Effects of variations of river stage and hydraulic conductivity on temporal scaling of groundwater levels: numerical simulations

It was found in previous studies that groundwater levels may fluctuate as a temporal fractal. In this study numerical simulations of groundwater level fluctuations in an unconfined aquifer near a river were conducted to investigate the effects of aquifer heterogeneity and river stage variations on the fractal behavior of the water levels, h(t). Groundwater recharge was taken to be a white-noise process. The aquifer heterogeneity was simulated with a second-order stationary field of hydraulic conductivity (K) with an exponential variogram model. The results showed that groundwater levels fluctuate as a temporal fractal in both homogeneous and heterogeneous aquifers as long as K is less than 10 m/d. Most aquifers may indeed act as a fractal filter which takes a random non-fractal recharge inputs and produces a fractal responses of groundwater level fluctuations. A crossover in temporal scaling of h(t) may appear in more permeable aquifers. Fluctuations of the groundwater level in a homogeneous aquifer are dominated by the recharge process when the river stage is constant or by the river stage variations when the river stage varies in highly permeable aquifers. Heterogeneity plays an important role in the temporal scaling of h(t) in more permeable aquifers: the stronger the heterogeneity, the stronger the temporal scaling of h(t).     

A general solution for groundwater flow in an estuarine's leaky aquifer system after considering aquifer anisotropy

This paper presents an analytical model for describing the tidal effects in a two‐dimensional leaky confined aquifer system in an estuarine delta where ocean and river meet. This system has an unconfined aquifer on top and a confined aquifer on the bottom with an aquitard in between the two. The unconfined and confined aquifers interact with each other through leakage. It was assumed that the aquitard storage was negligible and that the leakage was linearly proportional to the head difference between the unconfined and confined aquifers. This model's solution was based on the separation of variables method. Two existing solutions that deal with the head fluctuation in one‐dimensional or two‐dimensional leaky confined aquifers are shown as special cases in the present solution. Based on this new solution, the dynamic effect of the water table's fluctuations can be clearly explored, as well as the influence of leakage on the behaviour of fluctuations in groundwater levels in the leaky aquifer system. Copyright © 2015 John Wiley & Sons, Ltd.     

Numerical Simulations of Seasonally Oscillated Groundwater Dynamics in Coastal Confined Aquifers

Studies investigating the effects of inland recharge on coastal groundwater dynamics were carried out typically in unconfined aquifers, with few in confined aquifers. This study focused on the groundwater dynamics in confined aquifers with seasonally sinusoidally fluctuated inland groundwater head and constant sea level by numerical simulations. It is known that the mixing zone (MZ) of saltwater wedge in response to the seasonal oscillations of inland groundwater head swings around the steady-state MZ. However, our simulation results indicate that even the most landward freshwater-saltwater interface over a year is seaward from the steady-state location when the hydraulic conductivity K is ≤10⁻⁴ m/s under certain boundary conditions with given parameter values. That is, seasonal oscillations of inland groundwater head may reduce seawater intrusion in confined coastal aquifers when K ≤ 10⁻⁴ m/s. Sensitivity analysis indicates that for aquifers of K ≤ 10⁻⁴ m/s, the larger the inland head fluctuation amplitude is, the less the seawater intrudes. This is probably due to the reason that the seawater intrusion time decreases with the increase of fluctuation amplitude when K ≤ 10⁻⁴ m/s. Numerical simulations demonstrate that seasonal inland groundwater head oscillations promote the annual averaged recirculated seawater discharge across the seaward boundary.     

Identification and mapping of riverbed sediment facies in the Columbia River through integration of field observations and numerical simulations

In the Hanford Reach of the Columbia River, a thin layer of recent alluvium overlies the sedimentary formations that comprise the unconfined groundwater aquifer. Experimental and modelling studies have demonstrated that this alluvial layer exerts significant control on the exchange of groundwater and surface water (hydrologic exchange flux), and is associated with elevated levels of biogeochemical activity. This layer is also observed to be strongly heterogeneous, and quantifying the spatial distribution of properties over the range of scales of interest is challenging. Facies are elements of a sediment classification scheme that groups complex geologic materials into a set of discrete classes according to distinguishing features. Facies classifications have been used as a framework for assigning heterogeneous material properties to grid cells of numerical models of flow and reactive transport in subsurface media. The usefulness of such an approach hinges on being able to relate facies to quantitative properties needed for flow and reactive transport modelling, and on being able to map facies over the domain of interest using readily available information. Although aquifer facies have been used in various modelling contexts, application of this concept to riverbed sediments is relatively new. Here, we describe an approach for categorizing and mapping recent alluvial (riverbed) sediments based on the integration of diverse observations with numerical simulations of river hydrodynamics. The facies have distinct distributions of sediment texture that correspond to variations in hydraulic properties, and therefore provide a useful framework for assigning heterogeneous properties in numerical simulations of hydrologic exchange flows and biogeochemical processes.     

