Incorporating Super‐Diffusion due to Sub‐Grid Heterogeneity to Capture Non‐Fickian Transport

Numerical transport models based on the advection‐dispersion equation (ADE) are built on the assumption that sub‐grid cell transport is Fickian such that dispersive spreading around the average velocity is symmetric and without significant tailing on the front edge of a solute plume. However, anomalous diffusion in the form of super‐diffusion due to preferential pathways in an aquifer has been observed in field data, challenging the assumption of Fickian dispersion at the local scale. This study develops a fully Lagrangian method to simulate sub‐grid super‐diffusion in a multidimensional regional‐scale transport model by using a recent mathematical model allowing super‐diffusion along the flow direction given by the regional model. Here, the time randomizing procedure known as subordination is applied to flow field output from MODFLOW simulations. Numerical tests check the applicability of the novel method in mapping regional‐scale super‐diffusive transport conditioned on local properties of multidimensional heterogeneous media.     

Local Equilibrium and Retardation Revisited

In modeling solute transport with mobile‐immobile mass transfer (MIMT), it is common to use an advection‐dispersion equation (ADE) with a retardation factor, or retarded ADE. This is commonly referred to as making the local equilibrium assumption (LEA). Assuming local equilibrium, Eulerian textbook treatments derive the retarded ADE, ostensibly exactly. However, other authors have presented rigorous mathematical derivations of the dispersive effect of MIMT, applicable even in the case of arbitrarily fast mass transfer. We resolve the apparent contradiction between these seemingly exact derivations by adopting a Lagrangian point of view. We show that local equilibrium constrains the expected time immobile, whereas the retarded ADE actually embeds a stronger, nonphysical, constraint: that all particles spend the same amount of every time increment immobile. Eulerian derivations of the retarded ADE thus silently commit the gambler's fallacy, leading them to ignore dispersion due to mass transfer that is correctly modeled by other approaches. We then present a particle tracking simulation illustrating how poor an approximation the retarded ADE may be, even when mobile and immobile plumes are continually near local equilibrium. We note that classic “LEA” (actually, retarded ADE validity) criteria test for insignificance of MIMT‐driven dispersion relative to hydrodynamic dispersion, rather than for local equilibrium.     

Estimation of vertical water fluxes from temperature time series by the inverse numerical computer program FLUX‐BOT

The application of heat as a hydrological tracer has become a standard method for quantifying water fluxes between groundwater and surface water. The typical application is to estimate vertical water fluxes in the shallow subsurface beneath streams or lakes. For this purpose, time series of temperatures in the surface water and in the sediment are measured and evaluated by a vertical 1D representation of heat transport by advection and conduction. Several analytical solutions exist to calculate the vertical water flux from the measured temperatures. Although analytical solutions can be easily implemented, they are restricted to specific boundary conditions such as a sinusoidal upper temperature boundary. Numerical solutions offer higher flexibility in the selection of the boundary conditions. This, in turn, reduces the effort of data preprocessing, such as the extraction of the diurnal temperature variation from the raw data. Here, we present software to estimate water fluxes based on temperatures—FLUX‐BOT. FLUX‐BOT is a numerical code written in MATLAB that calculates vertical water fluxes in saturated sediments based on the inversion of measured temperature time series observed at multiple depths. FLUX‐BOT applies a centred Crank–Nicolson implicit finite difference scheme to solve the one‐dimensional heat advection–conduction equation. FLUX‐BOT includes functions for the inverse numerical routines, functions for visualizing the results, and a function for performing uncertainty analysis. We present applications of FLUX‐BOT to synthetic and to real temperature data to demonstrate its performance.     

