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.     

Numerical modelling of stream–aquifer interaction: Quantifying the impact of transient streambed permeability and aquifer heterogeneity

Stream–aquifer interaction plays a vital role in the water cycle, and a proper study of this interaction is needed for understanding groundwater recharge, contaminants migration, and for managing surface water and groundwater resources. A model‐based investigation of a field experiment in a riparian zone of the Schwarzbach river, a tributary of the Rhine River in Germany, was conducted to understand stream–aquifer interaction under alternative gaining and losing streamflow conditions. An equivalent streambed permeability, estimated by inverting aquifer responses to flood waves, shows that streambed permeability increased during infiltration of stream water to aquifer and decreased during exfiltration. Aquifer permeability realizations generated by multiple‐point geostatistics exhibit a high degree of heterogeneity and anisotropy. A coupled surface water groundwater flow model was developed incorporating the time‐varying streambed permeability and heterogeneous aquifer permeability realizations. The model was able to reproduce varying pressure heads at two observation wells near the stream over a period of 55 days. A Monte Carlo analysis was also carried out to simulate groundwater flow, its age distribution, and the release of a hypothetical wastewater plume into the aquifer from the stream. Results of this uncertainty analysis suggest (a) stream–aquifer exchange flux during the infiltration periods was constrained by aquifer permeability; (b) during exfiltration, this flux was constrained by the reduced streambed permeability; (c) the effect of temporally variable streambed permeability and aquifer heterogeneity were found important to improve the accurate capture of the uncertainty; and (d) probabilistic infiltration paths in the aquifer reveal that such pathways and the associated prediction of the extent of the contaminant plume are highly dependent on aquifer heterogeneity.     

A two‐dimensional analytical solution for groundwater flow in a leaky confined aquifer system near open tidal water

Groundwater in coastal areas is commonly disturbed by tidal fluctuations. A two‐dimensional analytical solution is derived to describe the groundwater fluctuation in a leaky confined aquifer system near open tidal water under the assumption that the groundwater head in the confined aquifer fluctuates in response to sea tide whereas that of the overlying unconfined aquifer remains constant. The analytical solution presented here is an extension of the solution by Sun for two‐dimensional groundwater flow in a confined aquifer and the solution by Jiao and Tang for one‐dimensional groundwater flow in a leaky confined aquifer. The analytical solution is compared with a two‐dimensional finite difference solution. On the basis of the analytical solution, the groundwater head distribution in a leaky confined aquifer in response to tidal boundaries is examined and the influence of leakage on groundwater fluctuation is discussed. Copyright © 2001 John Wiley & Sons, Ltd.     

Recovering the release history of a groundwater contaminant using a non‐linear least‐squares method

A non‐linear least‐squares (NLS) method is used without regularization to recover the release history of a groundwater contaminant plume from its current measured spatial distribution. The flow system is assumed to be one‐dimensional, with the plume originating from a known single site. The solution is found to be very sensitive to noise and to the extent to which the plume is dissipated. Although the NLS method is extremely sensitive to measurement errors for the gradual release scenario, it can resolve the release histories for catastrophic release scenarios reasonably well, even in the presence of moderate measurement errors. A number of synthetic numerical examples are analysed. We find that for catastrophic contaminant releases the NLS method may be an alternative to the Tikhonov regularization approach. Copyright © 2000 John Wiley & Sons, Ltd.     

Reducing monitoring gaps at the aquifer–river interface by modelling groundwater–surface water exchange flow patterns

This study investigates spatial patterns and temporal dynamics of aquifer–river exchange flow at a reach of the River Leith, UK. Observations of sub‐channel vertical hydraulic gradients at the field site indicate the dominance of groundwater up‐welling into the river and the absence of groundwater recharge from surface water. However, observed hydraulic heads do not provide information on potential surface water infiltration into the top 0–15 cm of the streambed as these depths are not covered by the existing experimental infrastructure. In order to evaluate whether surface water infiltration is likely to occur outside the ‘window of detection’, i.e. the shallow streambed, a numerical groundwater model is used to simulate hydrological exchanges between the aquifer and the river. Transient simulations of the successfully validated model (Nash and Sutcliff efficiency of 0·91) suggest that surface water infiltration is marginal and that the possibility of significant volumes of surface water infiltrating into non‐monitored shallow streambed sediments can be excluded for the simulation period. Furthermore, the simulation results show that with increasing head differences between river and aquifer towards the end of the simulation period, the impact of streambed topography and hydraulic conductivity on spatial patterns of exchange flow rates decreases. A set of peak flow scenarios with altered groundwater‐surface water head gradients is simulated in order to quantify the potential for surface water infiltration during characteristic winter flow conditions following the observation period. The results indicate that, particularly at the beginning of peak flow conditions, head gradients are likely to cause substantial increase in surface water infiltration into the streambed. The study highlights the potential for the improvement of process understanding of hyporheic exchange flow patterns at the stream reach scale by simulating aquifer‐river exchange fluxes with a standard numerical groundwater model and a simple but robust model structure and parameterization. Copyright © 2011 John Wiley & Sons, Ltd.     

