Quantifying bank storage of variably saturated aquifers

Numerical simulations were conducted to quantify bank storage in a variably saturated, homogenous, and anisotropic aquifer abutting a stream during rising stream stage. Seepage faces and bank slopes ranging from 1/3 to 100/3 were simulated. The initial conditions were assumed steady-state flow with water draining toward the stream. Then, the stream level rose at a constant rate to the specified elevation of the water table given by the landward boundary condition and stayed there until the system reached a new steady state. This represents a highly simplified version of a real world hydrograph. For the specific examples considered, the following conclusions can be made. The volume of surface water entering the bank increased with the rate of stream level rise, became negligible when the rate of rise was slow, and approached a positive constant when the rate was large. Also, the volume decreased with the dimensionless parameter M (the product of the anisotropy ratio and the square of the domain's aspect ratio). When M was large (>10), bank storage was small because most pore space was initially saturated with ground water due to the presence of a significant seepage face. When M was small, the seepage face became insignificant and capillarity began to play a role. The weaker the capillary effect, the easier for surface water to enter the bank. The effect of the capillary forces on the volume of surface water entering the bank was significant and could not be neglected.     

Seepage face height, water table position, and well efficiency at steady state

When a fully penetrating well pumps an ideal unconfined aquifer at steady state, the water table usually does not join the water level in the well. There is a seepage face inside the well, which is a key element in evaluating the well performance. This problem is analyzed using the finite-element method, solving the complete equations for saturated and unsaturated flow. The seepage face position is found to be almost independent of the unsaturated zone properties. The numerical results are used to test the validity of several analytic approximations. Equations are proposed to predict the seepage face position at the pumping well for any well drawdown, and the water table position at any distance from the pumping well for any in-well drawdown. Practical hints are provided for installing monitoring wells and evaluating well efficiency.     

Stream depletion by a pumping well including the effects of nonlinear variation of captured evaporation from a phreatic aquifer / Vidange en cours d’eau par puits de pompage incluant les effets de la variation non-linéaire de l’évaporation capturée d’une nappe à surface libre

Abstract

Abstract A study was made to develop a model that can be used to predict the steady-state stream depletion rates caused by a continuous pumping well located in a water table aquifer. The effects of nonlinear variation of evaporation with the depth to water table on steady-state stream depletion rate were investigated using model results. Dimensional analysis was used to determine the relationship between the scaled steady-state stream depletion, the scaled pumping distance, the scaled hydraulic conductivity, and the scaled initial depth to the water table. A dimensionless graph was developed for a wide range of these parameters. Analysis of this graph showed that the steady-state stream depletion rate decreases as the pumping distance between the well and the stream increases. The dimensionless graph also showed that steady-state stream depletion rates strongly depended on the initial position of the water table. Analysis indicated that, as the saturated conductivity increased, the effect of the initial position of the water table on the magnitude of stream depletion rate was more influential. Analysis also showed that, as the value of saturated conductivity decreased, the relative error produced by the assumption that at steady state all the pumped water is captured from the evaporation, also decreased.     

On the interpretation of recharge estimates from steady-state model calibrations

Ground water recharge is often estimated through the calibration of ground water flow models. We examine the nature of calibration errors by considering some simple mathematical and numerical calculations. From these calculations, we conclude that calibrating a steady-state ground water flow model to water level extremes yields estimates of recharge that have the same value as the time-varying recharge at the time the water levels are measured. These recharge values, however, are a subdued version of the actual transient recharge signal. In addition, calibrating a steady-state ground water flow model to data collected during periods of rising water levels will produce recharge values that underestimate the actual transient recharge. Similarly, calibrating during periods of falling water levels will overestimate the actual transient recharge. We also demonstrate that average water levels can be used to estimate the actual average recharge rate provided that water level data have been collected for a sufficient amount of time.     