A Practical Modeling Framework for Non‐Fickian Transport and Multi‐Species Sequential First‐Order Reaction

Many studies indicate that small‐scale heterogeneity and/or mobile–immobile mass exchange produce transient non‐Fickian plume behavior that is not well captured by the use of the standard, deterministic advection‐dispersion equation (ADE). An extended ADE modeling framework is presented here that is based on continuous time random walk theory. It can be used to characterize non‐Fickian transport coupled with simultaneous sequential first‐order reactions (e.g., biodegradation or radioactive decay) for multiple degrading contaminants such as chlorinated solvents, royal demolition explosive, pesticides, and radionuclides. To demonstrate this modeling framework, new transient analytical solutions are derived and are inverted in Laplace space. Closed‐form, steady‐state, multi‐species analytical solutions are also derived for non‐Fickian transport in highly heterogeneous aquifers with linear sorption–desorption and matrix diffusion for use in spreadsheets. The solutions are general enough to allow different degradation rates for the mobile and immobile zones. The transient solutions for multi‐species transport are applied to examine the effects of source remediation on the natural attenuation of downgradient plumes of both parent and degradation products in highly heterogeneous aquifers. Results for representative settings show that the use of the standard, deterministic ADE can over‐estimate cleanup rates and under‐predict the cleanup timeframe in comparison to the extended ADE analytical model. The modeling framework and calculations introduced here are also applied for a 30 year groundwater cleanup program at a site in Palm Bay, Florida. The simulated plume concentrations using the extended ADE exhibited agreement with observed long concentration tails of trichloroethene, cis 1,2 DCE, and VC that remained above cleanup goals.     

Conceptual modelling to assess how the interplay of hydrological connectivity,catchment storage and tracer dynamics controls nonstationary water age estimates

Although catchment storage is an intrinsic control on the rainfall–runoff response of streams, direct measurement remains a major challenge. Coupled models that integrate long‐term hydrometric and isotope tracer data are useful tools that can provide insights into the dynamics of catchment storage and the volumes of water involved. In this study, we use a tracer‐aided hydrological model to characterize catchment storage as a dynamic control on system function related to streamflow generation, which also allows direct estimation of the nonstationarity of water ages. We show that in a wet Scottish upland catchment dominated by runoff generation from riparian peats (histosols) with high water storage, nonstationarity in water age distributions is only clearly detectable during more extreme wet and dry periods. This is explained by the frequency and longevity of hydrological connectivity and the associated relative importance of flow paths contributing younger or older waters to the stream. Generally, these saturated riparian soils represent large mixing zones that buffer the time variance of water age and integrate catchment‐scale partial mixing processes. Although storage simulations depend on model performance, which is influenced by input variability and the degree of isotopic damping in the stream, a longer‐term storage analysis of this model indicates a system that is only sensitive to more extreme hydroclimatic variability. Copyright © 2014 John Wiley & Sons, Ltd.     

Factors controlling seasonal groundwater and solute flux from snow‐dominated basins

Critical zone influences on hydrologic partitioning, subsurface flow paths and reactions along these flow paths dictate the timing and magnitude of groundwater and solute flux to streams. To isolate first‐order controls on seasonal streamflow generation within highly heterogeneous, snow‐dominated basins of the Colorado River, we employ a multivariate statistical approach of end‐member mixing analysis using a suite of daily chemical and isotopic observations. Mixing models are developed across 11 nested basins (0.4 to 85 km²) spanning a gradient of climatological, physical, and geological characteristics. Hydrograph separation using rain, snow, and groundwater as end‐members indicates that seasonal contributions of groundwater to streams is significant. Mean annual groundwater flux ranges from 12% to 33% whereas maximum groundwater contributions of 17% to 50% occur during baseflow. The direct relationship between snow water equivalent and groundwater flux to streams is scale dependent with a trend toward self‐similarity when basins exceed 5.5 km². We find groundwater recharge increases in basins of high relief and within the upper subalpine where maximum snow accumulation is coincident with reduced conifer cover and lower canopy densities. The mixing model developed for the furthest downstream site did not transfer to upstream basins. The resulting error in predicted stream concentrations points toward weathering reactions as a function of source rock and seasonal shifts in flow path. Additionally, the potential for microbial sulfate reduction in floodplain sediments along a low‐gradient, meandering portion of the river is sufficient to modify hillslope contributions and alter mixing ratios in the analysis. Soil flushing in response to snowmelt is not included as an end‐member but is identified as an important mechanism for release of solutes from these mountainous watersheds. End‐member mixing analysis used in combination with high‐frequency observations reveals important aspects of catchment hydrodynamics across scale.     

