Analytical solution for drainage and recession from an unconfined aquifer

One-dimensional transient groundwater flow from a divide to a river in an unconfined aquifer described by the Boussinesq equation was studied. We derived the analytical solution for the water table recession and drainage change process described with a linearized Boussinesq equation with a physically based initial condition. A method for determining the average water table in the solutions was proposed. It is shown that the solution derived in the form of infinite series can be well approximated with the simplified solution which contains only the leading term of the original solution. The solution and their simplification can be easily evaluated and used by others to study the groundwater flow problems, such as drainage and base flow estimation, in an unconfined aquifer.     

Analysis of steady ground water flow toward wells in a confined-unconfined aquifer

A confined aquifer may become unconfined near the pumping wells when the water level falls below the confining unit in the case where the pumping rate is great and the excess hydraulic head over the top of the aquifer is small. Girinskii's potential function is applied to analyze the steady ground water flow induced by pumping wells with a constant-head boundary in a mixed confined-unconfined aquifer. The solution of the single-well problem is derived, and the critical radial distance at which the flow changes from confined to unconfined condition is obtained. Using image wells and the superposition method, an analytic solution is presented to study steady ground water flow induced by a group of pumping wells in an aquifer bounded by a river with constant head. A dimensionless function is introduced to determine whether a water table condition exists or not near the pumping wells. An example with three pumping wells is used to demonstrate the patterns of potentiometric surface and development of water table around the wells.     

How processing digital elevation models can affect simulated water budgets

For regional models, the shallow water table surface is often used as a source/sink boundary condition, as model grid scale precludes simulation of the water table aquifer. This approach is appropriate when the water table surface is relatively stationary. Since water table surface maps are not readily available, the elevation of the water table used in model cells is estimated via a two-step process. First, a regression equation is developed using existing land and water table elevations from wells in the area. This equation is then used to predict the water table surface for each model cell using land surface elevation available from digital elevation models (DEM). Two methods of processing DEM for estimating the land surface for each cell are commonly used (value nearest the cell centroid or mean value in the cell). This article demonstrates how these two methods of DEM processing can affect the simulated water budget. For the example presented, approximately 20% more total flow through the aquifer system is simulated if the centroid value rather than the mean value is used. This is due to the one-third greater average ground water gradients associated with the centroid value than the mean value. The results will vary depending on the particular model area topography and cell size. The use of the mean DEM value in each model cell will result in a more conservative water budget and is more appropriate because the model cell water table value should be representative of the entire cell area, not the centroid of the model cell.     

Underdamped slug tests with unsaturated‐saturated flows by considering effects of wellbore skins

An analytical solution is presented for the slug tests conducted in a partially penetrating well in an unconfined aquifer affected from above by an unsaturated zone. The solution considers the effects of wellbore skin and oscillatory responses on underdamped slug tests. The flow in the saturated zone is described by a two‐dimensional, axially symmetric governing equation, and the flow in the unsaturated zone above the water table by a linearized one‐dimensional Richards' equation. The unsaturated medium properties are represented by the exponential constitutive relationships. A Laplace domain solution is derived using the Laplace and finite Fourier transform and the solution in the real‐time domain is evaluated using the numerical inverse Laplace transform method. The solution derived in this study is more general and reduces to the most commonly used solutions for slug tests in their specified conditions. It is found that the unsaturated flow has a significant impact on the slug test conducted in an unconfined aquifer. The impact of unsaturated flow on such a slug test is enhanced with a larger anisotropy ratio, a shorter well screen length, a shorter distance between the well screen and the water table, or a larger well screen radius. The impact of unsaturated flow on slug tests decreases as the degree of penetration (the length of well screen) increases. For a fixed well screen length, the impact of unsaturated flow on slug tests decreases as the distance between the centre of screen and the water table increases. A large dimensionless well screen radius (>0.01) leads to significant effects of unsaturated flow on slug tests. The unsaturated flow reduces the oscillatory responses to underdamped slug tests. The unsaturated zone has significant impact on slug test under high‐permeability wellbore skin.     