A transient phreatic surface mound,evidenced by a strip of vegetation on an earth dam

Abstract

On the slopes of the embankment of the Al-Khod groundwater recharge–flood protection dam (Oman), a band of scrub vegetation community emerged after torrential rains and temporary filling of the dam reservoir. Species composition differs markedly on both sides of the embankment, with many exotics found on the reservoir side and more typical gravel-desert species on the outside. Hydro-ecologically, the vegetation is interpreted as the footprint of a temporary storage of water, which is a small-sized groundwater mound within the permeable shoulder of the levee. The levee, as an anthropogenic landform, induces a U-turn (gravitational slumping–lateral seepage–transpirational moisture ascent) topology of seepage. The Lembke method of successive variations of steady states is used in modelling the water table dynamics. In the early stage of the mound decay, outflow through a seepage face of the shoulder is modelled by the Barenblatt slumping parabola of the phreatic-zone part of the flow domain, which is perfectly matched with the Youngs exact solution for a purely horizontal flow through a porous wedge. At the stitching cross-section, the flow rates and saturated depths in the two zones coincide. The late stage of mound evolution is characterized by transpiration by the plant roots projected onto a shrinking free surface, with the Barenblatt and Youngs solutions conjugated but without the outcrop of the saturated mound on the levee slope. Ordinary differential equations for the sliding or descending locus of the intersection of the parabola and the triangle hypotenuse are integrated in a closed form or by the Runge-Kutta method. The dwindling saturated volume and the rate of drainage are obtained. They can be used in assessments of the hydro-ecological sustainability of slope-rooted shrubs (vegetation survival between rare rainfall episodes).

Editor D. Koutsoyiannis; Associate editor A. Porporato     

Development and application of an analytical model of stream/aquifer interaction

A mathematical model to simulate stream/aquifer interactions in an unconfined aquifer subjected to time varying river stage was developed from the linearized Boussinesq equation using the principle of superposition and the concept of semigroups. The mathematical model requires an estimate of three parameters to simulate ground-water elevations; transmissivity, specific yield, and recharge. The solution has physical significance and includes terms for the steady-state water level, the steady-state water level as influenced by a change in river stage, a transient redistribution of water levels in the aquifer from the previous day, and a transient change in water level caused by a change in river stage. The mathematical model was tested using observed water table elevations at three locations across a 2-km-wide alluvial valley aquifer. The average absolute deviation between observed and simulated daily water levels was 0.09 m. The difference in river stage over the test year was 4.9 m.     

Tidal effects on groundwater dynamics in unconfined aquifers

The variation of seawater level resulting from tidal fluctuations is usually neglected in regional groundwater flow studies. Although the tidal oscillation is damped near the shoreline, there is a quasi‐steady‐state rise in the mean water‐table position, which may have an influence on regional groundwater flow. In this paper the effects of tidal fluctuations on groundwater hydraulics are investigated using a variably saturated numerical model that includes the effects of a realistic mild beach slope, seepage face and the unsaturated zone. In particular the impact of these factors on the velocity field in the aquifer is assessed. Simulations show that the tidal fluctuation has substantial consequences for the local velocity field in the vicinity of the exit face, which affects the nearshore migration of contaminant in coastal aquifers. An overheight in the water table as a result of the tidal fluctuation is observed and this has a significant effect on groundwater discharge to the sea when the landward boundary condition is a constant water level. The effect of beach slope is very significant and simplifying the problem by considering a vertical beach face causes serious errors in predicting the water‐table position and the groundwater flux. For media with a high effective capillary fringe, the moisture retained above the water table is important in determining the effects of the tidal fluctuations. Copyright © 2001 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.     

Transient analysis of the source of water to wells: Cape Cod, Massachusetts

A transient flow modeling analysis for potential public-supply wells on western Cape Cod, Massachusetts, demonstrates the difference between transient and steady-state recharge areas can have important implications for wellhead protection. An example of a single pumping well illustrates that commonly used steady-state time-related capture areas do not represent the recharge area and travel times of water being pumped from the well until sufficient time has elapsed for steady-state flow conditions to be established. Until that time, transient recharge areas are needed to account for the portion of water discharging from the well that entered the aquifer before pumping started. An example of two pumping wells demonstrates the same area at the water table cannot supply water to more than one well under steady-state flow conditions. Transient recharge areas to multiple wells can overlap, however, until steady-state flow conditions are established. The same area can, therefore, be a source of water to more than one well during early pumping times, and the water pumped from a given well may derive from source areas, including contaminated areas, that do not lie within the well's steady-state recharge area.     