Hydraulic diffusivity and macrodispersivity calculations embedded in a geographic information system

Abstract

A numerical technique is presented whereby aquifer hydraulic diffusivities (D) and macrodispersivities (α) are calculated by linear equations rewritten from flow and solute transport differential equations. The approach requires a GIS to calculate spatial and temporal hydraulic head (h) and solute concentration gradients. The model is tested in Portugal, in a semi-confined aquifer periodically monitored for h and chloride/sulphate concentrations. Average D (0.46 m²/s) and α (1975 m) compare favourably with literature results. The relationship between α and scale (L) is also investigated. In this context, two aquifer groups could be identified: the first group is heterogeneous at the “macroscopic” scale (solute travelled distances <1 km), but homogeneous at the “megascopic” scale. The overall scale dependency in this case is given by an equation of logarithmic type. The second group is heterogeneous at the macroscopic and megascopic scales, with a scale dependency of linear type.

Citation Pacheco, F.A.L., 2013. Hydraulic diffusivity and macrodispersivity calculations embedded in a geographic information system. Hydrological Sciences Journal, 58 (4), 930–944.     

Can we determine the transverse macrodispersivity by using the method of moments?

One of the main assumptions that renders the stochastic theories applicable to real aquifers is the ergodic hypothesis, i.e. the possibility to exchange ensemble and spatial averages of a variable of interest. The principal aim of this paper is to elucidate the conditions that allow for an exchange between ensemble and spatially averaged second moments of concentration field (S_ij); the fulfillment of the ergodic condition underlies the applicability of the dispersion coefficients or other related quantities obtained by the stochastic theories to actual aquifers. The fulfillment of the ergodic hypothesis is assessed here by analyzing the diminishing of the variance of S_ij as the initial size of the plume V₀ grows, i.e. the tendency of S_ij toward its expected value 〈S_ij〉. It is shown that it is not always possible to assume ergodicity for solute plumes in heterogeneous aquifers. For the typical plume configurations encountered in applications, transverse and vertical spreading are the most problematic in this respect. In particular, satisfying the ergodic hypothesis depends largely on the initial plume configuration and size, on one hand, and the direction of the moment of interest, on the other. Numerical simulations based on the analytic element method elucidate the results. The relevance of the results is mostly felt for the inference of macrodispersive parameters, which are often derived through S_ij. The work indicates that S_ij may be a distorted and inadequate measure of the plume spread. This should serve as a warning against application of results based on ensemble averages to real-life plumes, particularly when estimating macrodispersion coefficient from field experiment.     

Obtaining the steady‐state drawdown solutions of constant‐head and constant‐flux tests

The solutions of constant‐head and constant‐flux tests are commonly used to predict the temporal or spatial drawdown distribution or to determine aquifer parameters. Theis and Thiem equations, for instance, are well‐known transient and steady‐state drawdown solutions, respectively, of the constant‐flux test. It is known that the Theis equation is not applicable to the case where the aquifer has a finite boundary or the pumping time tends to infinity. On the other hand, the Thiem equation does not apply to the case where the aquifer boundary is infinite. However, the issue of obtaining the Thiem equation from the transient drawdown solution has not previously been addressed. In this paper, the drawdown solutions for constant‐head and constant‐flux tests conducted in finite or infinite confined aquifers with or without consideration of the effect of the well radius are examined comprehensively. Mathematical verification and physical interpretation of the solutions to these two tests converging or not converging to the Thiem equation are presented. The result shows that there are some finite‐domain solutions for these two tests that can converge to the Thiem equation when the time becomes infinitely large. In addition, the time criteria to give a good approximation to the finite‐domain solution by the infinite‐domain solution and the Thiem equation are investigated and presented. Copyright © 2008 John Wiley & Sons, Ltd.     

