Transport In Streams Research Articles

A Regional Modeling Framework of Phosphorus Sources and Transport in Streams of the Southeastern United States1

We applied the SPARROW model to estimate phosphorus transport from catchments to stream reaches and subsequent delivery to major receiving water bodies in the Southeastern United States (U.S.). We show that six source variables and five land-to-water transport variables are significant (p<0.05) in explaining 67% of the variability in long-term log-transformed mean annual phosphorus yields. Three land-to-water variables are a subset of landscape characteristics that have been used as transport factors in phosphorus indices developed by state agencies and are identified through experimental research as influencing land-to-water phosphorus transport at field and plot scales. Two land-to-water variables – soil organic matter and soil pH – are associated with phosphorus sorption, a significant finding given that most state-developed phosphorus indices do not explicitly contain variables for sorption processes. Our findings for Southeastern U.S. streams emphasize the importance of accounting for phosphorus present in the soil profile to predict attainable instream water quality. Regional estimates of phosphorus associated with soil-parent rock were highly significant in explaining instream phosphorus yield variability. Model predictions associate 31% of phosphorus delivered to receiving water bodies to geology and the highest total phosphorus yields in the Southeast were catchments with already high background levels that have been impacted by human activity.

Start and end of bedload transport in gravel-bed streams

[1] The threshold of incipient bedload motion, expressed either as a critical force or as a critical water discharge, is a key parameter in bedload transport prediction. Measuring the threshold of motion is difficult, and reliable data from natural streams are rare. By recording the vibrations triggered by bedload particles when moving over a steel plate mounted in the channel bed, we determined the time at start and end of bedload transport in four streams, where discharge is continuously monitored. The threshold discharge scatters over approximately one order of magnitude for each stream, reinforcing previous observations that critical discharge is characterized by a distribution of values. We interpret a strong correlation between the discharge at the start of transport and the discharge at the end of transport of the previous event to reflect temporal changes in bed structure and consequent effects on the driving and resisting forces acting on the bed.

Bedload Transport and Morphological Effects of High-Magnitude Floods in Small Headwater Streams - Moravskoslezské Beskydy Mts. (Czech Republic)

Bedload transport observed during a flood in May 2010 gave rise to several forms of accumulations in small headwater basins located in the Western Flysch Carpathian Mountains, Czech Republic. We have investigated critical conditions of incipient motion of the largest boulders deposited during a c. Q100 flood event (flood competence method). We have tested several formulas designed for high gradient streams in two small basins in the conditions of local mid-mountain relief. The results show that a flood of such a magnitude is able to transport almost all surface bed material and that bedload transport in steep headwater streams (A ≤ 1 km 2 ) is probably less selective as for the grain size than that in lower gradient gravel-bed streams. The authors discuss the importance of local basin predispostion factors in order to determine critical conditions for the onset of bedload transport.

Analytical Solution for Spatially Dependent Solute Transport in Streams with Storage Zone

The transient storage model with space-variable coefficients is solved by using the generalized integral transform technique (GITT) coupled with Laplace transform method. The spatially dependent flow velocity and solute dispersion are considered in the governing equations of the transient storage model. The correctness and accuracy of the derived analytical solution is verified by comparison with the analytical solution for constant flow velocity and the dispersion coefficient. Some illustrative examples are presented to demonstrate the application of the derived analytical solution. The increasing flow velocity and solute dispersion cause the faster transport of solute. Moreover, the faster the flow velocity and solute dispersion increase, the faster the solute transports.

