ArticlePDF Available

An evaluation of analytical stream to groundwater exchange models: A comparison of gross exchanges based on different spatial flow distribution assumptions

Authors:
  • Headwaters Hydrology

Abstract

In this paper, a new method for estimating gross gains and losses between streams and groundwater is developed and evaluated against two existing approaches. These three stream to groundwater exchange (SGE) estimation methods are distinct in their assumptions on the spatial distribution of the inflowing and outflowing fluxes along the stream. The two existing methods assume that the fluxes are independent and in a specific sequence, while the third and newly derived method assumes that both fluxes occur simultaneously and uniformly throughout the stream. The analytic expressions in connection to the underlying assumptions are investigated through numerical stream simulations to evaluate the individual and mutual dynamics of the SGE estimation methods and to understand the causes for the differences in performance. The results show that the three methods produce significantly different results and that the mean absolute normalized error can have up to an order of magnitude difference between the methods. These differences between the SGE methods are entirely due to the assumptions of the SGE spatial dynamics of the methods, and the performance for a particular approach strongly decreases if its assumptions are not fulfilled. The assessment of the three methods through numerical simulations, representing a variety of SGE dynamics, shows that the method introduced, considering simultaneous stream gains and losses, presents overall the highest performance according to the simulations. As the existing methods provide the minimum and maximum realistic values of SGE within a stream reach, all three methods could be used in conjunction for a full range of estimates. These SGE methods can also be used in conjunction with other end-member mixing models to acquire even more hydrologic information as both require the same type of input data.
A preview of the PDF is not available
... The surface application of manure slurry as performed in the HOAL catchment volatilizes significant amounts of ammonia from the slurry into the atmosphere. Many studies have measured or estimated the ammonia volatilization from manure slurry and have found that there is a wide range in the rates (Huijsmans et al., 2003;Misselbrook et al., 2004;Mkhabela et al., 2009;Gordon et al., 2001;Chantigny et al., 2004;Moal et al., 1995). We decided to assume that 35% of the manure application was lost as ammonia volatilization based on both (Huijsmans et al., 2003;Misselbrook et al., 2004), because the value is consistent and fairly average throughout the literature. ...
... The end member mixing analysis (EMMA) performed on the outlet baseflow used mass balance equations for a two end member EMMA (Exner-Kittridge et al., 2014). The aggregated nitrate concentrations of known deep aquifer inputs (i.e. ...
Full-text available
Article
Abstract Our study examines the source aquifers and stream inputs of the seasonal water and nitrogen dynamics of a headwater agricultural catchment to determine the dominant driving forces for the seasonal dynamics in the surface water nitrogen loads and concentrations. We found that the alternating aquifer contributions throughout the year of the deep and shallow aquifers were the main cause for the seasonality of the nitrate concentration. The deep aquifer water typically contributed 75% of the total outlet discharge in the summer and 50% in the winter when the shallow aquifer recharges due to low crop evapotranspiration. The shallow aquifer supplied the vast majority of the nitrogen load to the stream due to the significantly higher total nitrogen concentration (11 mg-N/l) compared to the deep aquifer (0.50 mg-N/l). The main stream input pathway for the shallow aquifer nitrogen load was from the perennial tile drainages providing 60% of the total load to the stream outlet, while only providing 26% of the total flow volume. The diffuse groundwater input to the stream was the largest input to the stream (39%), but only supplied 27% to the total nitrogen load as the diffuse water was mostly composed of deep aquifer water.
... As one of the important physical quantity indexes for characterizing the HE process, the HE flux can not only reflect the volume of water exchange between SW-GW in the HZ, but can also be used indirectly as an index for estimating the seepage losses of multiscale rivers and the amount of pollutant retention in the HZ (Cranswick et al. 2014;Exner-kittridge et al. 2014;Grant et al. 2014). Therefore, the quantification model of HZ flux has important practical applications for leakage loss estimation in arid-semiarid rivers and long diversion channel projects. ...
Full-text available
Article
Recently, the use of temperature tracer methods to investigate hyporheic exchange in rivers has attracted widespread attention. The quantification of the hyporheic exchange flux using temperature has been a topic of interest. Based on a summary and elaboration of the one-dimensional (1-D) analytical models for quantifying the hyporheic exchange flux based on the temperature tracer method, a hydrothermal coupling numerical model for the hyporheic zone considering the overall model of a river is further constructed. Combined with the water level and temperature time-series monitoring data collected from relevant rivers in the Walker Lake Basin in the United States, the effectiveness of the constructed numerical model in simulating the temperature and seepage patterns in the hyporheic zone is verified. Based on the verified hydrothermal coupling numerical model, the differences in the quantification of the vertical hyporheic exchange flux between different models are compared and analyzed. In addition, a sensitivity analysis based on the orthogonal test method is carried out to investigate the uncertainty of the 1-D analytical solution model. Finally, the advantages and disadvantages of the 1-D analytical model and the numerical model are discussed from the perspective of theoretical analysis. The results show that the constructed numerical model can be used to effectively characterize the heat transfer and fluid flow patterns in the hyporheic zone. When the result from the numerical model is not considered, the l-D analytical model based on the Hatch amplitude method is an ideal model for quantifying the vertical hyporheic exchange flux using temperature. The sensitivity analysis results reveal that the volumetric heat capacity of the soil (C s) and the porosity (n) are relatively sensitive parameters for the Hatch solution.