Predicting acid neutralizing capacity from landscape classification: application to Galloway,south‐west Scotland

Regional estimates of acid neutralizing capacity (ANC) in stream waters are found using a regression model. The model has landscape classifications based on catchment characteristics as its main independent variables. It also includes continuously varying covariates. Landscape classifications and covariates are selected from a priori scientific understanding of acidification processes. Parameter estimates for the model are found using measurements of ANC in 50 streams in Galloway, south‐west Scotland with a history of acidification. The parameterized model is then used to provide ANC simulations for streams throughout a subregion, assuming conservative mixing of ANC through the flow network. The stream water sampling survey is designed to reduce the variance of parameter estimates. A variance model is suggested for the concentrations, and this is used to simulate the variance of ANC concentrations throughout the subregion. Monte Carlo simulation is used to estimate the distribution of the length of river reach with ANC less than zero. © Crown Copyright 2004. Reproduced with the permission of Her Majesty's Stationery Office. Published by John Wiley & Sons, Ltd.     

Insights on stream temperature processes through development of a coupled hydrologic and stream temperature model for forested coastal headwater catchments

Stream temperature controls a number of biological, chemical, and physical processes occurring in aquatic environments. Transient snow cover and advection associated with lateral throughflow inputs can have a dominant influence on stream thermal regimes for headwater catchments in the rain‐on‐snow zone. Most existing stream temperature models lack the ability to properly simulate these processes. We developed and evaluated a conceptual‐parametric catchment‐scale stream temperature model that includes the role of transient snow cover and lateral advection associated with throughflow. The model consists of routines for simulating canopy interception, snow accumulation and melt, hillslope throughflow runoff and temperature, and stream channel energy exchange processes. The model was used to predict discharge and stream temperature for a small forested headwater catchment near Vancouver, Canada, using long‐term (1963–2013) weather data to compute model forcing variables. The model was evaluated against 4 years of observed stream temperature. The model generally predicted daily mean stream temperature accurately (annual RMSE between 0.57 and 1.24 °C) although it overpredicted daily summer stream temperatures by up to 3 °C during extended low streamflow conditions. Model development and testing provided insights on the roles of advection associated with lateral throughflow, channel interception of snow, and surface–subsurface water interactions on stream thermal regimes. This study shows that a relatively simple but process‐based model can provide reasonable stream temperature predictions for forested headwater catchments located in the rain‐on‐snow zone.     

A comparison of high‐resolution specific conductance‐based end‐member mixing analysis and a graphical method for baseflow separation of four streams in hydrologically challenging agricultural watersheds

Quantifying the relative contributions of different sources of water to a stream hydrograph is important for understanding the hydrology and water quality dynamics of a given watershed. To compare the performance of two methods of hydrograph separation, a graphical program [baseflow index (BFI)] and an end‐member mixing analysis that used high‐resolution specific conductance measurements (SC‐EMMA) were used to estimate daily and average long‐term slowflow additions of water to four small, primarily agricultural streams with different dominant sources of water (natural groundwater, overland flow, subsurface drain outflow, and groundwater from irrigation). Because the result of hydrograph separation by SC‐EMMA is strongly related to the choice of slowflow and fastflow end‐member values, a sensitivity analysis was conducted based on the various approaches reported in the literature to inform the selection of end‐members. There were substantial discrepancies among the BFI and SC‐EMMA, and neither method produced reasonable results for all four streams. Streams that had a small difference in the SC of slowflow compared with fastflow or did not have a monotonic relationship between streamflow and stream SC posed a challenge to the SC‐EMMA method. The utility of the graphical BFI program was limited in the stream that had only gradual changes in streamflow. The results of this comparison suggest that the two methods may be quantifying different sources of water. Even though both methods are easy to apply, they should be applied with consideration of the streamflow and/or SC characteristics of a stream, especially where anthropogenic water sources (irrigation and subsurface drainage) are present. Copyright © 2014 John Wiley & Sons, Ltd.     