Climate change effects on nitrogen loading from cultivated catchments in Europe: implications for nitrogen retention, ecological state of lakes and adaptation

Climate change might have profound effects on the nitrogen (N) dynamics in the cultivated landscape as well as on N transport in streams and the eutrophication of lakes. N loading from land to streams is expected to increase in North European temperate lakes due to higher winter rainfall and changes in cropping patterns. Scenario (IPCC, A2) analyses using a number of models of various complexity for Danish streams and lakes suggest an increase in runoff and N transport on an annual basis (higher during winter and typically lower during summer) in streams, a slight increase in N concentrations in streams despite higher losses in riparian wetlands, higher absolute retention of N in lakes (but not as percentage of loading), but only minor changes in lake water concentrations. However, when taking into account also a predicted higher temperature there is a risk of higher frequency and abundance of potentially toxic cyanobacteria in lakes and they may stay longer during the season. Somewhat higher risk of loss of submerged macrophytes at increased N and phosphorus (P) loading and a shift to dominance of small-sized fish preying upon the key grazers on phytoplankton may also enhance the risk of lake shifts from clear to turbid in a warmer North European temperate climate. However, it must be emphasised that the prediction of N transport and thus effects is uncertain as the prediction of regional precipitation and changes in land-use is uncertain. By contrast, N loading is expected to decline in warm temperate and arid climates. However, in warm arid lakes much higher N concentrations are currently observed despite reduced external loading. This is due to increased evapotranspiration leading to higher nutrient concentrations in the remaining water, but may also reflect a low-oxygen induced reduction of nitrification. Therefore, the critical N as well as P loading for good ecological state in lakes likely has to be lower in a future warmer climate in both north temperate and Mediterranean lakes. To obtain this objective, adaptation measures are required. In both climate zones the obvious methods are to change agricultural practices for reducing the loss of nutrients to surface waters, to improve sewage treatment and to reduce the storm-water nutrient runoff. In north temperate zones adaptations may also include re-establishment of artificial and natural wetlands, introduction of riparian buffer zones and re-meandering of channelised streams, which may all have a large impact on, not least, the N loading of lakes. In the arid zone, also restrictions on human use of water are urgently needed, not least on the quantity of water used for irrigation purposes.

Characterizing solute transport with transient storage across a range of flow rates: The evidence of repeated tracer experiments in Austrian and Italian streams

Solute transport in rivers and streams with hyporheic zone exchange and/or in-stream storage is typically affected by the prevailing flow rate. The research reported here focuses on stream tracer experiments repeated many times along the same Austrian (Mödlingbach) and Italian (Torrente Lura) channel reaches to characterize parameter dependency on flow rate. Both groups of data sets showed an increase of storage zone area and main stream area with discharge. In either case, a strong negative correlation was obtained between storage zone residence time and flow rate. From the Mödlingbach data, no clear relationship with Q emerged for the dispersion coefficient and the dead zone ratio, whereas Torrente Lura showed a clear positive correlation of the dispersion coefficient with the flow rate and a slightly negative Q-dependency for the dead zone ratio. Mödlingbach and Torrente Lura results are presented against the background of other repeat experiments reported in literature. In practical applications, the computation of peak concentrations frequently rests on the transfer of transport parameters from one flow rate to another. Using the above Austrian and Italian data sets it was shown that the errors in simulated Mödlingbach peak concentrations remain within a 40% margin, if the ratio of flow rates (for calibration and simulation, resp.) does not exceed 2:1. With Torrente Lura, parameter transfer resulted in somewhat lower peak errors.

Heavy‐tailed travel distance in gravel bed transport: An exploratory enquiry

Bed load transport, where particles move intermittently in frequent contact with the bed, is the dominant mode of particle transport in gravel bed rivers and streams. Complex fluid/particle and particle/particle interactions lead to a broad distribution of transport behaviors under the same set of flow conditions. In this paper, we investigate the plausibility of heavy‐tailed movements for particles in bed load transport using carefully controlled flume experiments and theoretical analysis. In our experimental setting, we find travel distances for particles of a given size follow an exponential distribution whose mean varies with grain size. Building on previous work of Stark et al. (2009), we then develop a probability model to show how heavy‐tailed distributions of travel distance can emerge from a mixture of particle sizes. Heavy‐tailed travel distance can lead to anomalous diffusion in bed load transport, modeled by fractional derivatives in the transport equation.

