing hyporheic redox conditions and on biogeochemical transformations occurring within Streambeds. We focus on the dissolved inorganic reactive forms of nitrogen, ammonium and nitrate, because nitrogen is one of the most common reactive solutes and an essential nutrient found in stream waters. Our objectives are to explore the influence of stream morphology, hyporheic water temperature and relative abundance of ammonium and nitrate, on transformation of ammonium, removal of nitrates and production of nitrous oxide, a potent greenhouse gas. We address our objectives with analytical solutions of the Multispecies Reactive Advection-Dispersion Equation coupled with linearized Monod's kinetics and analytical solutions of the hyporheic flow for alternate-bar morphology. We introduce a new Damkohler number,Da, defined as the ratio between the median hyporheic residence time and the time scale of oxygen consumption, which we prove to be a good indicator of where aerobic or anaerobic conditions prevail. In addition, Dais a key index to quantify hyporheic nitrification and denitrification efficiencies and defines a new theoretical framework for scaling results at both the morphological-unit and stream-reach scales.

Mario Schirmer - One of the best experts on this subject based on the ideXlab platform.

  • influence of aquifer and Streambed heterogeneity on the distribution of groundwater discharge
    2009
    Co-Authors: Christian Schmidt, E Kalbus, John Molson, Frido Reinstorf, Mario Schirmer
    Abstract:

    Abstract. The spatial distribution of groundwater fluxes through a Streambed can be highly variable, most often resulting from a heterogeneous distribution of aquifer and Streambed permeabilities along the flow pathways. Using a groundwater flow and heat transport model, we defined four scenarios of aquifer and Streambed permeability distributions to simulate and assess the impact of subsurface heterogeneity on the distribution of groundwater fluxes through the Streambed: (a) a homogeneous low-K Streambed within a heterogeneous aquifer; (b) a heterogeneous Streambed within a homogeneous aquifer; (c) a well connected heterogeneous low-K Streambed within a heterogeneous aquifer; and (d) a poorly connected heterogeneous low-K Streambed within a heterogeneous aquifer. The simulation results were compared with a base case scenario, in which the Streambed had the same properties as the aquifer, and with observed data. The results indicated that the aquifer has a stronger influence on the distribution of groundwater fluxes through the Streambed than the Streambed itself. However, a homogeneous low-K Streambed, a case often implemented in regional-scale groundwater flow models, resulted in a strong homogenization of fluxes, which may have important implications for the estimation of peak mass flows. The flux distributions simulated with heterogeneous low-K Streambeds were similar to the flux distributions of the base case scenario, despite the lower permeability. The representation of heterogeneous distributions of aquifer and Streambed properties in the model has been proven to be beneficial for the accuracy of flow simulations.

  • evaluation and field scale application of an analytical method to quantify groundwater discharge using mapped Streambed temperatures
    2007
    Co-Authors: Christian Schmidt, Brewster Conant, Marti Bayerraich, Mario Schirmer
    Abstract:

    Summary A method for calculating groundwater discharge through a Streambed on a sub-reach to a reach scale has been developed using data from plan-view mapping of Streambed temperatures at a uniform depth along a reach of a river or stream. An analytical solution of the one-dimensional steady-state heat-diffusion–advection equation was used to determine fluxes from observed temperature data. The method was applied to point measurements of Streambed temperatures used to map a 60 m long reach of a river by Conant Jr. [Conant Jr. B., 2004. Delineating and quantifying ground water discharge zones using Streambed temperatures. Ground Water 42(2), 243–257] and relies on the underlying assumption that Streambed temperatures are in a quasi-steady-state during the period of mapping. The analytical method was able to match the values and pattern of flux previously obtained using an empirical relationship that related Streambed temperatures to fluxes obtained from piezometers and using Darcy’s law. A second independent test of the analytical method using temperature mapping and seepage meter fluxes along a first-order stream confirmed the validity of the approach. The USGS numerical heat transport model VS2DH was also used to evaluate the thermal response of the Streambed sediments to transient variations in surface water temperatures and showed that quasi-steady-state conditions occurred for most, but not all, conditions. During mapping events in the winter, quasi-steady-state conditions were typically observed for both high and low groundwater discharge conditions, but during summer mapping events quasi-steady-state conditions were typically not achieved at low flux areas or where measurements were made at shallow depths. Major advantages of using this analytical method include: it can be implemented using a spreadsheet; it does not require the installation or testing of piezometers or seepage meters (although they would help to confirm the results); and it needs only a minimal amount of input data related to water temperatures and the thermal properties of water and the sediments. The field results showed the analytical solution tends to underestimate high fluxes. However, a sensitivity analysis of possible model inputs shows the solution is relatively robust and not particularly sensitive to small uncertainties in input data and can produce reasonable flux estimates without the need for calibration.

  • characterization of spatial heterogeneity of groundwater stream water interactions using multiple depth Streambed temperature measurements at the reach scale
    2006
    Co-Authors: Christian Schmidt, Marti Bayerraich, Mario Schirmer
    Abstract:

    Abstract. Streambed temperatures can be easily, accurately and inexpensively measured at many locations. To characterize patterns of groundwater-stream water interaction with a high spatial resolution, we measured 140 vertical Streambed temperature profiles along a 220 m section of a small man-made stream. Groundwater temperature at a sufficient depth remains nearly constant while stream water temperatures vary seasonally and diurnally. In summer, Streambed temperatures of groundwater discharge zones are relatively colder than downwelling zones of stream water. Assuming vertical flow in the Streambed, the observed temperatures are correlated to the magnitude of water fluxes. The water fluxes are then estimated by applying a simple analytical solution of the heat conduction-advection equation to the observed vertical temperature profiles. The calculated water fluxes through the Streambed ranged between 455 Lm−2 d−1 of groundwater discharging to the stream and approximately 10 Lm−2 d−1 of stream water entering the Streambed. The investigated reach was dominated by groundwater discharge with two distinct high discharge locations accounting for 50% of the total flux on 20% of the reach length.