Benzene Dynamics and Biodegradation in Alluvial Aquifers Affected by River Fluctuations

The spatial distribution and temporal dynamics of a benzene plume in an alluvial aquifer strongly affected by river fluctuations was studied. Benzene concentrations, aquifer geochemistry datasets, past river morphology, and benzene degradation rates estimated in situ using stable carbon isotope enrichment were analyzed in concert with aquifer heterogeneity and river fluctuations. Geochemistry data demonstrated that benzene biodegradation was on‐going under sulfate reducing conditions. Long‐term monitoring of hydraulic heads and characterization of the alluvial aquifer formed the basis of a detailed modeled image of aquifer heterogeneity. Hydraulic conductivity was found to strongly correlate with benzene degradation, indicating that low hydraulic conductivity areas are capable of sustaining benzene anaerobic biodegradation provided the electron acceptor (SO₄^2–) does not become rate limiting. Modeling results demonstrated that the groundwater flux direction is reversed on annual basis when the river level rises up to 2 m, thereby forcing the infiltration of oxygenated surface water into the aquifer. The mobilization state of metal trace elements such as Zn, Cd, and As present in the aquifer predominantly depended on the strong potential gradient within the plume. However, infiltration of oxygenated water was found to trigger a change from strongly reducing to oxic conditions near the river, causing mobilization of previously immobile metal species and vice versa. MNA appears to be an appropriate remediation strategy in this type of dynamic environment provided that aquifer characterization and targeted monitoring of redox conditions are adequate and electron acceptors remain available until concentrations of toxic compounds reduce to acceptable levels.     

An ANN‐based model for spatiotemporal groundwater level forecasting

This paper evaluates the feasibility of using an artificial neural network (ANN) methodology for estimating the groundwater levels in some piezometers placed in an aquifer in north‐western Iran. This aquifer is multilayer and has a high groundwater level in urban areas. Spatiotemporal groundwater level simulation in a multilayer aquifer is regarded as difficult in hydrogeology due to the complexity of the different aquifer materials. In the present research the performance of different neural networks for groundwater level forecasting is examined in order to identify an optimal ANN architecture that can simulate the piezometers water levels. Six different types of network architectures and training algorithms are investigated and compared in terms of model prediction efficiency and accuracy. The results of different experiments show that accurate predictions can be achieved with a standard feedforward neural network trained usung the Levenberg–Marquardt algorithm. The structure and spatial regressions of the ANN parameters (weights and biases) are then used for spatiotemporal model presentation. The efficiency of the spatio‐temporal ANN (STANN) model is compared with two hybrid neural‐geostatistics (NG) and multivariate time series‐geostatistics (TSG) models. It is found in this study that the ANNs provide the most accurate predictions in comparison with the other models. Based on the nonlinear intrinsic ANN approach, the developed STANN model gives acceptable results for the Tabriz multilayer aquifer. Copyright © 2008 John Wiley & Sons, Ltd.     

Analysis of benzene transport in a two‐dimensional aquifer model

In this study, the fate and transport of aqueous benzene was investigated in a laboratory‐scale homogeneous aquifer by conducting a two‐dimensional plume test. Benzene solution was introduced as a pulse type along the width of the aquifer model through a recharge zone situated at the upper‐left part of the model and followed by a steady state flow. Solution samples were collected at various locations on the front side of the model to capture two‐dimensional plumes at discrete time intervals. The benzene plumes showed a moderate retardation relative to chloride plumes observed from the previous study conducted for the same aquifer model. The retardation factor was obtained from the ratio of travel distances of benzene peaks to chloride peaks from the injection point, computed using a line integral method. Mass recovery of aqueous benzene revealed that there was a significant reduction of benzene mass, indicating the occurrence of volatilization and/or irreversible sorption during transport. Thus, retardation along with volatilization and/or irreversible sorption may be important processes affecting the fate and transport of aqueous benzene in the aquifer model. Copyright © 2005 John Wiley & Sons, Ltd.     

Evaluation of confidence intervals for a steady-state leaky aquifer model

The fact that dependent variables of groundwater models are generally nonlinear functions of model parameters is shown to be a potentially significant factor in calculating accurate confidence intervals for both model parameters and functions of the parameters, such as the values of dependent variables calculated by the model. The Lagrangian method of Vecchia and Cooley [Vecchia, A.V. & Cooley, R.L., Water Resources Research, 1987, 23(7), 1237–1250] was used to calculate nonlinear Scheffé-type confidence intervals for the parameters and the simulated heads of a steady-state groundwater flow model covering 450 km² of a leaky aquifer. The nonlinear confidence intervals are compared to corresponding linear intervals. As suggested by the significant nonlinearity of the regression model, linear confidence intervals are often not accurate. The commonly made assumption that widths of linear confidence intervals always underestimate the actual (nonlinear) widths was not correct. Results show that nonlinear effects can cause the nonlinear intervals to be asymmetric and either larger or smaller than the linear approximations. Prior information on transmissivities helps reduce the size of the confidence intervals, with the most notable effects occurring for the parameters on which there is prior information and for head values in parameter zones for which there is prior information on the parameters.     