A one-dimensional bedload transport model for steep slopes

A sediment routing model called SETRAC has been developed to simulate bedload transport in torrents and mountain streams. SETRAC is the acronym for Sediment Transport in Alpine Catchments. Flow resistance is modelled using an approach proposed by Smart and Jäggi, and bedload transport is predicted with an equation by Rickenmann. Form roughness losses are accounted for by an empirical approach which is based on flow resistance observations in mountain streams. It is possible to compute fractional bedload transport taking grain sorting effects into account. Flow hydrographs are routed through the channel network by using the kinematic wave approach. An application of the model is discussed for an extreme flood event of August 2005 in the Chiene catchment, Switzerland, which mobilized 120,000 m3 of bedload along the mountain stream. The simulation results underline the importance of form resistance when modelling bedload transport in steep and rough channels.

Pool Effects on Longitudinal Dispersion in Streams and Rivers

Surface storage (pools, pockets, and stagnant areas caused by woody debris, bars etc) is very important to solute transport in streams as it attenuates the peak of a spill but releases the solute back to the stream over a long time. The latter results in long exposure time of biota. Pools as fundamental stream morphology unit are commonly found in streams with mixed bed materials in pool-riffle or pool-step sequences. Fitting the transient storage model (TSM) to stream tracer test data may be problematic when pools present. A fully hydrodynamic 2-D, depth averaged advection-dispersion solute transport numerical simulation study on hypothetical stream with pool reveals that a pool can sharply enhance longitudinal spreading, cause a lag in the plume travel-time and radically increase solute residence time in the stream. These effects fade like a “wake” as the solute plume moves downstream of the pool. Further, these effects are strongly influenced by a dimensionless number derived from the 2-D transport equation ? or , which outlines the relative transverse mixing intensity of a stream or river, where, of the stream reach concerned, W is the flow width, Q0 is the volumetric flow rate, q is the longitudinal flux density, and Dt is the transverse turbulent diffusion coefficient. The breakthrough curves (BTCs) downstream of a pool may be “heavy tailed” which cannot be modeled accurately by the TSM. The internal transport and mixing condition (including the secondary circulations) in a pool together with the pool’s dimension determine the pool’s storage effects especially when >> 1. Results also suggest that the falling limb of a BTC more accurately characterizes the pool's storage because the corresponding solute has more chance to sample the entire storage area.

The biogeochemical influences of NO3−, dissolved O2, and dissolved organic C on stream NO3− uptake

AbstractStreams are potential hotspots for retention and removal of NO3−, and understanding the mechanisms that enhance NO3− reactivity in stream systems is critical for predicting and preventing eutrophication. Both dissolved organic C (DOC) and dissolved O2 (DO) influence NO3− removal processes. Assessing the individual impacts of NO3−, DO, and DOC concentrations on stream NO3− removal is difficult because these factors covary and are coupled through the C and N cycles. We used an experimental approach to quantify the influences of NO3−, DOC, and DO on NO3− transport in headwater streams of the Ipswich and Parker River watersheds (Massachusetts, USA) with contrasting levels of DOC and DO. In a 1st set of experiments, we added NO3− to address how uptake kinetics differed between a low-DO/high-DOC stream (Cedar Swamp Creek) and a high-DO/low-DOC stream (Cart Creek). In a 2nd set of experiments, we manipulated, for the first time at the reach scale, both DO and DOC in a factorial experiment. DO was added t...