... The discharge lost (Q lost ) in each reach was calculated as the product of the percent of tracer mass lost by the average discharge in the reach. Using an average discharge assumes concurrent gain and loss within a reach [Payn et al., 2009;Exner-Kittridge et al., 2014]. ...
Full-text available
Article
Quantifying how watershed structure influences the exchanges of water among component parts of a watershed, particularly the connection between uplands, valley bottoms, and in-stream hydrologic exchange, remains a challenge. However, this understanding is critical for ascertaining the source areas and temporal contributions of water and associated biogeochemical constituents in streams. We used dilution gauging, mass recovery, and recording discharge stations to characterize streamflow dynamics across 52 reaches, from peak snowmelt to base flow, in the Tenderfoot Creek Experimental forest, Montana, USA. We found that watershed-contributing area was only a significant predictor of net changes in streamflow at high moisture states and larger spatial scales. However, at the scale of individual stream reaches, the lateral contributing area in conjunction with underlying lithology and vegetation densities were significant predictors of gross hydrologic gains to the stream. Reach lateral contributing areas underlain by more permeable sandstone yielded less water across flow states relative to those with granite gneiss. Additionally, increases in the frequency of steps across each stream reach contributed to greater hydrologic gross losses. Together, gross gains and losses of water along individual reaches resulted in net changes of discharge that cumulatively scale to the observed outlet discharge dynamics. Our results provide a framework for understanding how hillslope topography, geology, vegetation, and valley bottom structure contribute to the exchange of water and cumulative increases of stream flow across watersheds of increasing size.
... Well pumping in aquifers near streams may cause groundwater-surface water interactions (e.g., Rodriguez et al., 2013;Chen et al., 2013;Zhou et al., 2013;Exner-Kittridge et al., 2014;Flipo et al., 2014;Unland et al., 2014). The stream depletion rate (SDR), commonly used to quantify stream water filtration into the adjacent aquifer, is defined as the ratio of the filtration rate to a pumping rate. ...
Full-text available
Article
This study develops a three-dimensional (3-D) mathematical model for describing transient hydraulic head distributions due to pumping at a radial collector well (RCW) in a rectangular confined or unconfined aquifer bounded by two parallel streams and no-flow boundaries. The streams with low-permeability streambeds fully penetrate the aquifer. The governing equation with a point-sink term is employed. A first-order free surface equation delineating the water table decline induced by the well is considered. Robin boundary conditions are adopted to describe fluxes across the streambeds. The head solution for the point sink is derived by applying the methods of finite integral transform and Laplace transform. The head solution for a RCW is obtained by integrating the point-sink solution along the laterals of the RCW and then dividing the integration result by the sum of lateral lengths. On the basis of Darcy's law and head distributions along the streams, the solution for the stream depletion rate (SDR) can also be developed. With the aid of the head and SDR solutions, the sensitivity analysis can then be performed to explore the response of the hydraulic head to the change in a specific parameter such as the horizontal and vertical hydraulic conductivities, streambed permeability, specific storage, specific yield, lateral length, and well depth. Spatial head distributions subject to the anisotropy of aquifer hydraulic conductivities are analyzed. A quantitative criterion is provided to identify whether groundwater flow at a specific region is 3-D or 2-D without the vertical component. In addition, another criterion is also given to allow for the neglect of vertical flow effect on SDR. Conventional 2-D flow models can be used to provide accurate head and SDR predictions if satisfying these two criteria.
... Zhan et al. (2001) presented an analytical solution for drawdown induced by a horizontal well in confined aquifers and compared the difference in the type curves produced by the well and by a vertical well. Zhan and Zlotnik (2002) developed a semi-analytical solution of drawdown due to pumping from a nonvertical well in an unconfined aquifer accounting for the ef-Introduction Kittridge et al., 2014;Flipo et al., 2014;Unland et al., 2014). The stream depletion rate (SDR), commonly used to quantify stream water filtration into the adjacent aquifer, is defined as the ratio of a filtration rate to a pumping rate. ...