Perspective on theories of non-Fickian transport in heterogeneous media

Subsurface fluid flow and solute transport take place in a multiscale heterogeneous environment. Neither these phenomena nor their host environment can be observed or described with certainty at all scales and locations of relevance. The resulting ambiguity has led to alternative conceptualizations of flow and transport and multiple ways of addressing their scale and space–time dependencies. We focus our attention on four approaches that give rise to nonlocal representations of advective and dispersive transport of nonreactive tracers in randomly heterogeneous porous or fractured continua. We compare these approaches theoretically on the basis of their underlying premises and the mathematical forms of the corresponding nonlocal advective–dispersive terms. One of the four approaches describes transport at some reference support scale by a classical (Fickian) advection–dispersion equation (ADE) in which velocity is a spatially (and possibly temporally) correlated random field. The randomness of the velocity, which is given by Darcy’s law, stems from random fluctuations in hydraulic conductivity (and advective porosity though this is often disregarded). Averaging the stochastic ADE over an ensemble of velocity fields results in a space–time-nonlocal representation of mean advective–dispersive flux, an approach we designate as stnADE. A closely related space–time-nonlocal representation of ensemble mean transport is obtained upon averaging the motion of solute particles through a random velocity field within a Lagrangian framework, an approach we designate stnL. The concept of continuous time random walk (CTRW) yields a representation of advective–dispersive flux that is nonlocal in time but local in space. Closely related to the latter are forms of ADE entailing fractional derivatives (fADE) which leads to representations of advective–dispersive flux that are nonlocal in space but local in time; nonlocality in time arises in the context of multirate mass transfer models, which we exclude from consideration in this paper. We describe briefly each of these four nonlocal approaches and offer a perspective on their differences, commonalities, and relative merits as analytical and predictive tools.     

Hyporheic and total transient storage in small,sand‐bed streams

Key processes in stream ecosystems are linked to hydraulic retention, which is the departure of stream flow from ideal ‘plug flow’, and reflects fluid movement through surface and hyporheic storage zones. Most existing information about hyporheic exchange is based on flume studies or field measurements in relatively steep streams with beds coarser than sand. Stream tracer studies may be used to quantify overall hydraulic retention, but disaggregation of surface and hyporheic retention remains difficult. A stream tracer approach was used to compute the rates at which stream water is exchanged with water in storage zones (total storage) in short reaches of two small, sand‐bed streams under free and obstructed flow conditions. Tracer curves were fit to the one‐dimensional transport with inflow storage model OTIS‐P. Networks of piezometers were used to measure specific discharge between the stream and the groundwater. In the sand‐bed streams studied, parameters describing total retention were in the upper 50% of data compiled from the literature, most of which represented streams with beds coarser than sand. However, hyporheic storage was an insignificant component of total hydraulic retention, representing only 0·01–0·49% of total exchange, and this fraction did not increase after installation of flow obstructions. Total retention did not vary systematically with bed material size, but increased 50–100% following flow obstruction. Removal of roughness elements, such as large wood and debris dams, is detrimental to processes dependent upon transient storage in small, sand‐bed streams. Copyright © 2007 John Wiley & Sons, Ltd.     

