Analytical solutions for transport of decaying solutes in rivers with transient storage

Analytical solutions are presented for solute transport in rivers including the effects of transient storage and first order decay. The solute transport model considers an advection–dispersion equation for transport in the main channel linked to a first order mass exchange between the main channel and the transient storage zones. In case of a conservative tracer, it is shown that different analytical solutions presented in the literature are mathematically identical. For non-conservative solutes, first order decay reactions are considered with different reaction rate coefficients in the main river channel and in the dead zones. New analytical solutions are presented for different boundary conditions, i.e. instantaneous injection in an infinite river reach, and variable concentration time series input in a semi-infinite river reach. The correctness and accuracy of the analytical solutions is verified by comparison with the OTIS numerical model. The results of analytical and numerical approaches compare favourably and small differences can be attributed to the influence of boundary conditions. It is concluded that the presented analytical solutions for solute transport in rivers with transient storage and solute decay are accurate and correct, and can be usefully applied for analyses of tracer experiments and transport characteristics in rivers with mass exchange in dead zones.     

Routing procedures for observed dispersion coefficients in two-dimensional river mixing

Routing procedures have been used for determining the observed values of the dispersion coefficient in river mixing studies. In order to overcome the shortcomings of the existing routing procedures, we developed a new routing procedure capable of being applied under a transient concentration situation while accounting for river irregularities. The proposed routing procedure is based on the exact solution of the depth-averaged, two-dimensional, mass transport equation combined with the stream-tube concept and was verified through the tracer data acquired from field tests conducted in natural rivers located in Korea. The observed dispersion coefficients evaluated by the routing procedure exhibited a stream-wise variation along the rivers, in that a minimum value was seen in the straight region and a maximum value downstream of the apex of the bend. This variation was attributed to the flow dynamics of secondary currents induced by the meandering of the rivers. The dispersion coefficients obtained by the new method over the reach were in the same range of those calculated by other methods.     

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.     

On the methods for determining the transverse dispersion coefficient in river mixing

In this study, the strengths and weaknesses of existing methods for determining the dispersion coefficient in the two-dimensional river mixing model were assessed based on hydraulic and tracer data sets acquired from experiments conducted on either laboratory channels or natural rivers. From the results of this study, it can be concluded that, when the longitudinal dispersion coefficient as well as the transverse dispersion coefficients must be determined in the transient concentration situation, the two-dimensional routing procedures, 2D RP and 2D STRP, can be employed to calculate dispersion coefficients among the observation methods. For the steady concentration situation, the STRP can be applied to calculate the transverse dispersion coefficient. When the tracer data are not available, either theoretical or empirical equations by the estimation method can be used to calculate the dispersion coefficient using the geometric and hydraulic data sets. Application of the theoretical and empirical equations to the laboratory channel showed that equations by Baek and Seo [[3], 2011] predicted reasonable values while equations by Fischer [23] and Boxwall and Guymer (2003) overestimated by factors of ten to one hundred. Among existing empirical equations, those by Jeon et al. [28] and Baek and Seo [6] gave the agreeable values of the transverse dispersion coefficient for most cases of natural rivers. Further, the theoretical equation by Baek and Seo [5] has the potential to be broadly applied to both laboratory and natural channels.     

Numerical modelling-based comparison of longitudinal dispersion coefficient formulas for solute transport in rivers

River water quality models usually apply the Fischer equation to determine the longitudinal dispersion coefficient (D_x) in solving the advection–dispersion equation (ADE). Recently, more accurate formulas have been introduced to determine D_x in rivers, which could strongly affect the accuracy of the ADE results. A numerical modelling-based approach is presented to evaluate the performance of various D_x formulas using the ADE. This approach consists of a finite difference approximation of the ADE, a MATLAB code and a MS Excel interface; it was tested against the analytical ADE solution and demonstrated using eight well-known D_x formulas and tracer study data for the Chattahoochee River (USA), the Severn (UK) and the Athabasca (Canada). The results show that D_x has an important effect on tracer concentrations simulated with the ADE. Comparison between the simulated and measured concentrations confirms the appropriate performance of Zeng and Huai’s formula for D_x estimation. Use of the newly proposed equations for D_x estimation could enhance the accuracy of solving the ADE.     