Full-text available
Article
This study develops a three-dimensional mathematical model for describing transient hydraulic head distributions due to pumping at a radial collector well (RCW) in a rectangular confined or unconfined aquifer bounded by two parallel streams and no-flow boundaries. The governing equation with a point-sink term is employed. A first-order free surface equation delineating the water table decline induced by the well is considered. The head solution for the point sink is derived by applying the methods of double-integral transform and Laplace transform. The head solution for a RCW is obtained by integrating the point-sink solution along the laterals of the RCW and then dividing the integration result by the sum of lateral lengths. On the basis of Darcy’s law and head distributions along the streams, the solution for the stream depletion rate (SDR) can also be developed. With the aid of the head and SDR solutions, the sensitivity analysis can then be performed to explore the response of the hydraulic head to the change in a specific parameter such as the horizontal and vertical hydraulic conductivities, streambed permeability, specific storage, specific yield, lateral length and well depth. Spatial head distributions subject to the anisotropy of aquifer hydraulic conductivities are analyzed. A quantitative criterion is provided to identify whether groundwater flow at a specific region is 3-D or 2-D without the vertical component. In addition, another criterion is also given to allow the neglect of vertical flow effect on SDR. Conventional 2-D flow models can be used to provide accurate head and SDR predictions if satisfying these two criteria.
Full-text available
Article
Hydrological observatories bear a lot of resemblance to the more traditional research catchment concept, but tend to differ in providing more long-term facilities that transcend the lifetime of individual projects, are more strongly geared towards performing interdisciplinary research, and are often designed as networks to assist in performing collaborative science. This paper illustrates how the experimental and monitoring set-up of an observatory, the 66 ha Hydrological Open Air Laboratory (HOAL) in Petzenkirchen, Lower Austria, has been established in a way that allows meaningful hypothesis testing. The overarching science questions guided site selection, identification of dissertation topics and the base monitoring. The specific hypotheses guided the dedicated monitoring and sampling, individual experiments, and repeated experiments with controlled boundary conditions. The purpose of the HOAL is to advance the understanding of water-related flow and transport processes involving sediments, nutrients and microbes in small catchments. The HOAL catchment is ideally suited for this purpose, because it features a range of different runoff generation processes (surface runoff, springs, tile drains, wetlands), the nutrient inputs are known, and it is convenient from a logistic point of view as all instruments can be connected to the power grid and a high-speed glassfibre local area network (LAN). The multitude of runoff generation mechanisms in the catchment provides a genuine laboratory where hypotheses of flow and transport can be tested, either by controlled experiments or by contrasting sub-regions of different characteristics. This diversity also ensures that the HOAL is representative of a range of catchments around the world, and the specific process findings from the HOAL are applicable to a variety of agricultural catchment settings. The HOAL is operated jointly by the Vienna University of Technology and the Federal Agency for Water Management and takes advantage of the Vienna Doctoral Programme on Water Resource Systems funded by the Austrian Science Funds. The paper presents the science strategy of the set-up of the observatory, discusses the implementation of the HOAL, gives examples of the hypothesis testing and summarises the lessons learned. The paper concludes with an outlook on future developments.
Full-text available
Article
A novel method is presented to estimate exfiltration from sewer systems using artificial tracers. The method relies upon use of an upstream indicator signal and a downstream reference signal to eliminate the dependence of exfiltration estimates on the accuracy of discharge measurement. An experimental design, a data analysis procedure, and an uncertainty assessment process are described and illustrated by a case study. In a 2-km reach of unknown condition, exfiltration was estimated at 9.9 +/- 2.7%. Uncertainty in this estimate was primarily due to the use of sodium chloride (NaCl) as the tracer substance. NaCl is measured using conductivity, which is present at nonnegligible levels in wastewater, thus confounding accurate identification of tracer peaks. As estimates of exfiltration should have as low a measurement error as possible, future development of the method will concentrate on improved experimental design and tracer selection. Although the method is not intended to replace traditional CCTV inspections, it can provide additional information to urban water managers for rational rehabilitation planning.
Full-text available
Article
Characterization of groundwater-surface water exchange is essential for improving understanding of contaminant transport between aquifers and rivers. Fiber-optic distributed temperature sensing (FODTS) provides rich spatiotemporal datasets for quantitative and qualitative analysis of groundwater-surface water exchange. We demonstrate how time-frequency analysis of FODTS and synchronous river stage time series from the Columbia River adjacent to the Hanford 300-Area, Richland, Washington, provides spatial information on the strength of stage-driven exchange of uranium contaminated groundwater in response to subsurface heterogeneity. Although used in previous studies, the stage-temperature correlation coefficient proved an unreliable indicator of the stage-driven forcing on groundwater discharge in the presence of other factors influencing river water temperature. In contrast, S-transform analysis of the stage and FODTS data definitively identifies the spatial distribution of discharge zones and provided information on the dominant forcing periods (≥2 d) of the complex dam operations driving stage fluctuations and hence groundwater-surface water exchange at the 300-Area.