Determining long time‐scale hyporheic zone flow paths in Antarctic streams

In the McMurdo Dry Valleys of Antarctica, glaciers are the source of meltwater during the austral summer, and the streams and adjacent hyporheic zones constitute the entire physical watershed; there are no hillslope processes in these systems. Hyporheic zones can extend several metres from each side of the stream, and are up to 70 cm deep, corresponding to a lateral cross‐section as large as 12 m², and water resides in the subsurface year around. In this study, we differentiate between the near‐stream hyporheic zone, which can be characterized with stream tracer experiments, and the extended hyporheic zone, which has a longer time‐scale of exchange. We sampled stream water from Green Creek and from the adjacent saturated alluvium for stable isotopes of D and ¹⁸O to assess the significance and extent of stream‐water exchange between the streams and extended hyporheic zones over long time‐scales (days to weeks). Our results show that water residing in the extended hyporheic zone is much more isotopically enriched (up to 11‰ D and 2·2‰ ¹⁸O) than stream water. This result suggests a long residence time within the extended hyporheic zone, during which fractionation has occurred owing to summer evaporation and winter sublimation of hyporheic water. We found less enriched water in the extended hyporheic zone later in the flow season, suggesting that stream water may be exchanged into and out of this zone, on the time‐scale of weeks to months. The transient storage model OTIS was used to characterize the exchange of stream water with the extended hyporheic zone. Model results yield exchange rates (α) generally an order magnitude lower (10^?5 s^?1) than those determined using stream‐tracer techniques on the same stream. In light of previous studies in these streams, these results suggest that the hyporheic zones in Antarctic streams have near‐stream zones of rapid stream‐water exchange, where ‘fast’ biogeochemical reactions may influence water chemistry, and extended hyporheic zones, in which slower biogeochemical reaction rates may affect stream‐water chemistry at longer time‐scales. Copyright © 2003 John Wiley & Sons, Ltd.     

Spatially varying dispersion to model breakthrough curves

Often the water flowing in a karst conduit is a combination of contaminated water entering at a sinkhole and cleaner water released from the limestone matrix. Transport processes in the conduit are controlled by advection, mixing (dilution and dispersion), and retention-release. In this article, a karst transport model considering advection, spatially varying dispersion, and dilution (from matrix seepage) is developed. Two approximate Green's functions are obtained using transformation of variables, respectively, for the initial-value problem and for the boundary-value problem. A numerical example illustrates that mixing associated with strong spatially varying conduit dispersion can cause strong skewness and long tailing in spring breakthrough curves. Comparison of the predicted breakthrough curve against that measured from a dye-tracing experiment between Ames Sink and Indian Spring, Northwest Florida, shows that the conduit dispersivity can be as large as 400 m. Such a large number is believed to imply strong solute interaction between the conduit and the matrix and/or multiple flow paths in a conduit network. It is concluded that Taylor dispersion is not dominant in transport in a karst conduit, and the complicated retention-release process between mobile- and immobile waters may be described by strong spatially varying conduit dispersion.     

A comparison of stream water temperature regimes from open and afforested moorland,Yorkshire Dales,northern England

Despite the known importance of water temperature for river ecosystems, the thermal regime of streams and rivers can be heavily modified by afforestation. Although the nature of the heat budget affecting streams in forested catchments shows high variability in space and time, most of the studies of stream temperature response to afforestation have lacked replication among streams. This study examined the impacts of coniferous forest plantations on stream water temperature at six sites (three forested and three open moorland) in the Yorkshire Dales, northern England. Our aim was to test the hypothesis that afforestation would alter the thermal regime of streams, leading to reduced year‐round thermal variability, and cooler summer/warmer winter water temperatures, relative to streams flowing across open moorland. Data collected from April 2007 to March 2009 showed similar thermal dynamics among all six streams over the study period, although variability in forested streams was markedly lower as expected. Mean and maximum daily water temperatures were significantly higher in open moorland streams for much of the year but while some forested streams were warmer than individual moorland streams during winter months (November to February), there was considerable overlap in water temperature between moorland and forest streams. Most stream temperature records showed evidence of low/no winter flow and freezing. These results contrast with many previous studies that have reported warmer temperatures in forested versus open moorland streams during winter, a finding that most likely reflects site‐specific hydrological, geomorphological and climatological influences on water temperature in addition to afforestation. This study demonstrates the need for replication of hydrological monitoring when examining the effects of basin‐scale management practices and provides further evidence for changes in stream thermal regime following afforestation, a practice that is likely to increase in future due to growing demands for increased forest cover in the UK uplands. Copyright © 2010 John Wiley & Sons, Ltd.     