Transient two-dimensional groundwater flow

ABSTRACT

A set of simple analytical solutions are presented for estimation of drawdowns and groundwater flow rates into two-dimensional excavation, such as those in open-cut strip mines, for confined, leaky and unconfined aquifers.     

A low‐dimensional hillslope‐based catchment model for layered groundwater flow

Despite the strong interaction between surface and subsurface waters, groundwater flow representation is often oversimplified in hydrological models. For instance, the interplay between local or shallow aquifers and deeper regional‐scale aquifers is typically neglected. In this work, a novel hillslope‐based catchment model for the simulation of combined shallow and deep groundwater flow is presented. The model consists of the hillslope‐storage Boussinesq (hsB) model representing shallow groundwater flow and an analytic element (AE) model representing deep regional groundwater flow. The component models are iteratively coupled via a leakage term based on Darcy's law, representing delayed recharge to the regional aquifer through a low conductivity layer. Simulations on synthetic single hillslopes and on a two‐hillslope open‐book catchment are presented, and the results are compared against a benchmark three‐dimensional Richards equation model. The impact of hydraulic conductivity, hillslope plan geometry (uniform, convergent, divergent), and hillslope inclination (0.2%, 5%, and 30%) under drainage and recharge conditions are examined. On the single hillslopes, good matches for heads, hydrographs, and exchange fluxes are generally obtained, with the most significant differences in outflows and heads observed for the 30% slope and for hillslopes with convergent geometry. On the open‐book catchment, cumulative outflows are overestimated by 1–4%. Heads in the confined and unconfined aquifers are adequately reproduced throughout the catchment, whereas exchange fluxes are found to be very sensitive to the hillslope drainable porosity. The new model is highly efficient computationally compared to the benchmark model. The coupled hsB/AE model represents an alternative to commonly used groundwater flow representations in hydrological models, of particular appeal when surface–subsurface exchanges, local aquifer–regional aquifer interactions, and low flows play a key role in a watershed's dynamics. Copyright © 2011 John Wiley & Sons, Ltd.     

Using principal component analysis in the investigation of groundwater hydrochemistry of Upper Jezireh Basin,Syria

Principal component analysis (PCA) was applied to hydrochemical and isotopic data of 34 groundwater samples. This allowed the reduction of 20 variables to four significant PCs that explain 81.9% of the total variance; F1 (47.1%) explains the groundwater mineralization, whereas F2 (17%) shows isotopic enrichment and nitrate pollution. Based on an iso-factor scores map of F1, three water zones were delineated: Zone A (F1 < ?1), with fresh groundwater from the unconfined aquifer; Zone B (1 > F1 > ?1), with moderate mineralization from the confined–unconfined aquifer boundary; and Zone C (F1 > 1), with the most mineralized hot water from the confined aquifer. The iso-factor scores map of F2 delineates positive values representing samples from the unconfined aquifer, with freshwater and nitrate contamination associated with stable isotope enrichment, whereas negative values represent samples from the confined aquifer. The results clearly demonstrate the usefulness of PCA in groundwater hydrochemistry investigations.     

Modeling Steady Sea Water Intrusion with Single‐Density Groundwater Codes

Steady interface flow in heterogeneous aquifer systems is simulated with single‐density groundwater codes by using transformed values for the hydraulic conductivity and thickness of the aquifers and aquitards. For example, unconfined interface flow may be simulated with a transformed model by setting the base of the aquifer to sea level and by multiplying the hydraulic conductivity with 41 (for sea water density of 1025 kg/m³). Similar transformations are derived for unconfined interface flow with a finite aquifer base and for confined multi‐aquifer interface flow. The head and flow distribution are identical in the transformed and original model domains. The location of the interface is obtained through application of the Ghyben‐Herzberg formula. The transformed problem may be solved with a single‐density code that is able to simulate unconfined flow where the saturated thickness is a linear function of the head and, depending on the boundary conditions, the code needs to be able to simulate dry cells where the saturated thickness is zero. For multi‐aquifer interface flow, an additional requirement is that the code must be able to handle vertical leakage in situations where flow in an aquifer is unconfined while there is also flow in the aquifer directly above it. Specific examples and limitations are discussed for the application of the approach with MODFLOW. Comparisons between exact interface flow solutions and MODFLOW solutions of the transformed model domain show good agreement. The presented approach is an efficient alternative to running transient sea water intrusion models until steady state is reached.     