Semi‐analytical solution for a slug test in partially penetrating wells including the effect of finite‐thickness skin

This paper presents a new semi‐analytical solution for a slug test in a well partially penetrating a confined aquifer, accounting for the skin effect. This solution is developed based on the solution for a constant‐flux pumping test and a formula given by Peres and co‐workers in 1989. The solution agrees with that of Cooper and co‐workers and the KGS model when the well is fully penetrating. The present solution can be applied to simulate the temporal and spatial head distributions in both the skin and formation zones. It can also be used to demonstrate the influences of skin type or skin thickness on the well water level and to estimate the hydraulic parameters of the skin and formation zones using a least‐squares approach. The results of this study indicate that the determination of hydraulic conductivity using a conventional slug‐test data analysis that neglects the presence of a skin zone will give an incorrect result if the aquifer has a skin zone. Copyright © 2008 John Wiley & Sons, Ltd.     

Reliability of recharge rates estimated from groundwater age with a simplified analytical approach

Groundwater age is often used to estimate groundwater recharge through a simplified analytical approach. This estimated recharge is thought to be representative of the mean recharge between the point of entry and the sampling point. However, given the complexity in actual recharge, whether the mean recharge is reasonable is still unclear. This study examined the validity of the method to estimate long-term average groundwater recharge and the possibility of obtaining reasonable spatial recharge pattern. We first validated our model in producing reasonable age distributions using a constant flux boundary condition. We then generated different flow fields and age patterns by using various spatially varying flux boundary conditions with different magnitudes and wavelengths. Groundwater recharge was estimated and analysed afterwards using the method at the spatial scale. We illustrated the main findings with a field example in the end. Our results suggest that we can estimate long-term average groundwater recharge with 10% error in many parts of an aquifer. The size of these areas decreases with the increase in both the amplitude and the wavelength. The chance of obtaining a reasonable groundwater recharge is higher if an age sample is collected from the middle of an aquifer and at downstream areas. Our study also indicates that the method can also be used to estimate local groundwater recharge if age samples are collected close to the water table. However, care must be taken to determine groundwater age regardless of conditions.     

δCa evolution in a carbonate aquifer and its bearing on the equilibrium isotope fractionation factor for calcite

To improve understanding of Ca isotope transport during water-rock interaction on the continents, we measured dissolved δ⁴⁴Ca values along a 236 km flow path in the Madison aquifer, South Dakota, where fluids have chemically evolved according to dolomite and anhydrite dissolution, calcite precipitation, and Ca-for-Na ion-exchange over a timescale spanning ~ 15 kyr. We used a reactive transport model employing rate data constrained from major ion mass-balances to evaluate the extent to which calcite precipitation and ion-exchange fractionate Ca isotopes. Elevated δ⁴⁴Ca values during the initial and final stages of water transport possibly result from calcite precipitation under supersaturated conditions and Ca-for-Na ion-exchange, respectively. However, for the bulk of the flow path, δ⁴⁴Ca values evolve by mixing between anhydrite and dolomite dissolution, with no fractionation during calcite precipitation under saturated conditions. We attribute the absence of Ca isotope fractionation to the long timescale of water-rock interaction and slow rate of calcite precipitation, which have enabled fluids to chemically and isotopically equilibrate with calcite. We therefore conclude that the equilibrium Ca isotope fractionation factor between calcite and water (Δ_cal–w) is very close to zero. To the extent that the Madison aquifer typifies other groundwater systems where calcite slowly precipitates from solutions at or near chemical equilibrium, this study suggests that groundwater contributions to δ⁴⁴Ca variability on the continents can be modeled according to simple mixing theory without invoking isotope discrimination.     

A two-dimensional analytical solution of groundwater responses to tidal loading in an estuary and ocean

Previous studies on tidal dynamics of coastal aquifers have focussed on the inland propagation of oceanic tides in the cross-shore direction, a configuration that is essentially one-dimensional. Aquifers at natural coasts can also be influenced by tidal waves in nearby estuaries, resulting in a more complex behaviour of head fluctuations in the aquifers. We present an analytical solution to the two-dimensional depth-averaged groundwater flow equation for a semi-infinite aquifer subject to oscillating head conditions at the boundaries. The solution describes the tidal dynamics of a coastal aquifer that is adjacent to a cross-shore estuary. Both the effects of oceanic and estuarine tides on the aquifer are included in the solution. The analytical prediction of the head fluctuations is verified by comparison with numerical solutions computed using a standard finite-difference method. An essential feature of the present analytical solution is the interaction between the cross- and along-shore tidal waves in the aquifer area near the estuary’s entry. As the distance from the estuary or coastline increases, the wave interaction is weakened and the aquifer response is reduced, respectively, to the one-dimensional solution for oceanic tides or the solution of Sun (Sun H. A two-dimensional analytical solution of groundwater response to tidal loading in an estuary, Water Resour Res 1997;33:1429–35) for two-dimensional non-interacting tidal waves.     