Hydrogeologic controls on peatland development in the Malloryville Wetland, New York (USA)

The Malloryville Wetland Complex, a small kettle-hole peatland, contains a diversity of peatland types. The wetland has a ‘rich’ side that contains wetland vegetation associated with solute-rich, near-neutral pH (minerotrophic) water, and a ‘poor’ side containing vegetation that grows in solute-poor and acidic (ombrotrophic) water. Vertical head gradients at piezometer clusters located in the rich side clearly show that groundwater is moving upwards towards the land surface, consistent with the vegetation types and surface water quality. In contrast, vertical head gradients also show that groundwater is moving upward in the poor side even though the vegetation and surface water chemistry are not minerotrophic. An incipient raised bog in the center of the poor side is the only site where groundwater moves consistently downward.

A peat core collected at the bog center shows that the bog site was initially covered by minerotrophic vegetation, typically found in groundwater discharge zones, which was later replaced by ombrotrophic bog vegetation. Theoretical computer simulation experiments of the bog hydrogeologic setting through time suggest that the direction of vertical groundwater flow at the bog site permanently changed from up to down when a water table mound developed under a convex-shaped fen peat mound that probably formed because of differential peat accumulation. Ombrotrophic conditions and bog vegetation probably began when the fen water table mound grew sufficiently large enough to divert the upward movement of regional groundwater. The transition from rich to poor environments probably occurred when the wetland water table was substantially below the elevation of the surrounding regional water table.     

Particular solutions to the problem of horizontal flow of water and air through porous media near a water table

Particular solutions to the problem of horizontal flow of water and air through porous media near a water table are derived and regularity properties of the solutions are presented. It is found that a singularity occurs in the solutions at the water table and the water table can be interpreted as an acceleration wave of the nth order in terms of either air or water flow where n is a positive integer. Effects of air flow on water flow are discussed.     

A Stable and Efficient Numerical Algorithm for Unconfined Aquifer Analysis

The nonlinearity of equations governing flow in unconfined aquifers poses challenges for numerical models, particularly in field-scale applications. Existing methods are often unstable, do not converge, or require extremely fine grids and small time steps. Standard modeling procedures such as automated model calibration and Monte Carlo uncertainty analysis typically require thousands of model runs. Stable and efficient model performance is essential to these analyses. We propose a new method that offers improvements in stability and efficiency and is relatively tolerant of coarse grids. It applies a strategy similar to that in the MODFLOW code to the solution of Richard's equation with a grid-dependent pressure/saturation relationship. The method imposes a contrast between horizontal and vertical permeability in gridblocks containing the water table, does not require "dry" cells to convert to inactive cells, and allows recharge to flow through relatively dry cells to the water table. We establish the accuracy of the method by comparison to an analytical solution for radial flow to a well in an unconfined aquifer with delayed yield. Using a suite of test problems, we demonstrate the efficiencies gained in speed and accuracy over two-phase simulations, and improved stability when compared to MODFLOW. The advantages for applications to transient unconfined aquifer analysis are clearly demonstrated by our examples. We also demonstrate applicability to mixed vadose zone/saturated zone applications, including transport, and find that the method shows great promise for these types of problem as well.     

Ground Water Sampling Bias Observed in Shallow, Conventional Wells

A previous field demonstration project on nitrate-based bioremediation of a fuel-contaminated aquifer used short-screened clustered well points in addition to shallow (10 foot), conventional monitoring wells to monitor the progress of remediation during surface application of recharge. These well systems were placed in the center and at one edge of each of two treatment cells. One cell received recharge amended with nitrate (nitrate cell), and the other received unamended recharge (control cell). Data from the clustered well points were averaged to provide a mean estimate for comparison with the associated conventional monitoring well.
Conservative tracer profiles were similar for each of the four systems, with better fits obtained for well systems located at the edge of the treatment cells. However, aromatic hydrocarbon and electron acceptor profiles varied greatly for the two center well systems, with the conventional monitoring well data suggesting that remediation was proceeding at a much more rapid rate than indicated by the cluster well points. Later tests with an electromagnetic borehole flowmeter demonstrated a significant vertical flow through the well-bore of the conventional monitoring well under simulated operating conditions. This created an artifact during sampling, thought to arise from preferential flow of recharge water from the water table to deeper portions of the contaminated zone resulting in several effects, including an actual decreased residence time of water sampled by the conventional well. These data provide additional evidence that conventional monitoring wells may be inadequate for monitoring remediation in the presence of significant vertical hydraulic gradients, even for fairly shallow homogeneous aquifers.     