The effect of riparian land use on transport hydraulics in agricultural headwater streams located in northeast Ohio, USA

AbstractThis study examined if riparian land use (forested vs agricultural) affects hydraulic transport in headwater streams located in an agriculturally fragmented watershed. We identified paired 50‐m reaches (one reach in agricultural land use and the other in forested land use) along three headwater streams in the Upper Sugar Creek Watershed in northeast Ohio, USA (40° 51′42″N, 81° 50′29″W). Using breakthrough curves obtained by Rhodamine WT slug injections and the one‐dimensional transport with inflow and storage model (OTIS), hydraulic transport parameters were obtained for each reach on six different occasions (n = 36). Relative transient storage (AS:A) was similar between both reach types (As: A = 0·3 ± 0·1 for both agricultural and forested reaches). Comparing values of Fmed200 to those in the literature indicates that the effect of transient storage was moderately high in the study streams in the Upper Sugar Creek Watershed. Examining travel times revealed that overall residence time (HRT) and residence time in transient storage (TSTO) were both longer in forested reaches (forested HRT = 19·1 ± 11·5 min and TSTO = 4·0 ± 3·8 min; agricultural HRT = 9·3 ± 5·3 min and TSTO = 1·7 ± 1·4 min). We concluded that the effect of transient storage on solute transport was similar between the forested and agricultural reaches but the forested reaches had a greater potential to retain solutes as a result of longer travel times. Copyright © 2009 John Wiley &amp; Sons, Ltd.

Climate Change Effects on Runoff, Catchment Phosphorus Loading and Lake Ecological State, and Potential Adaptations

Climate change may have profound effects on phosphorus (P) transport in streams and on lake eutrophication. Phosphorus loading from land to streams is expected to increase in northern temperate coastal regions due to higher winter rainfall and to a decline in warm temperate and arid climates. Model results suggest a 3.3 to 16.5% increase within the next 100 yr in the P loading of Danish streams depending on soil type and region. In lakes, higher eutrophication can be expected, reinforced by temperature-mediated higher P release from the sediment. Furthermore, a shift in fish community structure toward small and abundant plankti-benthivorous fish enhances predator control of zooplankton, resulting in higher phytoplankton biomass. Data from Danish lakes indicate increased chlorophyll a and phytoplankton biomass, higher dominance of dinophytes and cyanobacteria (most notably of nitrogen fixing forms), but lower abundance of diatoms and chrysophytes, reduced size of copepods and cladocerans, and a tendency to reduced zooplankton biomass and zooplankton:phytoplankton biomass ratio when lakes warm. Higher P concentrations are also seen in warm arid lakes despite reduced external loading due to increased evapotranspiration and reduced inflow. Therefore, the critical loading for good ecological state in lakes has to be lowered in a future warmer climate. This calls for adaptation measures, which in the northern temperate zone should include improved P cycling in agriculture, reduced loading from point sources, and (re)-establishment of wetlands and riparian buffer zones. In the arid Southern Europe, restrictions on human use of water are also needed, not least on irrigation.

Transient storage and downstream solute transport in nested stream reaches affected by beaver dams

AbstractTransient storage constitutes a key element in the hydrologic cycle of watersheds. Both in‐channel slow moving water (dead zones) and hyporheic zones can contribute to transient storage, which retains water and solutes, increases residence time and influences solute transport in streams. Beaver dams and other in‐stream obstructions throughout low‐order streams attenuate streamflow and provide dead zone storage in pools. In this article, we report the results of four tracer tests in nested stream reaches in Cherry Creek (Wyoming, USA) covering ∼2·5 km of stream length to explore how the degree of beaver dam obstructions and their impoundments influence water transient storage and downstream solute transport in low‐order streams in the Rocky Mountain region of the American West. Travel‐time parameters for the tracer tests increased linearly with beaver dam number (N) and pond size (V). Linear regression of the travel time to the peak concentration (Tp), the leading (Tl) and tailing edge (Tt) of the dye cloud and the duration of the dye cloud (Td) versus N and V were all significant (R2 = 0·99). Slopes of the linear regressions of Tt versus N and V, were three times larger than those for Tl, suggesting that longer residence times may be caused, in part, by transient storage in the stream system. One‐dimensional transport with inflow and storage (OTIS) modelled cross‐sectional area of transient storage zone (As) and dispersion coefficients (D) increased linearly with N and V and reach length. Two transient storage metrics, Fmean and $F_{\rm {med}}^{200}$, also showed a general increase with N and V, although the relationship was not as strong. This suggests that in‐channel dead zones associated with beaver dams provide opportunities for generating transient water storage. The linear relationship between dispersion coefficient and reach length suggests the dispersion process might be analogous to the hydrodynamic dispersion in groundwater settings. Copyright © 2009 John Wiley &amp; Sons, Ltd.