Modeling contaminant transport in homogeneous porous media with fractional advection-dispersion equation

The newly developed Fractional Advection-Dispersion Equation (FADE), which is FADE was extended and used in this paper for modelling adsorbing contaminant transport by adding an adsorbing term. A parameter estimation method and its corresponding FORTRAN based program named FADEMain were developed on the basis of Nonlinear Least Square Algorithm and the analytical solution for one-dimensional FADE under the conditions of step input and steady state flow. Data sets of adsorbing contaminants Cd and NH4+-N transport in short homogeneous soil columns and conservative solute NaCI transport in a long homogeneous soil column, respectively were used to estimate the transport parameters both by FADEMain and the advection-dispersion equation (ADE) based program CXTFIT2.1. Results indicated that the concentration simulated by FADE agreed well with the measured data. Compared to the ADE model, FADE can provide better simulation for the concentration in the initial lower concentration part and the late higher concentration part of the breakthrough curves for both adsorbing contaminants. The dispersion coefficients for ADE were from 0.13 to 7.06 cm2/min, while the dispersion coefficients for FADE ranged from 0.119 to 3.05 cm1.856/min for NaCI transport in the long homogeneous soil column. We found that the dispersion coefficient of FADE increased with the transport distance, and the relationship between them can be quantified with an exponential function. Less scale-dependent was also found for the dispersion coefficient of FADE with respect to ADE.     

Exact analytical solutions for two-dimensional advection-dispersion equation in cylindrical coordinates subject to third-type inlet boundary condition

Exact analytical solutions for two-dimensional advection-dispersion equation (ADE) in cylindrical coordinates subject to the third-type inlet boundary condition are presented in this study. The finite Hankel transform technique in combination with the Laplace transform method is adopted to solve the two-dimensional ADE in cylindrical coordinates. Solutions are derived for both continuous input and instantaneous slug input. The developed analytical solutions are compared with the solutions for first-type inlet boundary condition to illustrate the influence of the inlet condition on the two-dimensional solute transport in a porous medium system with a radial geometry. Results show significant discrepancies between the breakthrough curves obtained from analytical solutions for the first-type and third-type inlet boundary conditions for large longitudinal dispersion coefficients. The developed solutions conserve the solute mass and are efficient tools for simultaneous determination of the longitudinal and transverse dispersion coefficients from a laboratory-scale radial column experiment or an in situ infiltration test with a tracer.     

Evaluation of temporal concentration profiles for ungauged rivers following pollution incidents

Abstract

In order to predict the impact of pollution incidents on rivers, it is necessary to predict the dispersion coefficient and the flow velocity corresponding to the discharge in the river of interest. This paper explores methods for doing this, particularly with a view to applications on ungauged rivers, i.e. those for which little hydraulic or morphometric data are available. An approach based on neural networks, trained on a wide-ranging database of optimized parameter values from tracer experiments and corresponding physical variables assembled for American and European rivers, is proposed. Tests using independent cases showed that the neural networks generally gave more reliable parameter estimates than a second-order polynomial regression approach. The quality of predictions of temporal concentration profiles was heavily influenced by the accuracy of the velocity prediction.

Citation Piotrowski, A. P., Napiorkowski, J. J., Rowinski, P. M. & Wallis, S. G. (2011) Evaluation of temporal concentration profiles for ungauged rivers following pollution incidents. Hydrol. Sci. J. 56(5), 883–894.     

Relationship between the equilibrium morphology of river islands and flow-sediment dynamics based on the theory of minimum energy dissipation

River islands are vital geomorphic units in alluvial rivers, and the variation of their morphology and position plays a significant role in regulating flow-sediment transport and channel stability. Based on the theories of minimum energy dissipation theory of fluid movement and river morphodynamics, this study uses the river islands in anabranching channels to analyze the relationship between the shape coefficient of river island and the flow-sediment dynamics under stable equilibrium conditions...     