Analysis of an unconfined aquifer subject to asynchronous dual-tide propagation

Most published solutions for aquifer responses to ocean tides focus on the one-sided attenuation of the signal as it propagates inland. However, island aquifers experience periodic forcing from the entire coast, which can lead to integrated effects of different tidal signals, especially on narrow high-permeability islands. In general, studies disregard a potential time lag as the tidal wave sweeps around the island. We present a one-dimensional analytical solution to the ground water flow equation subject to asynchronous and asymmetric oscillating head conditions on opposite boundaries and test it on data from an unconfined volcanic aquifer in Maui. The solution considers sediment-damping effects at the coastline. The response of Maui Aquifers indicate that water table elevations near the center of the aquifer are influenced by a combination of tides from opposite coasts. A better match between the observed ground water head and the theoretical response can be obtained with the proposed dual-tide solution than with single-sided solutions. Hydraulic diffusivity was estimated to be 2.3 × 10⁷ m²/d. This translates into a hydraulic conductivity of 500 m/d, assuming a specific yield of 0.04 and an aquifer thickness of 1.8 km. A numerical experiment confirmed the hydraulic diffusivity value and showed that the y -intercepts of the modal attenuation and phase differences estimated by regression can approximate damping factors caused by low-permeability units at the boundary.     

A MODFLOW Infiltration Device Package for Simulating Storm Water Infiltration

This article describes a MODFLOW Infiltration Device (INFD) Package that can simulate infiltration devices and their two‐way interaction with groundwater. The INFD Package relies on a water balance including inflow of storm water, leakage‐like seepage through the device faces, overflow, and change in storage. The water balance for the device can be simulated in multiple INFD time steps within a single MODFLOW time step, and infiltration from the device can be routed through the unsaturated zone to the groundwater table. A benchmark test shows that the INFD Package's analytical solution for stage computes exact results for transient behavior. To achieve similar accuracy by the numerical solution of the MODFLOW Surface‐Water Routing (SWR1) Process requires many small time steps. Furthermore, the INFD Package includes an improved representation of flow through the INFD sides that results in lower infiltration rates than simulated by SWR1. The INFD Package is also demonstrated in a transient simulation of a hypothetical catchment where two devices interact differently with groundwater. This simulation demonstrates that device and groundwater interaction depends on the thickness of the unsaturated zone because a shallow groundwater table (a likely result from storm water infiltration itself) may occupy retention volume, whereas a thick unsaturated zone may cause a phase shift and a change of amplitude in groundwater table response to a change of infiltration. We thus find that the INFD Package accommodates the simulation of infiltration devices and groundwater in an integrated manner on small as well as large spatial and temporal scales.     

A new analytical solution for water table fluctuations in coastal aquifers with sloping beaches

The Boussinesq equation appears as the zeroth-order term in the shallow water flow expansion of the non-linear equation describing the flow of fluid in an unconfined aquifer. One-dimensional models based on the Boussinesq equation have been used to analyse tide-induced water table fluctuations in coastal aquifers. Previous analytical solutions for a sloping beach are based on the perturbation parameter, _N=αcotβ (in which β is the beach slope, α is the amplitude parameter and is the shallow water parameter) and are limited to tan⁻¹(α)βπ/2. In this paper, a new higher-order solution to the non-linear boundary value problem is derived. The results demonstrate the significant influence of the higher-order components and beach slope on the water table fluctuations. The relative difference between the linear solution and the present solution increases as and α increase, and reaches 7% of the linear solution.     

