Anisotropy and depth‐related heterogeneity of hydraulic conductivity in a bog peat. II: modelling the effects on groundwater flow

Anisotropy and heterogeneity of hydraulic conductivity (K) are seldom considered in models of mire hydrology. We investigated the effect of anisotropy and heterogeneity on groundwater flow in bog peat using a steady‐state groundwater model. In five model simulations, four sets of K data were used. The first set comprised measured K values from an anisotropic and heterogeneous bog peat. These data were aggregated to produce the following simplified data sets: an isotropic and heterogeneous distribution of K; an isotropic and homogeneous distribution; and an anisotropic and homogeneous distribution. We demonstrate that, where anisotropy and heterogeneity exist, groundwater flow in bog peat is complex. Fine‐scale variations in K have the potential to influence patterns and rates of groundwater flow. However, for our data at least, it is heterogeneity and not anisotropy that has the greater influence on producing complex patterns of groundwater flow. We also demonstrate that patterns and rates of groundwater flow are simplified and reduced when measured K values are aggregated to create a more uniform distribution of K. For example, when measured K values are aggregated to produce isotropy and homogeneity, the rate of modelled seepage is reduced by 28%. We also show that when measured K values are used, the presence of a drainage ditch can increase seepage through a modelled cross‐section. Our work has implications for the accurate interpretation of hydraulic head data obtained from peat soils, and also the understanding of the effect of drainage ditches on patterns and rates of groundwater flow. Copyright © 2002 John Wiley & Sons, Ltd.     

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.     

Numerical studies of two-dimensional saturated/ unsaturated drainage models

The partial differential equation which governs the seepage of water in unsaturated and saturated porous media is solved numerically by a generalized Newton iteration technique for two models, one ditch drainage model and one earth dam model. For each model, which is two-dimensional, a few hypothetical soils with different moisture retention curves are considered. In both models only drainage from an initially saturated soil occurs; thus, the problem of hysteresis is avoided. The results of the computations are compared with those of corresponding saturated (pure groundwater) models; solutions obtained earlier by this author and others.

Computational instability phenomena appear when the slope of the retention curves is made steep, i.e., for poorly-graded soils.     

Precision calculation of crustal deformation induced by radial steady laminellar flow of underground water from single well in multi-layered structural aquifers

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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.     

Flow in unsaturated random porous media,nonlinear numerical analysis and comparison to analytical stochastic models

This work presents a rigorous numerical validation of analytical stochastic models of steady state unsaturated flow in heterogeneous porous media. It also provides a crucial link between stochastic theory based on simplifying assumptions and empirical field and simulation evidence of variably saturated flow in actual or realistic hypothetical heterogeneous porous media. Statistical properties of unsaturated hydraulic conductivity, soil water tension, and soil water flux in heterogeneous soils are investigated through high resolution Monte Carlo simulations of a wide range of steady state flow problems in a quasi-unbounded domain. In agreement with assumptions in analytical stochastic models of unsaturated flow, hydraulic conductivity and soil water tension are found to be lognormally and normally distributed, respectively. In contrast, simulations indicate that in moderate to strong variable conductivity fields, longitudinal flux is highly skewed. Transverse flux distributions are leptokurtic. the moments of the probability distributions obtained from Monte Carlo simulations are compared to modified first-order analytical models. Under moderate to strong heterogeneous soil flux conditions (σ²_y≥1), analytical solutions overestimate variability in soil water tension by up to 40% as soil heterogeneity increases, and underestimate variability of both flux components by up to a factor 5. Theoretically predicted model (cross-)covariance agree well with the numerical sample (cross-)covarianaces. Statistical moments are shown to be consistent with observed physical characteristics of unsaturated flow in heterogeneous soils.©1998 Elsevier Science Limited. All rights reserved     

MAPPING AND INTERPRETATION OF FIELD PHENOMENA FOR GROUNDWATER RECONNAISSANCE IN A PRAIRIE ENVIRONMENT,ALBERTA, CANADA

ABSTRACT

Theoretically, a small drainage basin may be divided into equal areas of downward flow and upward flow of groundwater. In regions where surface water does not obscure the phenomena produced by groundwater, these areas can be differentiated by mapping springs, seepages, groundwater levels, flowing wells, chemical quality of water, natural vegetation, salt precipitates, quality of crops, soap holes, and moist and dry depressions.

Mapping and interpretation of field phenomena have been carried out in a section of the Ghostpine Creek valley in a Prairie environment. The relief is gently rolling, the geology is simple, and the climate is cold, humid, and continental. The area of the “north flow-systems” is apportioned as follows: 26 per cent underlain by downward flow; 42 per cent underlain by a mid-line area; and 32 per cent underlain by upward flow.