Predicting longitudinal dispersion coefficient in natural streams by artificial intelligence methods

In this study, three artificial neural network methods, i.e. feed forward back propagation, the radial basis function neural network, and the generalized regression neural network are employed to compute the longitudinal dispersion coefficient in order to evaluate its behaviour in predicting dispersion characteristics in natural streams. These methods, which use hydraulic and geometrical data to predict dispersion coefficients, can easily be applied to natural streams and are proven to be superior in explaining their dispersion characteristics more precisely than existing equations. This method of predicting the longitudinal dispersion coefficient in river flows was tested on 65 data sets, obtained by researchers from 30 rivers in the USA. Results using the models are compared with results obtained in many other studies, and are shown to be more accurate than the other methods considered. Copyright © 2008 John Wiley & Sons, Ltd.     

Importance of advective zone in longitudinal mixing experiments

One-dimensional Fickian dispersion models such as the advection diffusion equation (ADE) are commonly used to analyse and predict concentration distributions downstream of contamination events in watercourses. Such models are only valid once the tracer had entered the equilibrium zone. This paper compares previous theoretical, experimental and numerical estimates of the distance to reach the equilibrium zone with new experimental values, obtained by examining the change of skewness in a tracer profile, downstream of a cross-sectionally well mixed source. Closer agreement was found with Fischers’ theoretical estimate than prior experimental and numerical studies.     

Evidence of distinct contaminant transport patterns in rivers using tracer tests and a multiple domain retention model

Solute transport in rivers is controlled by surface hydrodynamics and by mass exchanges with distinct retention zones. Surface and hyporheic retention processes can be accounted for separately in solute transport models with multiple storage compartments. In the simplest two component model, short term storage can be associated to in-channel transient retention, e.g. produced by riparian vegetation or surface dead zones, and the long-term storage can be associated to hyporheic exchange. The STIR (Solute Transport In Rivers) multiple domain transport model is applied here to tracer test data from three very different Mediterranean streams with distinctive characteristics in terms of flow discharge, vegetation and substrate material. The model is used with an exponential residence time distribution (RTD) to represent surface storage processes and two distinct modeling closures are tested to simulate hyporheic retention: a second exponential RTD and a power-law distribution approximating a known solution for bedform-induced hyporheic exchange. Each stream shows distinct retention patterns characterized by different timescales of the storage time distribution. Both modeling closures lead to very good approximations of the observed breakthrough curves in the two rivers with permeable bed exposed to the flow, where hyporheic flows are expected to occur. In the one case where the occurrence of hyporheic flows is inhibited by bottom vegetation, only the two exponential RTD model is acceptable and the time scales of the two components are of the same magnitude. The significant finding of this work is the recognition of a strong signature of the river properties on tracer data and the evidence of the ability of multiple-component models to describe individual stream responses. This evidence may open a new perspective in river contamination studies, where rivers could possibly be classified based on their ability to trap and release pollutants.     

Effect of channel size on solute residence time distributions in rivers

The effect of channel size on residence time distributions (RTDs) of solute in rivers is investigated in this paper using tracer test data and the variable residence time (VART) model. Specifically, the investigation focuses on the influence of shear dispersion and hyporheic exchange on the shape of solute RTD, and how these two transport processes prevail in larger and smaller streams, respectively, leading to distinct tails of RTD. Simulation results show that (1) RTDs are dispersion-dependent and thereby channel-size (scale) dependent. RTDs increasing longitudinal dispersion coefficient. Small streams with negligible dispersion coefficient may display various types of RTD from upward curving patterns to a straight line (power-law distributions) and further to downward curving lognormal distributions when plotted in log–log coordinates. Moderate-sized rivers are transitional in terms of RTDs and commonly exhibit lognormal and power-law RTDs; (2) the incorporation of water and solute losses/gains in the VART model can improve simulation results and make parameter values more reasonable; (3) the ratio of time to peak concentration to the minimum mean residence time is equal to the recovery ratio of tracer. The relation provides a simple method for determining the minimum mean residence time; and (4) the VART model is able to reproduce various RTDs observed in rivers with 3–4 fitting parameters while no user-specified RTD functions are needed.     