Soil moisture dynamics at high temporal resolution in a semiarid Mediterranean watershed with scattered tree cover

Subsurface water flows play a key role in the distribution of water and solutes and thereby in the water availability for plants. However, the characterization of different flow processes (i.e. matrix and preferential flow), the frequency and factors that cause them, is relatively rare. This characterization enables a better understanding of spatio‐temporal variability of water resources and allows for the design of models to be improved. Using a method based on the time derivative of soil moisture variation known as maximum wetting slope, types of soil wetting processes were classified and quantified. For this, capacitance sensors, which registered the volumetric water content at high temporal resolution (30 min) for more than two hydrological years, were installed at different depths and placed in soil moisture stations with different vegetation covers, lithology and topographic position. Results indicated that there is a general behaviour or pattern of soil moisture dynamics in the catchment with a dominant occurrence of slower soil wetting processes (>50%), caused by matrix flows, and a low occurrence of those faster processes (<30%), originated by preferential flows. Nevertheless, when the total volume of water is considered, preferential flow becomes the dominant process, so that the ecological role of both flow types becomes prominent in water‐limited environments. Statistical multivariate analyses based on data‐mining techniques proved that although both flow types depend on variables associated with precipitation and antecedent soil moisture conditions, faster soil wetting processes are mainly related to variables such as rainfall intensity and topography, while slower soil wetting processes are related to flow velocity, soils or vegetation. Copyright © 2015 John Wiley & Sons, Ltd.     

Nitrate fluctuations at the water table: implications for recharge processes and solute transport in the Chalk aquifer

This study investigates fluctuations in nitrate concentration at the water table to improve understanding of unsaturated zone processes in the Chalk aquifer. Sampling was conducted using a novel multi‐level sampler during periods of water table rise over 5 years at a vertical resolution of 0.05 m. Nitrate concentration increased as the water table seasonally recovered, with similar inter‐annual trends with depth. The rising water table activated horizontal fractures facilitating the delivery of water elevated by up to 10 mg/l of nitrate with respect to the adjacent groundwater below. These fractures are considered to activate via piston displacement of water from the adjoining matrix. Hydrograph analysis identified 16 events which significantly perturbed the water table within 24–48 h of rainfall. Consistent nitrate concentrations indicate recharge through persistent fracture flow from the surface was not generally the primary driver of the rapid water table response during these events. Instead, the response was attributed to the piston displacement of porewater immediately above the water table. However, a single event in November 2012 delivered relatively dilute recharge indicating rapid persistent fracture flow following rainfall was possible to a depth of 14–15 m. Decreases in porewater nitrate concentration around fracture horizons and the dilution of many groundwater samples with respect to porewaters indicate a fresher source of water at depth. This was considered most likely to be a result of near surface water bypassing the matrix because of widespread mineralization on fracture surfaces, which retard water and solute exchange. Therefore, persistent fracture flow maybe considered a frequent process, operating independently of the matrix, and is not necessarily event driven. Copyright © 2015 John Wiley & Sons, Ltd.     

Changes in water table level influence solute transport in uniform porous media

Changes in the water table level result in variable water saturation and variable hydrological fluxes at the interface between the unsaturated and saturated zone. This may influence the transport and fate of contaminants in the subsurface. The objective of this study was to examine the impact of a decreasing and an increasing water table on solute transport. We conducted tracer experiments at downward flow conditions in laboratory columns filled with two different uniform porous media under static and transient flow conditions either increasing or decreasing the water table. Tracer breakthrough curves were simulated using a mobile–immobile transport model. The resulting transport parameters were compared to identify dominant transport processes. Changes in the water table level affected dispersivities and mobile water fractions depending on the direction of water table movement and the grain size of the porous media. In fine glass beads, the water flow velocity was similar to the decline rate of the water table, and the mobile water fraction was decreased compared with steady‐state saturated conditions. However, immobile water was negligible. In coarse glass beads, water flow was faster because of fingered flow in the unsaturated part, and the mobile water fraction was smaller than in the fine material. Here, a rising water table led to an even smaller mobile water fraction and increased solute spreading because of diffusive interaction with immobile water. We conclude that changes of the water table need to be considered to correctly simulate transport in the subsurface at the transition of the unsaturated–saturated zone. Copyright © 2014 John Wiley & Sons, Ltd.     