Base flow‐driven shifts in tropical stream temperature regimes across a mean annual rainfall gradient

Climate change is expected to affect air temperature and watershed hydrology, but the degree to which these concurrent changes affect stream temperature is not well documented in the tropics. How stream temperature varies over time under changing hydrologic conditions is difficult to isolate from seasonal changes in air temperature. Groundwater and bank storage contributions to stream flow (i.e., base flow [BF]) buffer water temperatures against seasonal and daily fluctuations in solar radiation and air temperature, whereas rainfall‐driven runoff produces flooding events that also influence stream temperature. We used a space‐for‐time substitution to examine how shifts in BF and runoff alter thermal regimes in streams by analyzing hydrological and temperature data collected from similar elevations (400–510 m above sea level) across a 3,500‐mm mean annual rainfall gradient on Hawai'i Island. Sub‐daily water temperature and stream flow gathered for 3 years were analyzed for daily, monthly, and seasonal trends and compared with air temperature measured at multiple elevations. Results indicate that decreases in median BF increased mean, maximum, and minimum water temperatures as well as daily temperature range. Monthly and daily trends in stream temperature among watersheds were more pronounced than air temperature, driven by differences in groundwater inputs and runoff. Stream temperature was strongly negatively correlated to BF during the dry season but not during the wet season due to frequent wet season runoff events contributing to total flow. In addition to projected increases in global air temperature, climate driven shifts in rainfall and runoff are likely to affect stream flow and groundwater recharge, with concurrent influences on BF resulting in shifts in water temperature that are likely to affect aquatic ecosystems.     

A three-dimensional numerical model of particulate transport for coastal waters

A Lagrangian marker particle in Eulerian finite difference cell solution to the three-dimensional incompressible mass transport equation was developed for predicting particulate transport in coastal and estuarine waters. Special features of the solution procedure include a finite difference grid network which translates horizontally and vertically with the mean particle motion and expands with the dispersive growth of the marker particle cloud. The cartesian vertical coordinate of the three-dimensional mass transport equation has been transformed, using instantaneous water column depth to allow adaptation to flow situations with a temporally and spatially varying bottom topography and free surface. Results from this model for turbulent diffusion and advection of a uniform plug flow of sediment in an unbounded uniform flow field with various sediment settling velocities were in excellent agreement with the corresponding analytic solutions. Using current information from a two-dimensional vertically averaged hydrodynamic's model, the model was utilized to predict the long term diffusion and advection of dilute neutrally and negatively buoyant suspended sediment clouds resulting from a hypothetical instantaneous release of dredge spoil waste at Brown's Ledge in Rhode Island Sound.     

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.     

Land management impacts on runoff sources in small Amazon watersheds

Forest clearing and conversion to cattle pasture in the lowland Amazon region has been linked to soil compaction and increased soil water storage, which combine to diminish soil infiltration, enhance quick lateral flows and increase the stream flow response to precipitation. Quantifying the importance of quick surficial flow in response to this land use change requires identification of water sources within catchments that contribute to stream flow. Using an end member mixing analysis approach, potential contributing sources of stream flow were evaluated during an entire rainy season in a forest and a pasture watershed drained by ephemeral‐to‐intermittent streams in the south‐western Amazon. Water yield was 17% of precipitation in the pasture and 0·8% of precipitation in the forest. During the early rainy season, throughfall, groundwater, and soil water contributed 79%, 18%, and 3%, respectively, to total forest stream flow. Over the entire rainy season, throughfall, groundwater, and shallow soil water provided 57%, 24%, and 19%, respectively, of stream flow. In the pasture watershed, overland flow dominated stream flow both in the early (67%) and late (57%) rainy season, with a mean contribution of 60% overland flow, 35% groundwater, and 5% soil water. The uncertainty associated with those estimates was studied using a Monte Carlo approach. In addition to large changes in total surface flow, marked differences were found in the proportions of total stream flow in the second half of the rainy season between the forest and pasture watershed. These results suggest that (1) there is great potential for alteration of the hydrological budgets of larger watersheds as the proportion of deforested land in the Amazon increases, and (2) as more rainfall is diverted into fast flowpaths to streams in established pastures, the potential to deliver water with higher solute concentrations generated by erosion or by bypassing sites of solute removal increases. Copyright © 2007 John Wiley & Sons, Ltd.     