Carbon release and cycling within epilithic biofilms in two contrasting headwater streams

AME Aquatic Microbial Ecology Contact the journal Facebook Twitter RSS Mailing List Subscribe to our mailing list via Mailchimp HomeLatest VolumeAbout the JournalEditorsSpecials AME 55:285-300 (2009) - DOI: https://doi.org/10.3354/ame01299 Carbon release and cycling within epilithic biofilms in two contrasting headwater streams Susan E. Ziegler1,*, David R. Lyon2, Sherri L. Townsend2,3 1Department of Earth Sciences, Memorial University, 4063 Alexander Murray Building, St. John’s, Newfoundland and Labrador A1B 3X5, Canada 2Environmental Dynamics Program, University of Arkansas, 113 Ozark Hall, Fayetteville, Arkansas 72701, USA 3Faculty of Science, North Arkansas College, 1515 Pioneer Drive, Harrison, Arkansas 72601, USA *Email: sziegler@mun.ca ABSTRACT: This study investigates the release of dissolved organic carbon (DOC) from epilithic biofilms and how the exchange of C between epilithic algae and bacteria varies between 2 contrasting headwater streams. During 3 seasons, light and dark enclosures were incubated in situ with rock substrate and stream water amended with 13C-labeled bicarbonate to follow newly fixed carbon into DOC, epilithic biofilm, and biofilm phospholipid fatty acids (PLFAs). Net release of DOC only occurred in the light enclosures and was significantly affected by net primary production (NPP). However, the net release of DOC as a proportion of NPP increased with light availability and decreased with dissolved inorganic nitrogen in Huey Hollow, the nutrient-deplete stream, and decreased with dissolved inorganic phosphorus (DIP) in Moore Creek, the nutrient-replete stream. Newly-fixed C, released as DOC, decreased with DIP but represented a greater proportion of net DOC release in Moore Creek (6 to 15%) relative to that in Huey Hollow (0.7 to 2%). Congruently, the quantity of newly-fixed C retained in the bulk biofilm and the bacterial PLFA ia15:0 increased together with DIP. Further, the proportion of NPP incorporated into bacterial PLFA in Huey Hollow was 4 times that in the Moore Creek biofilms, suggesting that bacteria accessed relatively more NPP in the low nutrient stream biofilms. Our data indicate that C-cycling differed between the contrasting streams in 2 significant ways. A larger proportion of DOC released from biofilms in the nutrient-rich stream was derived from new photosynthates, reducing the availability of this source of NPP to biofilm bacteria. Concurrently, a greater proportion of NPP was retained in heterotrophic bacterial PLFAs in the more nutrient-deplete stream biofilms. These results suggest that nutrient levels can greatly affect the source and processing of DOC, and emphasize the need to understand the mechanisms responsible for varied DOC cycling and transport in streams. KEY WORDS: Carbon cycling · Dissolved organic carbon · Epilithic biofilms · Bacterial–algal interaction · Phospholipid fatty acids · Headwater streams Full text in pdf format PreviousCite this article as: Ziegler SE, Lyon DR, Townsend SL (2009) Carbon release and cycling within epilithic biofilms in two contrasting headwater streams. Aquat Microb Ecol 55:285-300. https://doi.org/10.3354/ame01299 Export citation RSS - Facebook - Tweet - linkedIn Cited by Published in AME Vol. 55, No. 3. Online publication date: June 19, 2009 Print ISSN: 0948-3055; Online ISSN: 1616-1564 Copyright © 2009 Inter-Research.