Relating the depth of the water table to the depth of weathering

Weathering of bedrock creates and occludes permeability, affecting subsurface water flow. Often, weathering intensifies above the water table. On the contrary, weathering can also commence below the water table. To explore relationships between weathering and the water table, a simplified weathering model for an eroding hillslope was formulated that takes into account both saturated and unsaturated subsurface water flow (but does not fully account for changes in dissolved gas chemistry). The phreatic line was calculated using solutions to mathematical treatments for both zones. In the model, the infiltration rate at the hill surface sets both the original and the eventual steady-state position of the water table with respect to the weathering reaction front. Depending on parameters, the weathering front can locate either above or below the water table at steady state. Erosion also affects the water table position by changing porosity and permeability even when other hydrological conditions (e.g. hydraulic conductivity of parent material, infiltration rate at the surface) do not change. The total porosity in a hill (water storage capacity) was found to increase with infiltration rate (all else held constant). This effect was diminished by increasing the erosion rate. We also show examples of how the infiltration rate affects the position of the water table and how infiltration rate affects weathering advance. Published 2020. This article is a U.S. Government work and is in the public domain in the USA     

Analytical studies on transient groundwater flow induced by land reclamation using different fill materials

Land reclamation may have a significant influence on groundwater regimes. Analytical solutions have been developed in the past to study the impact of land reclamation on a steady‐state groundwater flow and transient flow in fill materials, assuming that the reclamation site consists of a single zone of uniform hydraulic parameters. In this paper, we derive analytical solutions to describe the transient water table change in response to multi‐stage land reclamation where the fill material is uniform in each stage but the hydraulic conductivity of the fill material varies from stage to stage. By introducing the method of separation of variables, we develop a transient analytical solution to study the impact of land reclamation consisting of fill material with different hydraulic properties on groundwater dynamics. The results show that the water table first increases significantly into the reclaimed zone following the fill material deposition, and then the increase gradually propagates into the original aquifer. The change of water table in the original aquifer mainly depends on the value of hydraulic conductivity of the fill materials. Examples in this paper illustrate how the aquifer system experiences a long time unsteady‐state flow as a result of the reclamation, and it takes at least tens of years for the system to approach a new equilibrium. It is suggested that for a large‐scale reclamation project, the response of the groundwater regime to reclamation should be carefully studied. Copyright © 2013 John Wiley & Sons, Ltd.     

An analytical study on three‐dimensional versus two‐dimensional water table‐induced flow patterns in a Tóthian basin

Although it has been increasingly acknowledged that groundwater flow pattern is complicated in the three‐dimensional (3‐D) domain, two‐dimensional (2‐D) water table‐induced flow models are still widely used to delineate basin‐scale groundwater circulation. However, the validity of 2‐D cross‐sectional flow field induced by water table has been seldom examined. Here, we derive the analytical solution of 3‐D water table‐induced hydraulic head in a Tóthian basin and then examine the validity of 2‐D cross‐sectional models by comparing the flow fields of selected cross sections calculated by the 2‐D cross‐sectional model with those by the 3‐D model, which represents the “true” cases. For cross sections in the recharge or discharge area of the 3‐D basin, even if head difference is not significant, the 2‐D cross‐sectional models result in flow patterns absolutely different from the true ones. For the cross section following the principal direction of groundwater flow, although 2‐D cross‐sectional models would overestimate the penetrating depth of local flow systems and underestimate the recharge/discharge flux, the flow pattern from the cross‐sectional model is similar to the true one and could be close enough to the true one by adjusting the decay exponent and anisotropy ratio of permeability. Consequently, to determine whether a 2‐D cross‐sectional model is applicable, a comparison of hydraulic head difference between 2‐D and 3‐D solutions is not enough. Instead, the similarity of flow pattern should be considered to determine whether a cross‐sectional model is applicable. This study improves understanding of groundwater flow induced by more natural water table undulations in the 3‐D domain and the limitations of 2‐D models accounting for cross‐sectional water table undulation only.     