Noting that groundwater flow is nearly parallel to the water table in the vicinity of the mid-line these results comply with the above-mentioned theory of groundwater flow distribution in small drainage basins. Thus, the method is suggested for: 1. A reconnaissance study of the groundwater regime in certain areas, and 2. Specific problems related to groundwater in a Prairie environment, such as: finding suitable locations for dug-out type water supplies, estimating prospects for slough-draining and irrigation, and explanation of the development of certain soil types. For such purposes, the method appears to be competitive with test drilling.     

Simulation of field‐scale water flow and bromide transport in a cracked clay soil

Single domain models may seriously underestimate leaching of nutrients and pesticides to groundwater in clay soils with shrinkage cracks. Various two‐domain models have been developed, either empirical or physically based, which take into account the effects of cracks on water flow and solute transport. This paper presents a model concept that uses the clay shrinkage characteristics to derive crack volume and crack depth under transient field conditions. The concept has been developed to simulate field average behaviour of a field with cracks, rather than flow and transport at a small plot. Water flow and solute transport are described with basic physics, which allow process and scenario analysis. The model concept is part of the more general agrohydrological model SWAP, and is applied to a field experiment on a cracked clay soil, at which water flow and bromide transport were measured during 572 days. A single domain model was not able to mimic the field‐average water flow and solute transport. Incorporation of the crack concept considerably improved the simulation of water content and bromide leaching to the groundwater. Still deviations existed between the measured and simulated bromide concentration profiles. The model did not reproduce the observed bromide retardation in the top layer and the high bromide dispersion resulting from water infiltration at various soil depths. A sensitivity analysis showed that the amounts of bromide leached were especially sensitive to the saturated hydraulic conductivity of the top layer, the solute transfer from the soil matrix to crack water flow and the mean residence time of rapid drainage. The shrinkage characteristic and the soil hydraulic properties of the clay matrix showed a low sensitivity. Copyright © 2000 John Wiley & Sons, Ltd.     

Recent advances in modeling of well hydraulics

Well hydraulics is a discipline to understand the process of flow to the well in an aquifer which is regarded as a source of groundwater. A variety of analytical and numerical models have been developed over the last few decades to provide a framework for understanding and quantifying the flow behavior in aquifer systems. In this review, we first briefly introduce the background of the theory of well hydraulics and the concepts, methodologies, and applications of analytical, semi-analytical, numerical and approximate methods in solving the well-hydraulic problems. We then address the subjects of current interests such as the incorporation of effects of finite well radius, wellbore storage, well partial penetration, and the presence of skin into various practical problems of groundwater flow. Furthermore, we also summarize recent developments of flow modeling such as the flow in aquifers with horizontal wells or collector wells, the capture zone delineation, and the non-Darcian flow in porous media and fractured formations. Finally, we present a comprehensive review on the numerical calculations for five well functions frequently appearing in well-hydraulic literature and suggest some topics in groundwater flow for future research.     

Understanding and modelling spatial drain–aquifer interactions in a low‐lying coastal aquifer—the Thurne catchment,Norfolk, UK

Seawater intrusion into fresh groundwater formations generally results inadvertently from human activities, such as over‐abstraction from coastal aquifers. This article describes the data analysis to quantify drain–aquifer interactions in a low‐lying pump‐drained coastal aquifer, which is subject to saline intrusion due to widespread land drainage, and the resulting development and application of a numerical groundwater model to understand the spatial groundwater system behaviour (including groundwater salinity fluxes). Without measured flow data in this pump‐drained catchment, a novel groundwater head‐dependent approach to hydrograph separation is described. Time‐variant and time‐invariant MODFLOW analyses are utilised to examine the flow processes. A new approach to calculate drain coefficients, which represent the extensive network of drainage ditches in the regional model, using field information, is described; the sum of the drainage coefficients are close to the values independently estimated from the head‐dependent hydrograph separation. Results show that (1) the groundwater flows into the drainage systems are well reproduced using the new drain coefficients, (2) particle tracking of fresh and saline water can explain observed spatial salinity distribution within drainage networks and (3) the modelled flow of seawater across the coast is approximately 25% greater than that discharged by the pumps, demonstrating the need for drainage management to be aware of the slow response of groundwater systems to past drainage system changes. The article demonstrates that numerical groundwater modelling can produce the improved understanding needed to inform management decisions in such complex environments. Copyright © 2010 John Wiley & Sons, Ltd.     

Groundwater Flow Field Distortion by Monitoring Wells and Passive Flux Meters

Due to differences in hydraulic conductivity and effects of well construction geometry, groundwater lateral flow through a monitoring well typically differs from groundwater flow in the surrounding aquifer. These differences must be well understood in order to apply passive measuring techniques, such as passive flux meters (PFMs) used for the measurement of groundwater and contaminant mass fluxes. To understand these differences, lab flow tank experiments were performed to evaluate the influences of the well screen, the surrounding filter pack and the presence of a PFM on the natural groundwater flux through a monitoring well. The results were compared with analytical calculations of flow field distortion based on the potential theory of Drost et al. (1968). Measured well flow field distortion factors were found to be lower than calculated flow field distortion factors, while measured PFM flow field distortion factors were comparable to the calculated ones. However, this latter is not the case for all conditions. The slotted geometry of the well screen seems to make a correct analytical calculation challenging for conditions where flow field deviation occurs, because the potential theory assumes a uniform flow field. Finally, plots of the functional relationships of the distortion of the flow field with the hydraulic conductivities of the filter screen, surrounding filter pack and corresponding radii make it possible to design well construction to optimally function during PFM applications.     

