APPLICATION OF UNIT HYDROGRAPH TECHNIQUES TO SOLUTE TRANSPORT IN CATCHMENTS

Current models of solute movement in catchments are based on rainfall–runoff models and are consequently biased towards processes which determine the magnitude and timing of water flux. It is shown here that the instantaneous unit hydrograph (IUH), or runoff response function, obtained from a hydrograph is fundamentally different from the residence time distribution which governs the response to solutes/tracers. Using hydrometric and tracer data obtained from a small (25 ha) catchment in the humid tropics a modification of the IUH technique is demonstrated which also allows approximate modelling of the tracer data. New features of the modified conceptual model are identified with known hillslope processes.     

The boundary layer of the residence time field

The residence time of a tracer in a control domain is usually computed by releasing tracer parcels and registering the time when each of these tracer parcels cross the boundary of the control domain. In this Lagrangian procedure, the particles are discarded or omitted as soon as they leave the control domain. In a Eulerian approach, the same approach can be implemented by integrating forward in time the advection–diffusion equation for a tracer. So far, the conditions to be applied at the boundary of the control domain were uncertain. We show here that it is necessary to prescribe that the tracer concentration vanishes at the boundary of the control domain to ensure the compatibility between the Lagrangian and Eulerian approaches. When we use the Constituent oriented Age and Residence time Theory (CART), this amounts to solving the differential equation for the residence time with boundary conditions forcing the residence time to vanish at the open boundaries of the control domain. Such boundary conditions are likely to induce the development of boundary layers (at outflow boundaries for the tracer concentration and at inflow boundaries for the residence time). The thickness of these boundary layers is of the order of the ratio of the diffusivity to the velocity. They can however be partly smoothed by tidal and other oscillating flows.     

鄱阳湖换水周期与示踪剂传输时间特征的数值模拟

在复杂湖泊水动力环境作用下,换水周期和传输时间变化直接影响着污染物的迁移和转化.本文运用数值模拟方法,定量研究了季节水情动态下鄱阳湖换水周期和示踪剂传输时间的空间分布.结果表明,不同季节下鄱阳湖换水周期均具有较高的空间异质性,贯穿整个湖区的主河道换水周期约10 d,大多湖湾区的换水周期则长达300多天.尽管不同季节下换水周期空间分布格局几乎相似,但受鄱阳湖水动力场的季节变化影响,夏、秋季的换水周期要明显大于春、冬季.基于换水周期频率分布曲线的统计表明,80%的鄱阳湖区的换水周期约30 d,其余湖区换水周期为几十天至几百天,表明鄱阳湖应该更加确切地描述为一个快速换水和慢速换水同时共存的湖泊系统.鄱阳湖示踪剂传输时间介于4~32 d,夏、秋季的传输时间(11~32 d)约为春、冬季(4~8 d)的4倍,主要与鄱阳湖季节性水情特征及示踪剂的迁移路径有关.本文所获取的换水周期和示踪剂传输时间的时空分布信息可为今后鄱阳湖水质、水环境和生态系统管理和维护等方面提供重要科学参考.     

Tracer measurements in groyne fields for the quantification of mean hydraulic residence times and of the exchange with the stream

Tracer experiments were carried out in groyne fields (GF) of the river Elbe near Havelberg (Germany) in order to estimate the hydraulic connectivity with the river channel. The characteristic times of the five groyne fields, which were estimated from the exponentially declining tracer curves in 43 runs, ranged between 15 min and 69 min and did not correlate with the water level. Methodological investigations show that single point injection and two measurements (in the outflowing water and in the dominant region) are sufficient to provide robust in‐situ tracer curves. Using simplified mathematical simulations with connected stirred tanks, the conditions are investigated for the development of breaks in tracer curves and for the occurrence of significant errors in the estimation of intrinsic residence times. It was shown that an initial uniform dye distribution is not mandatory for the estimation during steady states. In special cases, point injections are more advisable. Moreover, the mean hydraulic residence time was found to be not equivalent to the estimated characteristic time. In fact, it is mostly overestimated by tracer experiments. The degree of overestimation depends on mixing and the volumetric proportions between the different parts of the GF and can be calculated from measured dye concentration differences. For example, an overestimation of 32% was calculated for a groyne field with a commonly found circulation flow pattern.     