An analytical solution for predicting the transient seepage from a subsurface drainage system

Subsurface drainage systems have been widely used to deal with soil salinization and waterlogging problems around the world. In this paper, a mathematical model was introduced to quantify the transient behavior of the groundwater table and the seepage from a subsurface drainage system. Based on the assumption of a hydrostatic pressure distribution, the model considered the pore-water flow in both the phreatic and vadose soil zones. An approximate analytical solution for the model was derived to quantify the drainage of soils which were initially water-saturated. The analytical solution was validated against laboratory experiments and a 2-D Richards equation-based model, and found to predict well the transient water seepage from the subsurface drainage system. A saturated flow-based model was also tested and found to over-predict the time required for drainage and the total water seepage by nearly one order of magnitude, in comparison with the experimental results and the present analytical solution. During drainage, a vadose zone with a significant water storage capacity developed above the phreatic surface. A considerable amount of water still remained in the vadose zone at the steady state with the water table situated at the drain bottom. Sensitivity analyses demonstrated that effects of the vadose zone were intensified with an increased thickness of capillary fringe, capillary rise and/or burying depth of drains, in terms of the required drainage time and total water seepage. The analytical solution provides guidance for assessing the capillary effects on the effectiveness and efficiency of subsurface drainage systems for combating soil salinization and waterlogging problems.     

Influence of seepage undercutting on the stability of root‐reinforced streambanks

Several mechanisms contribute to streambank failure including fluvial toe undercutting, reduced soil shear strength by increased soil pore‐water pressure, and seepage erosion. Recent research has suggested that seepage erosion of noncohesive soil layers undercutting the banks may play an equivalent role in streambank failure to increased soil pore‐water pressure. However, this past research has primarily been limited to laboratory studies of non‐vegetated banks. The objective of this research was to utilize the Bank Stability and Toe Erosion Model (BSTEM) in order to determine the importance of seepage undercutting relative to bank shear strength, bank angle, soil pore‐water pressure, and root reinforcement. The BSTEM simulated two streambanks: Little Topashaw Creek and Goodwin Creek in northern Mississippi. Simulations included three bank angles (70° to 90°), four pore‐water pressure distributions (unsaturated, two partially saturated cases, and fully saturated), six distances of undercutting (0 to 40 cm), and 13 different vegetation conditions (root cohesions from 0·0 to 15·0 kPa). A relative sensitivity analysis suggested that BSTEM was approximately three to four times more sensitive to water table position than root cohesion or depth of seepage undercutting. Seepage undercutting becomes a prominent bank failure mechanism on unsaturated to partially saturated streambanks with root reinforcement, even with undercutting distances as small as 20 cm. Consideration of seepage undercutting is less important under conditions of partially to fully saturated soil pore‐water conditions. The distance at which instability by undercutting became equivalent to instability by increased soil pore‐water pressure decreased as root reinforcement increased, with values typically ranging between 20 and 40 cm at Little Topashaw Creek and between 20 and 55 cm at Goodwin Creek. This research depicts the baseline conditions at which seepage undercutting of vegetated streambanks needs to be considered for bank stability analyses. Copyright © 2008 John Wiley & Sons, Ltd.     