Environmental change, hillslope erosion and suspended sediment: Some observations from Hong Kong

Abstract Evidence of environmental change in Hong Kong, including vegetation, climate and the frequency of hillfires is presented. Hillfires may be an important influence upon slope degradation in the territory. Field observations made in the Northwest New Territories provide evidence that hillfires increase soil erosion on slopes and result in higher storm-period concentrations of suspended sediment. Monitoring carried out in a small drainage basin reveals that landslides deliver sediment to an upland stream giving very high concentrations and affecting sediment properties, with the C and N content declining under the influence of landslides. Should environmental change alter the frequency of landsliding and hillfire on natural terrain in Hong Kong this will have implications for hillslope degradation and sediment transport in upland streams.

Dynamics of surface water storage in the Amazon inferred from measurements of inter‐satellite distance change

Terrestrial water storage in the Amazon basin and its surrounding areas is studied by exploring the instantaneous measurements of distance changes between two satellites from the GRACE mission. The surface water in the channels and floodplains can be significant in weighing total water storage. Its magnitude can be as large as soil moisture perturbing the motions of the satellites to a detectable amount by the on‐board instrument. The river runoff routing simulations indicate the effective velocity throughout the Amazon basin over the years is about 30 cm/s with significant seasonal change. The lower velocity, during rising stages and peak water season, and the faster velocity, during falling stages, are delineated from the observations. The backwater effects may impact such seasonal change on the overall flow velocity. Direct assimilation of GRACE tracking data can contribute to land surface dynamic processes by resolving the time scale of transport in rivers and streams.

Variable residence time–based model for solute transport in streams

A variable residence time (VART) model is developed for longitudinal dispersion and transport of solutes in natural streams. The VART model is based on a “double‐layer” conceptual model of transient storage in streams. The upper layer is an advection‐dominated transient storage zone which includes instream and shallow hyporheic storage. The lower layer is an effective diffusion‐dominated storage zone that is deeper in the streambed and farther beneath the banks. The VART model is characterized by the following features. First, a varying residence time is used to simulate the transient storage process. Second, no user‐specified residence time distribution (RTD) functions are required. Third, there are only four parameters to estimate. Fourth, the VART model is also able to accommodate stream water/solute gains or losses in the reach caused by groundwater exchanges. Fifth, the simple VART model is able to produce various compound solute concentration breakthrough curves (BTCs) commonly observed in streams. The early portion of BTCs follows exponential RTDs. The late portion of BTCs can essentially be any distribution. Sixth, performance of the VART model in reproducing various RTDs is comparable to other widely used 1‐D solute transport models that commonly utilize five or more fitting parameters and are limited to the simulation of user‐specified RTDs or underlying RTDs within them. Applications in hydrologically and geomorphically varied streams have indicated that the VART model is a powerful and flexible numerical tool for simulating solute transport in natural streams.

Maintenance of terrestrial nutrient loss signatures during in‐stream transport

Small streams account for the majority of channel length in river basins worldwide and are the primary conveyors of terrestrial nutrients to rivers and ultimately the oceans. The controls of stream nutrient fluxes, however, are debated. Classical models emphasize that nutrient transport in streams integrates nutrient cycling in the terrestrial watershed while others argue that in-stream processes control nutrient flux. Recent studies have shown that in-stream cycling can be important in determining downstream nutrient fluxes, but results have not been reconciled with mass-balance calculations at the small-watershed scale. Here we use a simple analytical framework to assess nutrient cycling in streams and show that, under most conditions, longitudinally static nutrient concentrations reflect in-stream biotic balance between uptake and regeneration and groundwater inputs. Using measures of nutrient concentrations in small streams across four biomes, we provide evidence for generality of biogeochemical steady state (inputs = outputs) in stream ecosystems: overall, longitudinal profiles were flat for nitrogen and phosphorus and were similar in concentration to soil and ground waters. Deviation from flat longitudinal profiles was associated with seasonal or successional biomass growth and small groundwater inputs relative to in-stream sink strength. We conclude that streams tend strongly toward nutrient balance, allowing use of their chemistry as an integrated measure of terrestrial nutrient losses.