Heat Tracing in a Fractured Aquifer with Injection of Hot and Cold Water

Heat as a tracer in fractured porous aquifers is more sensitive to fracture-matrix processes than a solute tracer. Temperature evolution as a function of time can be used to differentiate fracture and matrix characteristics. Experimental hot (50 °C) and cold (10 °C) water injections were performed in a weathered and fractured granite aquifer where the natural background temperature is 30 °C. The tailing of the hot and cold breakthrough curves, observed under different hydraulic conditions, was characterized in a log–log plot of time vs. normalized temperature difference, also converted to a residence time distribution (normalized). Dimensionless tail slopes close to 1.5 were observed for hot and cold breakthrough curves, compared to solute tracer tests showing slopes between 2 and 3. This stronger thermal diffusive behavior is explained by heat conduction. Using a process-based numerical model, the impact of heat conduction toward and from the porous rock matrix on groundwater heat transport was explored. Fracture aperture was adjusted depending on the actual hydraulic conditions. Water density and viscosity were considered temperature dependent. The model simulated the increase or reduction of the energy level in the fracture-matrix system and satisfactorily reproduced breakthrough curves tail slopes. This study shows the feasibility and utility of cold water tracer tests in hot fractured aquifers to boost and characterize the thermal matrix diffusion from the matrix toward the flowing groundwater in the fractures. This can be used as complementary information to solute tracer tests that are largely influenced by strong advection in the fractures.     

DILUTION GAUGING ON THE RECESSION LIMB: 2. THE INTEGRATION METHOD / Mesures par dilution sur la courbe de tarissement: 2. Méthode par intégration

Abstract

The application of dilution gauging techniques to natural streams and other variable flows incurs a systematic error caused by the change in discharge with time. On the recession limb of a hydrograph the change is usually smooth and gradual, and errors can be expected intuitively to be small. In a preceding paper the author investigated errors arising from this cause in the case of a constant rate tracer injection, and developed formulae for the calculation of bias from known values of the recession constant and the distribution of residence time in the gauging reach. This paper extends the theory of the residence time model to the case of a dilution gauging by the integration method, and presents analogous formulae for the errors.     

Predicting Pesticide Attenuation in a Fractured Aquifer Using Lumped‐Parameter Models

Neighboring springs draining fractured‐rock aquifers can display large differences in water quality and flow regime, depending on local variations of the connectivity and the aperture size distribution of the fracture network. Consequently, because homogeneous equivalent parameters cannot be assumed a priori for the entire regional aquifer, the vulnerability to pollution of such springs has to be studied on a case by case basis. In this paper, a simple lumped‐parameter model usually applied to estimate the mean transit time of water (or tracer) is presented. The original exponential piston‐flow model was modified to take land‐use distribution into account and applied to predict the evolution of atrazine concentration in a series of springs draining a fractured sandstone aquifer in Luxembourg, where despite a nationwide ban in 2005, atrazine concentrations still had not begun to decrease in 2009. This persistence could be explained by exponentially distributed residence times in the aquifer, demonstrating that in some real world cases, models based on the groundwater residence time distribution can be a powerful tool for trend reversal assessments as recommended for instance by current European Union guidelines.     

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.     