Solute transport routing in a small stream

Abstract

The impact of pollution incidents on rivers and streams may be predicted using mathematical models of solute transport. Practical applications require an analytical or numerical solution to a governing solute mass balance equation together with appropriate values of relevant transport coefficients under the flow conditions of interest. This paper considers two such models, namely those proposed by Fischer and by Singh and Beck, and compares their performances using tracer data from a small stream in Edinburgh, UK. In calibrating the models, information on the magnitudes and the flow rate dependencies of the velocity and the dispersion coefficients was generated. The dispersion coefficient in the stream ranged between 0.1 and 0.9 m²/s for a flow rate range of 13–437 L/s. During calibration it was found that the Singh and Beck model fitted the tracer data a little better than the Fischer model in the majority of cases. In a validation exercise, however, both models gave similarly good predictions of solute transport at three different flow rates.     

Estimating sand concentrations using ADCP-based acoustic inversion in a large fluvial system characterized by bi-modal suspended-sediment distributions

Quantifying sediment flux within rivers is a challenge for many disciplines due, mainly, to difficulties inherent to traditional sediment sampling methods. These methods are operationally complex, high cost, and high risk. Additionally, the resulting data provide a low spatial and temporal resolution estimate of the total sediment flux, which has impeded advances in the understanding of the hydro-geomorphic characteristics of rivers. Acoustic technologies have been recognized as a leading tool for increasing the resolution of sediment data by relating their echo intensity level measurements to suspended sediment. Further effort is required to robustly test and develop these techniques across a wide range of conditions found in natural river systems. This article aims to evaluate the application of acoustic inversion techniques using commercially available, down-looking acoustic Doppler current profilers (ADCPs) in quantifying suspended sediment in a large sand bed river with varying bi-modal particle size distributions, wash load and suspended-sand ratios, and water stages. To achieve this objective, suspended sediment was physically sampled along the Paraná River, Argentina, under various hydro-sedimentological regimes. Two ADCPs emitting different sound frequencies were used to simultaneously profile echo intensity level within the water column. Using the sonar equation, calibrations were determined between suspended-sand concentrations and acoustic backscatter to solve the inverse problem. The study also analyzed the roles played by each term of the sonar equation, such as ADCP frequency, power supply, instrument constants, and particle size distributions typically found in sand bed rivers, on sediment attenuation and backscatter. Calibrations were successfully developed between corrected backscatter and suspended-sand concentrations for all sites and ADCP frequencies, resulting in mean suspended-sand concentration estimates within about 40% of the mean sampled concentrations. Noise values, calculated using the sonar equation and sediment sample characteristics, were fairly constant across evaluations, suggesting that they could be applied to other sand bed rivers. © 2018 John Wiley & Sons, Ltd.     

三维散射系数结构揭示的龙滩库区水的渗透特征

使用2006年10月1日至2010年5月14日9个固定台站和2009年4月4日至2010年5月14日15个临时台站记录的地震波形资料,采用尾波包络线反演方法,得到了龙滩库区地壳的三维散射系数结构,结果表明:(1)龙滩水库下方地壳中存在明显的非均匀结构.由大坝附近布柳河与红水河交汇处至三江(红水河、油拉河和牛河)交汇处的河段下方是研究区最明显的高散射系数区,高散射系数延伸深度达10 km,但在8 km以下高散射系数范围明显减小,除此之外,八茂断裂东西两端和八腊断裂周围也存在小范围的高散射系数区.(2)龙滩库区高散射系数主要分布在碳酸盐地层及与之接壤的透水性较好的砂页岩中,并且主要位于主干河流附近,河流和断层交汇处附近及与河流相交的断层附近,高散射系数分布与水的渗透密切相关.库区的水向河流两岸的渗透宽度约为10 km左右,深度不超过10 km.(3)龙滩库区地震主要集中在7~10 km深度的高散射系数区内,在水库地震中震源明显偏深,可能与库区水渗透引起的古岩溶水活化有关.     