Unsaturated Zone Flow Processes and Aquifer Response Time in the Chalk Aquifer,Brighton, South East England

The Chalk aquifer is one of the main sources of water in South East England. The unsaturated zone in the aquifer plays an important role controlling the time and magnitude of recharge and is major pathway for contaminant transport to the water table. A range of previous work has addressed flow processes in the Chalk unsaturated zone, but physical understanding is still incomplete. Here we present the results of a study on flow mechanism in the Chalk unsaturated zone using a combination of statistical analysis and novel laboratory methods. The study was undertaken at three sites (North Heath Barn [NHB], Pyecombe East [PE], and Preston Park [PP]) on the Chalk of the Brighton block, South East England. Daily and hourly time series data of groundwater level and rainfall were correlated. The results show that a slower groundwater level response to rainfall occurs during dry seasons (summer and autumn) when the amount of effective rainfall is less than 4 mm/day, with a thicker and drier unsaturated zone. A faster response occurs during wet seasons (winter and spring) when the daily effective rainfall exceeds 4 mm/day with a thinner and wetter unsaturated zone. Periods of very rapid response (within 15 h) were observed during wet seasons at NHB and PE sites, with unsaturated hydraulic conductivity (K_u) inferred to reach 839 mm/day. A slower response was observed at an urbanized site (PP) as a result of reduction in direct recharge due to reduced infiltration, due to presences of impermeable infrastructure covering the area around PP borehole. Laboratory measurements of K_u of the Chalk matrix using a geotechnical centrifuge show variation from 4.27 to 0.07 mm/day, according to the level of saturation. Thus, the rapid responses cannot be linked to matrix flow only but indicate the contribution of fracture and karstic flow processes in conducting water.     

Analytical solutions for 2D topography-driven flow in stratified and syncline aquifers

Two analytical solution methods are presented for regional steady-state groundwater flow in a two-dimensional stratified aquifer cross section where the water table is approximated by the topographic surface. For the first solution, the surficial aquifer is represented as a set of dipping parallel layers with different, but piecewise constant, anisotropic hydraulic conductivities, where the anisotropy is aligned with the dip of the layered formation. The model may be viewed as a generalization of the solutions developed by [Tóth JA. A theoretical analysis of groundwater flows in small drainage basins. J Geophys Res 1963;68(16):4795–812; Freeze R, Witherspoon P. Theoretical analysis of regional groundwater flow 1) analytical and numerical solution to the mathematical model, water resources research. Water Resour Res 1966;2(4):641–56; Selim HM. Water flow through multilayered stratified hillside. Water Resour Res 1975;11:949–57] to an multi-layer aquifer with general anisotropy, layer orientation, and a topographic surface that may intersect multiple layers. The second solution presumes curved (syncline) layer stratification with layer-dependent anisotropy aligned with the polar coordinate system. Both solutions are exact everywhere in the domain except at the topographic surface, where a Dirichlet condition is met in a least-squared sense at a set of control points; the governing equation and no-flow/continuity conditions are met exactly. The solutions are derived and demonstrated on multiple test cases. The error incurred at the location where the layer boundaries intersect the surface is assessed.     

Predicting Water Table Response to Rainfall Events,Central Florida

A rise in water table in response to a rainfall event is a complex function of permeability, specific yield, antecedent soil‐water conditions, water table level, evapotranspiration, vegetation, lateral groundwater flow, and rainfall volume and intensity. Predictions of water table response, however, commonly assume a linear relationship between response and rainfall based on cumulative analysis of water level and rainfall logs. By identifying individual rainfall events and responses, we examine how the response/rainfall ratio varies as a function of antecedent water table level (stage) and rainfall event size. For wells in wetlands and uplands in central Florida, incorporating stage and event size improves forecasting of water table rise by more than 30%, based on 10 years of data. At the 11 sites studied, the water table is generally least responsive to rainfall at smallest and largest rainfall event sizes and at lower stages. At most sites the minimum amount of rainfall required to induce a rise in water table is fairly uniform when the water table is within 50 to 100 cm of land surface. Below this depth, the minimum typically gradually increases with depth. These observations can be qualitatively explained by unsaturated zone flow processes. Overall, response/rainfall ratios are higher in wetlands and lower in uplands, presumably reflecting lower specific yields and greater lateral influx in wetland sites. Pronounced depth variations in rainfall/response ratios appear to correlate with soil layer boundaries, where corroborating data are available.