Tracer Method to Determine Residence Time in a Permeable Reactive Barrier

A method is presented to evaluate ground water residence time in a zero‐valent iron (ZVI) permeable reactive barrier (PRB) using radon‐222 (²²²Rn) as a radioactive tracer. Residence time is a useful indicator of PRB hydraulic performance, with application to estimating the volumetric rate of ground water flow through a PRB, identifying flow heterogeneity, and characterizing flow conditions over time as a PRB matures. The tracer method relies on monitoring the decay of naturally occurring aqueous ²²²Rn as ground water flows through a PRB. Application of the method at a PRB site near Monticello, Utah, shows that after 8 years of operation, residence times in the ZVI range from 80 to 486 h and correlate well with chemical parameters (pH, Ca, SO₄, and Fe) that indicate the relative residence time. Residence times in this case study are determined directly from the first‐order decay equation because we show no significant emanation of ²²²Rn within the PRB and no measurable loss of ²²²Rn other than by radioactive decay.     

Environmental tracer transport (H and SF6) in the saturated and unsaturated zones and its use in nitrate pollution management

An important quantity in groundwater protection is the residence time of water in an aquifer. It relates to both the travel time of a pollutant to arrive at a well and the time span required for self-purification of a polluted aquifer after removal of pollutant inputs. Time scales for aquifers can be gained from artificial tracer experiments or from environmental tracer data, the latter offering the only realistic alternative if time scales of years or decades have to be taken into account.

Different tracers show different time scales due to their different transport mechanisms especially in the unsaturated zone. While solute tracers are moved advectively with the seepage water, gas tracers pass the unsaturated zone diffusively through the air phase. Depending on the properties of the unsaturated zone (hydraulic properties, thickness) this difference in behavior can be used to separate the subsurface transport process into the unsaturated and the saturated parts.

In a field study in Germany, SF₆ and ³H were used as environmental tracers. Both have a relatively well-known input function. Interpretation of data from observation wells by a box model approach led to spatially and temporally varying residence times. This was an indication that the influence of the unsaturated zone could not be neglected. While the gas tracer SF₆ shows only residence times in the saturated zone, the tracer ³H reflects the whole travel time of water including both the unsaturated and saturated zones. Using a one-dimensional plug-flow model for the unsaturated zone combined with a detailed two-dimensional flow and transport model for the saturated zone leads to a holistic and consistent interpretation of the measured tracer concentrations. The observed pattern of old water under thick loess cover and younger water under areas where the fractured basalt aquifer crops out is reproduced after adjusting only two parameters: the effective porosity of the saturated aquifer and the product of field capacity and thickness of the unsaturated zone. While the effective porosity of the saturated zone is adjusted by means of the SF₆ data, the field capacity of the loess layer is adjusted by means of the ³H observations. The thickness of the unsaturated zone is deduced from geological and pedological maps. All flow data are obtained from a calibrated flow model, which is based on geological data, observed heads and pumping tests only.

The transport model for the saturated zone was calibrated by fitting the porosity by means of gaseous tracer concentrations (SF₆). The combined saturated–unsaturated zone model was then calibrated by fitting the field capacity of the unsaturated zone by means of ³H concentrations. With this model it was possible to verify the observed NO₃ concentrations at the drinking water wells and to develop predictions for their future development under various scenarios of fertilizer input reduction in specific areas.     

Hyporheic exchange flows induced by constructed riffles and steps in lowland streams in southern Ontario,Canada

Stream–subsurface water interaction induced by natural riffles and constructed riffles/steps was examined in lowland streams in southern Ontario, Canada. The penetration of stream water into the subsurface was analysed using hydrometric data, and the zone of > 10% stream water was calculated from a chemical mixing equation using tracer injection of bromide and background chloride concentrations. The constructed riffles studied induced more extensive hyporheic exchange than the natural riffles because of their steeper longitudinal hydraulic head gradients and coarser streambed sediments. The depth of > 10% stream water zone in a small and a large constructed riffle extended to > 0·2 m and > 1·4 m depths respectively. Flux and residence time distribution of hyporheic exchange were simulated in constructed riffles using MODFLOW, a finite‐difference groundwater flow model. Hyporheic flux and residence time distribution varied along the riffles, and the exchange occurring upstream from the riffle crest was small in flux and had a long residence time. In contrast, hyporheic exchange occurring downstream from the riffle crest had a relatively short residence time and accounted for 83% and 70% of total hyporheic exchange flow in a small and large riffle respectively. Although stream restoration projects have not considered the hyporheic zone, our data indicate that constructed riffles and steps can promote vertical hydrologic exchange and increase the groundwater–surface water linkage in degraded lowland streams. Copyright © 2006 John Wiley & Sons, Ltd.     