Investigation of submarine groundwater discharge to tidal rivers: Evidence for regional and local scale seepage

Fluxes of submarine groundwater discharge (SGD) were investigated into two tidal rivers on the north and south shore of Long Island, NY, during July 2015. Ground‐based handheld thermal infrared (TIR) imagery, combined with direct push‐point piezometer sampling, documented spatially heterogeneous small‐scale intertidal seepage zones. Pore waters were relatively fresh and enriched in nitrogen (N) within these small‐scale seeps. Pore waters sampled just 20 cm away, outside the boundary of the ground‐based TIR‐located seepage zone, were more saline and lower in N. These ground‐based TIR‐identified seeps geochemically represented the terrestrial fresh groundwater endmember, whereas N in pore waters sampled outside of the TIR‐identified seeps was derived from the remineralization of organic matter introduced into the sediment by tidal seawater infiltration. A ²²²Rn (radon‐222) time‐series was used to quantify fresh SGD‐associated N fluxes using the N endmembers sampled from the ground‐based TIR pore water profiles. N fluxes were up‐scaled to groundwater seepage zones identified from high‐resolution airborne TIR imagery using the two‐dimensional size of the airborne TIR surface water anomalies, relative to the N flux from the time‐series sampling location. Results suggest that the N load from the north‐shore tidal river to Long Island Sound is underrepresented by at least 1.6–3.6%, whereas the N load from SGD to a south‐shore tidal river may be up to 9% higher than previous estimates. These results demonstrate the importance of SGD in supplying nutrients to the lower reaches of tidal rivers and suggest that N loads in other tidal river environments may be underestimated if SGD is not accounted for.     

Study on the relation of river morphology and tsunami propagation in rivers

The relations of river morphology and tsunami propagation in rivers were studied at several rivers in the Tohoku region during The Great Chilean Tsunami of 2010 and The Great East Japan Tsunami of 2011. It was found that river mouth morphological features play an important role in the intrusion of low magnitude tsunamis in which the geological and geographical conditions are an important factor. Nevertheless, the effects of these features were not found in the case of an extreme tsunami wave. As the wave enters the river, the propagation depends on other factors. It was found that the intrusion distance correlates well to the riverbed slope. The measurements of water level and riverbed slope were analyzed to propose an empirical method for estimating the damping coefficient for the tsunami propagation in rivers based on the tsunami of 2011. The proposed empirical method was used to approximate the length of the tsunami intrusion into a river by assuming that the furthest distance is given for the ratio of local tsunami wave height to the tsunami wave height at the river entrance of 0.05 (5 %). The estimated intrusion length from the proposed method in this study shows a good comparison with measurement data.     

Tracking Groundwater Discharge to a Large River using Tracers and Geophysics

Few studies have investigated large reaches of rivers in which multiple sources of groundwater are responsible for maintaining baseflow. This paper builds upon previous work undertaken along the Fitzroy River, one of the largest perennial river systems in north‐western Australia. Synoptic regional‐scale sampling of both river water and groundwater for a suite of environmental tracers (⁴He, ⁸⁷Sr/⁸⁶Sr, ²²²Rn and major ions), and subsequent modeling of tracer behavior in the river, has enabled definition and quantification of groundwater input from at least three different sources. We show unambiguous evidence of both shallow “local” groundwater, possibly recharged to alluvial aquifers beneath the adjacent floodplain during recent high‐flow events, and old “regional” groundwater introduced via artesian flow from deep confined aquifers. We also invoke hyporheic exchange and either bank return flow or parafluvial flow to account for background ²²²Rn activities and anomalous chloride trends along river reaches where there is no evidence of the local or regional groundwater inputs. Vertical conductivity sections acquired through an airborne electromagnetic (AEM) survey provide insights to the architecture of the aquifers associated with these sources and general groundwater quality characteristics. These data indicate fresh groundwater from about 300 m below ground preferentially discharging to the river, at locations consistent with those inferred from tracer data. The results demonstrate how sampling rivers for multiple environmental tracers of different types—including stable and radioactive isotopes, dissolved gases and major ions—can significantly improve conceptualization of groundwater—surface water interaction processes, particularly when coupled with geophysical techniques in complex hydrogeological settings.