Three-dimensional semi-analytical solution to groundwater flow in confined and unconfined wedge-shaped aquifers

The Laplace domain solutions have been obtained for three-dimensional groundwater flow to a well in confined and unconfined wedge-shaped aquifers. The solutions take into account partial penetration effects, instantaneous drainage or delayed yield, vertical anisotropy and the water table boundary condition. As a basis, the Laplace domain solutions for drawdown created by a point source in uniform, anisotropic confined and unconfined wedge-shaped aquifers are first derived. Then, by the principle of superposition the point source solutions are extended to the cases of partially and fully penetrating wells. Unlike the previous solution for the confined aquifer that contains improper integrals arising from the Hankel transform [Yeh HD, Chang YC. New analytical solutions for groundwater flow in wedge-shaped aquifers with various topographic boundary conditions. Adv Water Resour 2006;26:471–80], numerical evaluation of our solution is relatively easy using well known numerical Laplace inversion methods. The effects of wedge angle, pumping well location and observation point location on drawdown and the effects of partial penetration, screen location and delay index on the wedge boundary hydraulic gradient in unconfined aquifers have also been investigated. The results are presented in the form of dimensionless drawdown-time and boundary gradient-time type curves. The curves are useful for parameter identification, calculation of stream depletion rates and the assessment of water budgets in river basins.     

Discussion about the validity of sharp‐interface models to deal with seawater intrusion in coastal aquifers

Analytical models have been exhaustively used to study simple seawater intrusion problems and the sustainable management of groundwater resources in coastal aquifers because of its simplicity, easy implementation, and low computational cost. Most of these models are based on the sharp‐interface approximation and the Ghyben–Herzberg relation, and their governing equations are expressed in terms of a single potential theory to calculate critical pumping rates in a coastal pumping scenario. The Ghyben–Herzberg approach neglects mixing of fresh water and seawater and implicitly assumes that salt water remains static. Therefore, the results of the analytical solutions may be inaccurate and unacceptable for some real‐complex case studies. This paper provides insight into the validity of sharp‐interface models to deal with seawater intrusion in coastal aquifers, i.e. when they can be applied to obtain accurate enough results. For that purpose, this work compares sharp‐interface solutions, based on the Ghyben–Herzberg approach, with numerical three‐dimensional variable‐density flow simulations for a set of heterogeneous groundwater flow and mass transport parameters, and different scenarios of spatially distributed recharge values and spatial wells placement. The numerical experiment has been carried out in a 3D unconfined synthetic aquifer using the finite difference numerical code SEAWAT for solving the coupled partial differential equations of flow and density‐dependent transport. This paper finds under which situations the sharp‐interface solution gives good predictions in terms of seawater penetration, transition zone width and critical pumping rates. Additionally, the simulation runs indicate to which parameters and scenarios the results are more sensitive. Copyright © 2013 John Wiley & Sons, Ltd.     

A moving mesh algorithm for 3-D regional groundwater flow with water table and seepage face

A numerical algorithm is described for solving the free-surface groundwater flow equations in 3-D large-scale unconfined aquifers with strongly heterogeneous conductivity and surface recharge. The algorithm uses a moving mesh to track the water-table as it evolves according to kinematic and seepage face boundary conditions. Both steady-state and transient algorithms are implemented in the SECO-Flow 3-D code and demonstrated on stratigraphy based on the Delaware Basin of south-eastern New Mexico.     

Topological groundwater hydrodynamics

Topological groundwater hydrodynamics is an emerging subdiscipline in the mechanics of fluids in porous media whose objective is to investigate the invariant geometric properties of subsurface flow and transport processes. In this paper, the topological characteristics of groundwater flows governed by the Darcy law are studied. It is demonstrated that: (i) the topological constraint of zero helicity density during flow is equivalent to the Darcy law; (ii) both steady and unsteady groundwater flows through aquifers whose hydraulic conductivity is an arbitrary scalar function of position and time are confined to surfaces on which the streamlines of the flow are geodesic curves; (iii) the surfaces to which the flows are confined either are flat or are tori; and (iv) chaotic streamlines are not possible for these flows, implying that they are inherently poorly mixing in advective solute transport.     