Exchange and transport time scales in the Seto Inland Sea

Five typical water volumes in the Seto Inland Sea are defined, and their average residence times, remnant functions, and residence time distribution functions are obtained, mainly from results of hydraulic model experiments; the average residence times and the functions well describe characteristics of exchange and transport of materials in the sea. A representative residence time, which is the average residence time of the total water in the inland sea, is about 15 months.     

Modelling travel and residence times in the eastern Irish Sea

The Irish Sea, which lies between 51 degrees N-56 degrees N and 2 degrees 50'W-7 degrees W, provides a sheltered environment to exploit valuable fisheries resource. Anthropogenic activity is a real threat to its water quality. The majority of freshwater input down rivers flows into the eastern Irish Sea. The structure of the water circulation was not well understood during the planning of Sellafield nuclear plant outfall site in the eastern Irish Sea. A three-dimensional primitive equation numerical model was applied to the Irish Sea to simulate both barotropic and baroclinic circulation within the region. High accuracy was achieved with regard to the prediction of both tidal circulation and surface and nearbed water temperatures across the region. The model properly represented the Western Irish Sea Gyre, induced by thermal stratification and not known during planning Sellafield. Passive tracer simulations based on the developed hydrodynamic model were used to deliver residence times of the eastern Irish Sea region for various times of the year as well as travel times from the Sellafield outfall site to various locations within the Irish Sea. The results indicate a strong seasonal variability of travel times from Sellafield to the examined locations. Travel time to the Clyde Sea is the shortest for the autumnal tracer release (90 days); it takes almost a year for the tracer to arrive at the same location if it is released in January. Travel times from Sellafield to Dublin Bay fall within the range of 180-360 days. The average residence time of the entire eastern Irish Sea is around 7 months. The areas surrounding the Isle of Man are initially flushed due to a predominant northward flow; a backwater is formed in Liverpool Bay. Thus, elevated tracer concentrations are predicted in Liverpool Bay in the case of accidental spills at the Sellafield outfall site.     

Numerical modelling of circulation and dispersion processes in Boulogne-sur-Mer harbour (Eastern English Channel): sensitivity to physical forcing and harbour design

The MARS-3D model in conjunction with the particle tracking module Ichthyop is used to study circulation and tracer dynamics under a variety of forcing conditions in the eastern English Channel, and in the Boulogne-sur-Mer harbour (referred to hereafter as BLH). Results of hydrodynamic modelling are validated against the tidal gauge data, VHF radar surface velocities and ADCP measurements. Lagrangian tracking experiments are performed with passive particles to study tracer dispersal along the northern French coast, with special emphasis on the BLH. Simulations revealed an anticyclonic eddy generated in the harbour at rising tide. Tracers, released during flood tide at the Liane river mouth, move northward with powerful clockwise rotating current. After the high water, the current direction changes to westward, and tracers leave the harbour through the open boundary. During ebb tide, currents convergence along the western open boundary but no eddy is formed, surface currents inside the harbour are much weaker and the tracer excursion length is small. After the current reversal at low water, particles are advected shoreward resulting in a significant increase of the residence time of tracers released during ebb tide. The effect of wind on particle dispersion was found to be particularly strong. Under strong SW wind, the residence time of particles released during flood tide increases from 1.5 to 6 days. For release during ebb tide, SW wind weakens the southward tidally induced drift and thus the residence time decreases. Similar effects are observed when the freshwater inflow to the harbour is increased from 2 to 10 m³/s during the ebb tide flow. For flood tide conditions, the effect of freshwater inflow is less significant. We also demonstrate an example of innovative coastal management targeted at the reduction of the residence time of the pathogenic material accidentally released in the harbour.