Full-text available
Article
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<sup>?2</sup> d<sup>?1</sup> of groundwater discharging to the stream and approximately 10 Lm<sup>?2</sup> d<sup>?1</sup> 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.
Full-text available
Article
A numerical hydrological simulation suggested that water exchange between stream channels and adjacent aquifers is enhanced by convexities and concavities in streambed topography. At St. Kevin Gulch, an effluent stream in the Rocky Mountains of Colorado, subsurface hydraulic gradients and movement of ionic tracers indicated that stream water was locally recharged into well-defined flow paths through the alluvium. Stream water-filled flow paths in the alluvium (referred to as substream flow paths) returned to the stream a short distance downstream (1 to 10 m). Recharge to the substream flow paths occurred where stream water slope increased, at the transition from pools (
Article
A stream solute workshop was held February 1-5, 1989, at The University of Mississippi with the goals of 1) suggesting a conceptual model for stream solute studies that integrates physical, chemical, and biological processes, and 2) identifying advantages and limitations of various methods for studying solute transport and exchanges. Solute dynamics refers to the spatial and temporal patterns of transport and transfers of materials that are chemically dissolved in water. Solute transport and exchange processes can be described by solute transport equations that relate solute concentration to advection, dispersion, groundwater and tributary inputs, transient storage zones, and biotic and abiotic transformations. Studies can be based on these model equations even if a full simulation of a particular system is not attempted. Although no common methodological approach can serve every investigation of solute dynamics, experimental approaches represent a range from greatest control and least realism to least control and greatest realism. The model parameters describe processes that can be investigated in laboratory, chamber, and flume experiments designed to reduce confounding experimental variables. Whole-stream studies, particularly solute injection experiments, provide estimates of solute transfer to and from the water column and can be used to calibrate the simulation models. Transport and transfer models can link experimental results obtained at different scales and increase the opportunity for inter-site comparisons and the extrapolation of results between laboratory, chamber, flume, and whole-stream studies.
Article
There are several methods for determining the spatial distribution and magnitude of groundwater inputs to streams. We compared the results of conventional methods [dye dilution gauging, acoustic Doppler velocimeter (ADV) differential gauging, and geochemical end‐member mixing] to distributed temperature sensing (DTS) using a fibre‐optic cable installed along 900 m of Ninemile Creek in Syracuse, New York, USA, during low‐flow conditions (discharge of 1·4 m3 s−1). With the exception of differential gauging, all methods identified a focused, contaminated groundwater inflow and produced similar groundwater discharge estimates for that point, with a mean of 66·8 l s−1 between all methods although the precision of these estimates varied. ADV discharge measurement accuracy was reduced by non‐ideal conditions and failed to identify, much less quantify, the modest groundwater input, which was only 5% of total stream flow. These results indicate ambient tracers, such as heat and geochemical mixing, can yield spatially and quantitatively refined estimates of relatively modest groundwater inflow even in large rivers. DTS heat tracing, in particular, provided the finest spatial characterization of groundwater inflow, and may be more universally applicable than geochemical methods, for which a distinct and consistent groundwater end member may be more difficult to identify. Copyright © 2011 John Wiley & Sons, Ltd.
Article
The accumulation of discharge along a stream valley is frequently assumed to be the primary control on solute transport processes. Relationships of both increasing and decreasing transient storage, and decreased gross losses of stream water have been reported with increasing discharge; however, we have yet to validate these relationships with extensive field study. We conducted transient storage and mass recovery analyses of artificial tracer studies completed for 28 contiguous 100 m reaches along a stream valley, repeated under four base-flow conditions. We calculated net and gross gains and losses, temporal moments of tracer breakthrough curves, and best fit transient storage model parameters (with uncertainty estimates) for 106 individual tracer injections. Results supported predictions that gross loss of channel water would decrease with increased discharge. However, results showed no clear relationship between discharge and transient storage, and further analysis of solute tracer methods demonstrated that the lack of this relation may be explained by uncertainty and equifinality in the transient storage model framework. Furthermore, comparison of water balance and transient storage approaches reveals complications in clear interpretation of either method due to changes in advective transport time, which sets a the temporal boundary separating transient storage and channel water balance. We have little ability to parse this limitation of solute tracer methods from the physical processes we seek to study. We suggest the combined analysis of both transient storage and channel water balance more completely characterizes transport of solutes in stream networks than can be inferred from either method alone.
Article
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.