Scaling dispersion model for pollutant transport in rivers

This communication presents a scale-dependent model, called Scaling Dispersion (SD) Model, for simulating solute dispersion and transport in rivers without using a user-specified residence time distribution function. The SD model consists of (1) the advection dispersion equation with a transient storage term which is characterized by a variable residence time, (2) a new method for estimation of the longitudinal Fickian dispersion coefficient involved in the model, and (3) a split-operator method for numerical solution of the equations involved in the model. Comparisons between the SD model and the most widely used transient storage model against tracer test data observed in three US rivers show that the SD model is capable of simulating different types of residence time distributions commonly observed in streams with an accuracy higher than or at least comparable with existing solute transport models, demonstrating the efficacy of the SD model. The SD model unifies the residence time distributions observed in natural rivers within a single modelling framework for the first time. The SD model provides an efficient and cost effective tool for predicting solute dispersion and transport in streams and rivers.

Longitudinal dispersion in a horizontal subsurface flow constructed wetland: a numerical solution

We present a numerical solution for the dead zone model which describes the solute transport in a subsurface and horizontal flow constructed wetland. This model is a system of two mass balance equations for two conceptual areas: the main channel and the storage zone. We use finite difference schemes to determine the numerical solution of the system and we study its convergence by presenting properties related to the stability and accuracy of the schemes. Concerning the experimental results, the magnitude of the longitudinal dispersion and the extension of dead volumes is estimated for clean conditions and after a certain operating period under organic loading conditions. The results showed a considerable amount of longitudinal dispersion through the bed, which was very strong near the feeding point, indicating the occurrence of mixing and significant presence of dead zones and short-circuiting. This approach is expected to be useful to determine operating conditions, such as, the control of the incoming organic loading, and also to avoid the increase of dead zones as a means to improve treatment performance. References J. M. Bahr and J. Rubin. Direct comparison of kinetic and local equilibrium formulations for solute transport affected by surface reactions. Water Resource Res. 23(3):438--452, 1987. doi:10.1029/WR023i003p00438 k: E. Bencala and R. A. Walters. Simulation of solute transport in a mountain pool-and-riffle stream: a transient storage model. Water Resour Res, 19(3):718--724, 1983. doi:10.1029/WR019i003p00718 K. Dekker and J. G. Verwer. Stability of Runge-Kutta Methods for Nonlinear Stiff Differential Equations. cwi Monograph 2, Elsevier, Amsterdam, 1984. S. H. Keefe, L. B. Barber, R. L. Runkel, J. N. Ryan, D. M. McKnight and R. D. Wass. Conservative and reactive solute transport in constructed wetlands. Water Resource Res., 40: W01201, 2004. doi:10.1029/2003WR002130 C. J. Martinez and W. R. Wise. Analysis of constructed treatment wetland hydraulics with the transient storage model otis. Ecological Engineering, 20(3):211, 2003. doi:10.1016/S0925-8574(03)00029-6 C. F. Nordin and B. M. Troutman. Longitudinal dispersion in rivers: the persistence of skewness in observed data. Water Resour Res, 16(1):123--128, 1980. doi:10.1029/WR016i001p00123 R. L. Runkel and S. C. Chapra. An efficient numerical solution of the transient storage equations for solute transport in small streams. Water Resour Res, 29(1):211--215, 1993. doi:10.1029/92WR02217 J. G. Verwer and J. M. Sanz-Serna. Convergence of Method of Lines Approximations to Partial Differential Equations. Computing, 33(3-4):297--313, 1984. doi:10.1007/BF02242274 B. J. Wagner and J. W Harvey. Experimental design for estimating parameters of rate-limited mass transfer: analysis of stream tracer studies. Water Resource Res., 33(7): 1731--1741, 1997. doi:10.1029/97WR01067