Analytical Solution for Modeling Discharge into a Tunnel Drilled in a Heterogeneous Unconfined Aquifer

Predicting transient inflow rates into a tunnel is an important issue faced by hydrogeologists. Most existing analytical solutions overestimate the initial discharge due to the assumption that drilling was instantaneous over the entire tunnel length. In addition, they assume a homogeneous system. An alternative model was recently developed for tunnels intersecting heterogeneous formations, but its application was reduced to the case of confined flow to deep tunnels in weakly diffusive aquifers. In this paper, we adapt existing analytical solutions for drainage systems to the specific case of a tunnel progressively drilled in a highly diffusive heterogeneous unconfined aquifer. The case of a tunnel overlying an impervious layer is analytically solved by applying the superposition principle, while the case of a tunnel constructed some distance above an impervious layer is solved by discretizing the tunnel length into subsectors. Both models can simulate transient discharge into a tunnel drilled at various speeds through a heterogeneous unconfined aquifer, and allow the prediction of discharge rates in shallow tunnels located in highly diffusive aquifers. We successfully applied this approach to a tunnel in heterogeneous volcanic rock.     

Dissolution in a variably confined carbonate platform: effects of allogenic runoff,hydraulic damming of groundwater inputs,and surface–groundwater exchange at the basin scale

In variably confined carbonate platforms, impermeable confining units collect rainfall over large areas and deliver runoff to rivers or conduits in unconfined portions of platforms. Runoff can increase river stage or conduit heads in unconfined portions of platforms faster than local infiltration of rainfall can increase groundwater heads, causing hydraulic gradients between rivers, conduits and the aquifer to reverse. Gradient reversals cause flood waters to flow from rivers and conduits into the aquifer where they can dissolve limestone. Previous work on impacts of gradient reversals on dissolution has primarily emphasized individual caves and little research has been conducted at basin scales. To address this gap in knowledge, we used legacy data to assess how a gradient of aquifer confinement across the Suwannee River Basin, north‐central Florida affected locations, magnitudes and processes of dissolution during 2005–2007, a period with extreme ranges of discharge. During intense rain events, runoff from the confining unit increased river stage above groundwater heads in unconfined portions of the platform, hydraulically damming inputs of groundwater along a 200 km reach of river. Hydraulic damming allowed allogenic runoff with SI_CAL < ?4 to fill the entire river channel and flow into the aquifer via reversing springs. Storage of runoff in the aquifer decreased peak river discharges downstream and contributed to dissolution within the aquifer. Temporary storage of allogenic runoff in karst aquifers represents hyporheic exchange at a scale that is larger than found in streams flowing over non‐karst aquifers because conduits in karst aquifers extend the area available for exchange beyond river beds deep into aquifers. Post‐depositional porosity in variably confined carbonate platforms should thus be enhanced along rivers that originate on confining units. This distribution should be considered in models of porosity distribution used to manage water and hydrocarbon resources in carbonate rocks. Copyright © 2013 John Wiley & Sons, Ltd.     

Time–space fractional governing equations of transient groundwater flow in confined aquifers: Numerical investigation

In order to model non‐Fickian transport behaviour in groundwater aquifers, various forms of the time–space fractional advection–dispersion equation have been developed and used by several researchers in the last decade. The solute transport in groundwater aquifers in fractional time–space takes place by means of an underlying groundwater flow field. However, the governing equations for such groundwater flow in fractional time–space are yet to be developed in a comprehensive framework. In this study, a finite difference numerical scheme based on Caputo fractional derivative is proposed to investigate the properties of a newly developed time–space fractional governing equations of transient groundwater flow in confined aquifers in terms of the time–space fractional mass conservation equation and the time–space fractional water flux equation. Here, we apply these time–space fractional governing equations numerically to transient groundwater flow in a confined aquifer for different boundary conditions to explore their behaviour in modelling groundwater flow in fractional time–space. The numerical results demonstrate that the proposed time–space fractional governing equation for groundwater flow in confined aquifers may provide a new perspective on modelling groundwater flow and on interpreting the dynamics of groundwater level fluctuations. Additionally, the numerical results may imply that the newly derived fractional groundwater governing equation may help explain the observed heavy‐tailed solute transport behaviour in groundwater flow by incorporating nonlocal or long‐range dependence of the underlying groundwater flow field.     