     

Numerical modelling of circulation and dispersion processes in Boulogne-sur-Mer harbour (Eastern English Channel): sensitivity to physical forcing and harbour design

The MARS-3D model in conjunction with the particle tracking module Ichthyop is used to study circulation and tracer dynamics under a variety of forcing conditions in the eastern English Channel, and in the Boulogne-sur-Mer harbour (referred to hereafter as BLH). Results of hydrodynamic modelling are validated against the tidal gauge data, VHF radar surface velocities and ADCP measurements. Lagrangian tracking experiments are performed with passive particles to study tracer dispersal along the northern French coast, with special emphasis on the BLH. Simulations revealed an anticyclonic eddy generated in the harbour at rising tide. Tracers, released during flood tide at the Liane river mouth, move northward with powerful clockwise rotating current. After the high water, the current direction changes to westward, and tracers leave the harbour through the open boundary. During ebb tide, currents convergence along the western open boundary but no eddy is formed, surface currents inside the harbour are much weaker and the tracer excursion length is small. After the current reversal at low water, particles are advected shoreward resulting in a significant increase of the residence time of tracers released during ebb tide. The effect of wind on particle dispersion was found to be particularly strong. Under strong SW wind, the residence time of particles released during flood tide increases from 1.5 to 6 days. For release during ebb tide, SW wind weakens the southward tidally induced drift and thus the residence time decreases. Similar effects are observed when the freshwater inflow to the harbour is increased from 2 to 10 m³/s during the ebb tide flow. For flood tide conditions, the effect of freshwater inflow is less significant. We also demonstrate an example of innovative coastal management targeted at the reduction of the residence time of the pathogenic material accidentally released in the harbour.     

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 morphology and discharge on hyporheic exchange flows in two small streams in the Cascade Mountains of Oregon,USA

Stream‐tracer injections were used to examine the effect of channel morphology and changing stream discharge on hyporheic exchange flows. Direct observations were made from well networks to follow tracer movement through the hyporheic zone. The reach‐integrated influence of hyporheic exchange was evaluated using the transient storage model (TSM) OTIS‐P. Transient storage modelling results were compared with direct observations to evaluate the reliability of the TSM. Results from the tracer injection in the bedrock reach supported the assumption that most transient storage in headwater mountain streams results from hyporheic exchange. Direct observations from the well networks in colluvial reaches showed that subsurface flow paths tended to parallel the valley axis. Cross‐valley gradients were weak except near steps, where vertical and cross‐valley hydraulic gradients indicated a strong potential for stream water to downwell into the hyporheic zone. The TSM parameters showed that both size and residence time of transient storage were greater in reaches with a few large log‐jam‐formed steps than in reaches with more frequent, but smaller steps. Direct observations showed that residence times in the unconstrained stream were longer than in the constrained stream and that little change occurred in the location and extent of the hyporheic zone between low‐ and high‐baseflow discharges in any of the colluvial reaches. The transient storage modelling results did not agree with these observations, suggesting that the TSM was insensitive to long residence‐time exchange flows and was very sensitive to changes in discharge. Disagreements between direct observations and the transient storage modelling results highlight fundamental problems with the TSM that confound comparisons between the transient storage modelling results for tracer injections conducted under differing flow conditions. Overall, the results showed that hyporheic exchange was little affected by stream discharge (at least over the range of baseflow discharges examined in this study). The results did show that channel morphology controlled development of the hyporheic zone in these steep mountain stream channels. Copyright © 2005 John Wiley & Sons, Ltd.