A Simple Method for Simulating Groundwater Interactions with Fens to Forecast Development Effects

Protection of fens–wetlands dependent on groundwater discharge–requires characterization of groundwater sources and stresses. Because instrumentation and numerical modeling of fens is labor intensive, easy-to-apply methods that model fen distribution and their vulnerability to development are desirable. Here we demonstrate that fen areas can be simulated using existing steady-state MODFLOW models when the unsaturated zone flow (UZF) package is included. In cells where the water table is near land surface, the UZF package calculates a head difference and scaled conductance at these “seepage drain” cells to generate average rates of vertical seepage to the land. This formulation, which represents an alternative to blanketing the MODFLOW domain with drains, requires very little input from the user because unsaturated flow-routing is inactive and results are primarily driven by easily obtained topographic information. Like the drain approach, it has the advantage that the distribution of seepage areas is not predetermined by the modeler, but rather emerges from simulated heads. Beyond the drain approach, it takes account of intracell land surface variation to explicitly quantify multiple surficial flows corresponding to infiltration, rejected recharge, recharge and land-surface seepage. Application of the method to a basin in southeastern Wisconsin demonstrates how it can be used as a decision-support tool to first, reproduce fen distribution and, second, forecast drawdown and reduced seepage at fens in response to shallow pumping.     

Quantifying groundwater dependency of riparian surface hydrologic features using the exit gradient

Numerical groundwater flow models necessarily are limited to subsurface flow evaluation. It is of interest, however, to examine the possibility that, for unconfined aquifer systems, they could be used to proportionately measure the magnitude of seepage they estimate when these aquifers intersect the landscape surface. Our goal in this study was to determine the degree to which an unconfined groundwater model can estimate run‐off or seepage at the land surface during winter time wet season conditions, as well as in the dry season, when evapotranspiration is a major part of the water balance, using a lowland basin‐fill example study area in the Pacific Northwest. The exit gradient is a metric describing the potential for vertical seepage at the landscape surface. We investigated the spatial relationship of mapped surface features, such as wetlands, streams and ponds, to the model‐predicted mapped exit gradient. We found that areas mapped as wetlands had positive exit gradients. During the wet season, modelled exit gradients predicted seepage throughout extensive areas of the groundwater shed, extending far beyond mapped wetland areas (355% increase), associated with previously observed increases in nitrate‐nitrogen in streams in wet season. During the dry season, exit gradients spatially corresponded with wetland areas. The increase in in‐stream nitrogen corresponds with shorter residence times in carbon‐rich wetland zones because of the onset of saturation overland flow. We present results that suggest that the exit gradient could be a useful concept in examining the groundwater–surface water linkage that is often under represented physically in watershed flow models. Published 2015. This article is a U.S. Government work and is in the public domain in the USA.     

River-aquifer interactions, geologic heterogeneity, and low-flow management

Low river flows are commonly controlled by river-aquifer exchange, the magnitude of which is governed by hydraulic properties of both aquifer and aquitard materials beneath the river. Low flows are often important ecologically. Numerical simulations were used to assess how textural heterogeneity of an alluvial system influences river seepage and low flows. The Cosumnes River in California was used as a test case. Declining fall flows in the Cosumnes River have threatened Chinook salmon runs. A ground water-surface water model for the lower river basin was developed, which incorporates detailed geostatistical simulations of aquifer heterogeneity. Six different realizations of heterogeneity and a homogenous model were run for a 3-year period. Net annual seepage from the river was found to be similar among the models. However, spatial distribution of seepage along the channel, water table configuration and the level of local connection, and disconnection between the river and aquifer showed strong variations among the different heterogeneous models. Most importantly, the heterogeneous models suggest that river seepage losses can be reduced by local reconnections, even when the regional water table remains well below the riverbed. The percentage of river channel responsible for 50% of total river seepage ranged from 10% to 26% in the heterogeneous models as opposed to 23% in the homogeneous model. Differences in seepage between the models resulted in up to 13 d difference in the number of days the river was open for salmon migration during the critical fall months in one given year.     

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     

Modelling water-table movement in flat low-lying lands

The unsteady water-table movement caused by intermittent rainfall and varying evaporation in flat lands intersected by a network of ditches is modelled using land-drainage theory. The unsteady water tables are assumed to behave as a continuous succession of steady states with the flux through the water table given by the sum of components due to rainfall and evaporation through the soil surface and due to water released or taken up by the unsaturated soil above the water table. A simple steady-state drainage equation is used for the relationship between water-table height and flux, and the specific yield is assumed to have a constant value. The simulated seasonal water table using estimated hydraulic soil properties and meteorological records for a field site agreed with available dip-well observations. The water table was much lower than the ditch-water level during the summer months. The sensitivity of simulated results to model parameters is demonstrated.     