Estimation of the inland extending length of the freshwater–saltwater interface in coastal unconfined aquifers

ABSTRACT

The inland extending length of the freshwater–saltwater interface toe is useful in studies of seawater intrusion in coastal areas. The submarine fresh groundwater discharge in coastal zones is affected not only by hydraulic conductivity and hydraulic gradient of the aquifer, but also by the position of the interface. Two observation wells at different distances from the coast are required to calculate the fresh groundwater flow rate in coastal unconfined aquifers. By considering that the submarine groundwater discharge is equal to the groundwater flow rate, the length of the interface toe extending inland can be estimated when the groundwater flow is at a steady-flow state. Aquifers with horizontal and sloping confined beds and without/with unique surface vertical infiltration are considered. Examples used to illustrate the application of these methods indicate that the inland extending lengths of the interface toe in aquifers with vertical surface infiltration are much shorter than those in aquifers without vertical surface infiltration, and the length of the interface in aquifers with a horizontal confining lower bed are smaller than those in aquifers with a confining lower bed sloping towards the sea. The extent of the interface on the northwestern coast near the city of Beihai in southern Guangxi, China, on 18 January 2013 was estimated as 471–478 m.

Editor M.C. Acreman Associate editor not assigned     

On the Coupling Between Channel Level and Surface Ground-Water Flows

This paper is devoted to a mathematical analysis of some general models of mass transport and other coupled physical processes developed in simultaneous flows of surface, soil and ground waters. Such models are widely used for forecasting (numerical simulation) of a hydrological cycle for concrete territories. The mathematical models that proved a more realistic approach are obtained by combining several mathematical models for local processes. The water-exchange models take into account the following factors: Water flows in confined and unconfined aquifers, vertical moisture migration allowing earth surface evaporation, open-channel flow simulated by one-dimensional hydraulic equations, transport of contamination, etc. These models may have different levels of sophistication. We illustrate the type of mathematical singularities which may appear by considering a simple model on the coupling of a surface flow of surface and ground waters with the flow of a line channel or river.     

Sulfur Hexafluoride and Potassium Bromide as Groundwater Tracers for Managed Aquifer Recharge

Sulfur hexafluoride (SF₆) is an established tracer for use in managed aquifer recharge projects. SF₆ exsolves from groundwater when it encounters trapped air according to Henry's law. This results in its retardation relative to groundwater flow, which can help determine porous media saturation and flow dynamics. SF₆ and the conservative, nonpartitioning tracer, bromide (Br⁻ added as KBr), were introduced to recharge water infiltrated into stacked glacial aquifers in Thurston County, Washington, providing the opportunity to observe SF₆ partitioning. Br⁻, which is assumed to travel at the same velocity as the groundwater, precedes SF₆ at most monitoring wells (MWs). Average groundwater velocity in the unconfined aquifer in the study area ranges from 3.9 to 40 m/d, except in the southwestern corner where it is slower. SF₆ in the shallow aquifer exhibits an average retardation factor of 2.5 ± 3.8, suggesting an air-to-water ratio on the order of 10⁻³ to 10⁻² in the pore space. Notable differences in tracer arrival times at adjacent wells indicate very heterogeneous conductivity. One MW exhibits double peaks in concentrations of both tracers with different degrees of retardation for the first and second peaks. This suggests multiple flowpaths to the well with variable saturation. The confining layer between the upper two aquifers appears to allow intermittent connection between aquifers but serves as an aquitard in most areas. This study demonstrates the utility of SF₆ partitioning for evaluating hydrologic conditions at prospective recharge sites.     

Modelling tidal signals enhanced by a submarine spring in a coastal confined aquifer extending under the sea

Submarine springs discharge offshore groundwater from confined aquifers extending under the sea. The effects of these springs on the propagation of tidal oscillations in coastal confined aquifers are not known. This paper presents an approximate analytical solution of tidal head fluctuations in a confined aquifer with one submarine spring. The aquifer is assumed to extend in all directions infinitely. The spring is represented by a permeable round column on the seabed, which penetrates completely the impermeable layer overlying the confined aquifer. The error of the approximate solution is negligible if the distance from the spring to the coastline is much greater than the radius of the permeable column representing the spring. Through a hypothetical example, we demonstrate that it is possible to identify the spring’s location using tidal signals observed from inland wells. Tidal groundwater head fluctuations from three inland observation wells at least are needed to determine the 5 model parameters, including the location (2 parameters), the radius of the permeable column representing the spring, the diffusivity of the aquifer, and the tidal loading efficiency of the system.