Surface water and groundwater interactions in an extensively mined watershed,upper Schuylkill River,Pennsylvania, USA

Streams crossing underground coal mines may lose flow, whereas abandoned mine drainage (AMD) restores flow downstream. During 2005–2012, discharge from the Pine Knot Mine Tunnel, the largest AMD source in the upper Schuylkill River Basin, had near‐neutral pH and elevated concentrations of iron, manganese and sulphate. Discharge from the tunnel responded rapidly to recharge but exhibited a prolonged recession compared with nearby streams, consistent with rapid infiltration of surface water and slow release of groundwater from the mine complex. Dissolved iron was attenuated downstream by oxidation and precipitation, whereas dissolved CO₂ degassed and pH increased. During high flow conditions, the AMD and downstream waters exhibited decreased pH, iron and sulphate with increased acidity that were modelled by mixing net‐alkaline AMD with recharge or run‐off having low ionic strength and low pH. Attenuation of dissolved iron within the river was least effective during high flow conditions because of decreased transport time coupled with inhibitory effects of low pH on oxidation kinetics. A numerical model of groundwater flow was calibrated by using groundwater levels in the Pine Knot Mine and discharge data for the Pine Knot Mine Tunnel and West Branch Schuylkill River during a snowmelt event in January 2012. Although the calibrated model indicated substantial recharge to the mine complex took place away from streams, simulation of rapid changes in mine pool level and tunnel discharge during a high flow event in May 2012 required a source of direct recharge to the Pine Knot Mine. Such recharge produced small changes in mine pool level and rapid changes in tunnel flow rate because of extensive unsaturated storage capacity and high transmissivity within the mine complex. Thus, elimination of stream leakage could have a small effect on the annual discharge from the tunnel, but a large effect on peak discharge and associated water quality downstream. Published 2013. This article is a U.S. Government work and is in the public domain in the USA.     

Continuous time random walks for non-local radial solute transport

This study formulates and analyzes continuous time random walk (CTRW) models in radial flow geometries for the quantification of non-local solute transport induced by heterogeneous flow distributions and by mobile–immobile mass transfer processes. To this end we derive a general CTRW framework in radial coordinates starting from the random walk equations for radial particle positions and times. The particle density, or solute concentration is governed by a non-local radial advection–dispersion equation (ADE). Unlike in CTRWs for uniform flow scenarios, particle transition times here depend on the radial particle position, which renders the CTRW non-stationary. As a consequence, the memory kernel characterizing the non-local ADE, is radially dependent. Based on this general formulation, we derive radial CTRW implementations that (i) emulate non-local radial transport due to heterogeneous advection, (ii) model multirate mass transfer (MRMT) between mobile and immobile continua, and (iii) quantify both heterogeneous advection in a mobile region and mass transfer between mobile and immobile regions. The expected solute breakthrough behavior is studied using numerical random walk particle tracking simulations. This behavior is analyzed by explicit analytical expressions for the asymptotic solute breakthrough curves. We observe clear power-law tails of the solute breakthrough for broad (power-law) distributions of particle transit times (heterogeneous advection) and particle trapping times (MRMT model). The combined model displays two distinct time regimes. An intermediate regime, in which the solute breakthrough is dominated by the particle transit times in the mobile zones, and a late time regime that is governed by the distribution of particle trapping times in immobile zones. These radial CTRW formulations allow for the identification of heterogeneous advection and mobile-immobile processes as drivers of anomalous transport, under conditions relevant for field tracer tests.