Water storage dynamics in a till hillslope: the foundation for modeling flows and turnover times

Studies on hydrology, biogeochemistry, or mineral weathering often rely on assumptions about flow paths, water storage dynamics, and transit times. Testing these assumptions requires detailed hydrometric data that are usually unavailable at the catchment scale. Hillslope studies provide an alternative for obtaining a better understanding, but even on such well‐defined and delimited scales, it is rare to have a comprehensive set of hydrometric observations from the water divide down to the stream that can constrain efforts to quantify water storage, movement, and turnover time. Here, we quantified water storage with daily resolution in a hillslope during the course of almost an entire year using hydrological measurements at the study site and an extended version of the vertical equilibrium model. We used an exponential function to simulate the relationship between hillslope discharge and water table; this was used to derive transmissivity profiles along the hillslope and map mean pore water velocities in the saturated zone. Based on the transmissivity profiles, the soil layer transmitting 99% of lateral flow to the stream had a depth that ranged from 8.9 m at the water divide to under 1 m closer to the stream. During the study period, the total storage of this layer varied from 1189 to 1485 mm, resulting in a turnover time of 2172 days. From the pore water velocities, we mapped the time it would take a water particle situated at any point of the saturated zone anywhere along the hillslope to exit as runoff. Our calculations point to the strengths as well as limitations of simple hydrometric data for inferring hydrological properties and water travel times in the subsurface.     

Laboratory and numerical investigation of flow and transport near a seepage-face boundary

Laboratory and numerical modeling investigations were completed to study the unconfined ground water flow and transport processes near a seepage-face boundary. The laboratory observations were made in a radial sand tank and included measurements of the height of the seepage face, flow velocity near the seepage face, travel time distribution of multiple tracer slugs, and streamlines. All the observations were reliably reproduced with a three-dimensional, axi-symmetric, variably saturated ground water flow model. Physical data presented in this work demonstrate and quantify the importance of three-dimensional transport patterns within a seepage-face zone. The results imply that vertically averaged flow models that employ Dupuit approximations might introduce error in the analysis of localized solute transport near a seepage-face boundary. The experimental dataset reported in this work will also be of interest for those who are attempting to validate a numerical algorithm for solving ground water and contaminant discharge patterns near a surface-water boundary.     

冷泉形成的数值模拟研究

海底冷泉形成的一种可能机制是海平面下降引起天然气水合物的分解.本文基于对冷泉渗漏特征的分析,建立了二维轴对称模型,利用有限元方法定量分析了南海区域海平面下降对冷泉形成的影响.结果表明,末次冰盛期(26.5~19.0ka BP)海平面下降引起的冷泉活动可以持续到现在,但是从水合物停止分解至今,超孔隙压力的极值在持续减小,而流体向海底的渗漏达西速度先快速减小、然后缓慢减小.同时发现,流体向海底的渗漏达西速度与管状通道的渗透率、通道周围介质的渗透率以及通道的半径等有关,估计目前的冷泉活动还可以持续10000年以上.海平面下降引起的天然气水合物分解,可能是影响全球气候变化的一个重要因素.     

Analytical solution of water table fluctuations above an inclined leaky layer due to ditch recharge

Ditch recharge is a method used for raising a water table. However, if the aquifer lies above a leaky layer, then the leaky bed will have an effect on the height of the water table. This paper attempts to provide an analytical solution of the transient state to the linearized Boussinesq equation. The solution proposed in this paper is intended for a generalized form of the leaky layer, with the boundary condition of the water level moving according to an exponential form. The results of theoretical analysis and experimental studies can provide a much better explanation of ditch recharge on an inclined leaky layer. Copyright © 2006 John Wiley & Sons, Ltd.