Application of Markovian models for non-ergodic and non-stationary earthquake times series for the identification of seismic patterns and future projections*

The current earthquake forecast algorithms are not free of shortcomings due to inherent limitations. Especially, the requirement of stationarity in the evaluation of earthquake time series as a prerequisite, significantly limits the use of forecast algorithms to areas where stationary data is not available. Another shortcoming of forecast algorithms is the ergodicity assumption, which states that certain characteristics of seismicity are spatially invariant. In this study, a new earthquake forecast approach is introduced for the locations where stationary data are not available. For this purpose, the spatial activity rate density for each spatial unit is evaluated as a parameter of a Markov chain. The temporal pattern is identified by setting the states at certain spatial activity rate densities. By using the transition patterns between the states, 1- and 5-year forecasts were computed. The method is suggested as an alternative and complementary to the existing methods by proposing a solution to the issues of ergodicity and stationarity assumptions at the same time.     

Impact of groundwater flow on meandering; example from the Geul River,The Netherlands

The Geul River, located in the south‐eastern part of The Netherlands, is a meandering river with a planform shape characterized by large loops consisting of multiple bends. We evaluate the effect(s) of groundwater flow on the shapes of meanders as a possible explanation for the multi‐bend loops, using a combined meandering–groundwater computer model. In the model seeping groundwater enhances bank erodibility. Based on the simulation results, we present a conceptual, generalized model for groundwater–meandering interaction, based on wavelength selection and fixation effects. Wavelength selection occurs because of the positive feedback between growing meander bends and groundwater flow patterns and velocities. The promoted wavelengths have the same spatial scale as the groundwater flow system in the aquifer underlying the floodplain. In the case of the Geul River these wavelengths are of the order of 100 m. Since groundwater flow velocities are largest close to the recharging hill‐slopes, the seepage‐enhanced bank erodibilities are at a maximum near the floodplain limits. At these locations the difference in erodibility between banks facing the floodplain and those facing the hill slopes is large, so it is difficult for the river to migrate away from the floodplain limits. This causes long stretches of the river to be aligned along the floodplain limits, which we term a fixation effect. This mechanism best explains the multi‐bend loops of the Geul River. The general interaction between groundwater flow and meandering is site specific since it depends on climatic, fluvial and hydrogeological parameters. The Geul is characterized by a wide floodplain and steep hill‐slopes, and it is underlain by coarse‐grained deposits with good aquifer properties, favoring an important groundwater system. Since this kind of river frequently occurs, our results could apply to many other river systems. Copyright © 2008 John Wiley & Sons, Ltd.     

Impact of complex aquifer geometry on groundwater storage in high‐elevation meadows of the Sierra Nevada Mountains,CA

Recent research has indicated that Sierra Nevada meadows are hydrologically more complex than previously considered. Improved understanding of the effects of aquifer parameters and climate change on water resources in and downstream of meadows is critically needed to effectively manage mountain meadows for ecosystem services and watershed contributions. This research investigates the roles of bedrock geometry, saturated hydraulic conductivity, and meadow gradient in affecting groundwater storage dynamics and surface‐water outflows in site‐scale high‐elevation meadows. Under current and projected lower snowpack conditions, we modeled groundwater flow in representative high‐elevation meadows considering 2 conceptual aquifer thickness models: uniform and variable thickness. Spatially, variable aquifer thicknesses interpreted from bedrock depths (0–28 m) were identified from a high‐resolution ground‐penetrating radar survey conducted at Tuolumne Meadows, CA. Our interpreted bedrock surface indicated several buried U‐shaped valleys including a buried ridge that separates 2 U‐shaped valleys. Groundwater flow simulations show that an increase in meadow gradient and hydraulic conductivity led to a decrease in seasonal storage and an increase in surface‐water outflow. However, models with varying bedrock geometries change the magnitude and timing of these processes. Uniform thickness models overestimated storage at the model edges and resulted in higher projected volumes of water being released to streams earlier than previously observed.