Low‐Resolution Modeling of Dense Drainage Networks in Confining Layers

Groundwater‐surface water (GW‐SW) interaction in numerical groundwater flow models is generally simulated using a Cauchy boundary condition, which relates the flow between the surface water and the groundwater to the product of the head difference between the node and the surface water level, and a coefficient, often referred to as the “conductance.” Previous studies have shown that in models with a low grid resolution, the resistance to GW‐SW interaction below the surface water bed should often be accounted for in the parameterization of the conductance, in addition to the resistance across the surface water bed. Three conductance expressions that take this resistance into account were investigated: two that were presented by Mehl and Hill (2010) and the one that was presented by De Lange (1999). Their accuracy in low‐resolution models regarding salt and water fluxes to a dense drainage network in a confined aquifer system was determined. For a wide range of hydrogeological conditions, the influence of (1) variable groundwater density; (2) vertical grid discretization; and (3) simulation of both ditches and tile drains in a single model cell was investigated. The results indicate that the conductance expression of De Lange (1999) should be used in similar hydrogeological conditions as considered in this paper, as it is better taking into account the resistance to flow below the surface water bed. For the cases that were considered, the influence of variable groundwater density and vertical grid discretization on the accuracy of the conductance expression of De Lange (1999) is small.     

Hydrogeochemistry of shallow groundwater in an upland Scottish catchment

The hydrogeochemistry of shallow groundwater has been characterized in the Allt a'Mharcaidh catchment in the Scottish Cairngorms in order to: (i) assess the spatial and temporal variation in groundwater chemistry; (ii) identify the hydrogeochemical processes regulating its evolution; and (iii) examine the influence of groundwater on the quality and quantity of stream flow. Shallow groundwater in superficial drift deposits is circumneutral (pH∽7·1) and base cation concentrations are enriched compared with precipitation and drainage water from overlying podzolic soils. Modelling with NETPATH suggests that the dominant geochemical processes that account for this are the dissolution of plagioclase, K-feldspar and biotite. Groundwater emerging as springs from weathered granite underlying high altitude (>900 m) alpine soils shows similar characteristics, though weathering rates are lower, probably as a result of reduced residence times and lower temperatures. Chemical hydrograph separation techniques using acid neutralizing capacity (ANC) and Si as tracers show that groundwater is the dominant source of baseflow in the catchment and also buffers the chemistry of stream water at high flows: groundwater may account for as much as 50–60% of annual runoff in the catchment. Climate and land use in the Cairngorms are vulnerable to future changes, which may have major implications for hydrogeological processes in the area. © 1998 John Wiley & Sons, Ltd.     

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.     

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.     

Modelling solute leaching during fingered flow by integrating and expanding various theoretical and empirical concepts

Abstract

Wetting front instability (fingered flow) accelerates solute transport through the unsaturated zone to the groundwater table. Whether fingers widen or dissipate close to the groundwater is unclear. Water flow in a two-dimensional artificial capillary fringe below a dry layer exhibiting fingered flow was investigated. The flow diverged strongly in the wet soil, suggesting that fingers dissipate. Expressions for the finger radius in dry and wet soil were combined and adapted to a soil hydraulic property parameterization popular in numerical modelling. The modified equation provided finger radii for soils in humid and arid climates. The fingers in the arid soil were excessively wide. The finger radii were used to model solute transport, assuming fingers dissipated in the subsoil. Modelling was cumbersome for the arid climate. One shower may often be insufficient to trigger fingering in arid regions with short, heavy showers. In soils with shallow groundwater, the diverging subsoil flow determines solute leaching.     

Lagged rejuvenation of groundwater indicates internal flow structures and hydrological connectivity

Large proportions of rainwater and snowmelt infiltrate into the subsurface before contributing to stream flow and stream water quality. Subsurface flow dynamics steer the transport and transformation of contaminants, carbon, weathering products and other biogeochemistry. The distribution of groundwater ages with depth is a key feature of these flow dynamics. Predicting these ages are a strong test of hypotheses about subsurface structures and time-varying processes. Chlorofluorocarbon (CFC)-based groundwater ages revealed an unexpected groundwater age stratification in a 0.47 km² forested catchment called Svartberget in northern Sweden. An overall groundwater age stratification, representative for the Svartberget site, was derived by measuring CFCs from nine different wells with depths of 2–18 m close to the stream network. Immediately below the water table, CFC-based groundwater ages of already 30 years that increased with depth were found. Using complementary groundwater flow models, we could reproduce the observed groundwater age stratification and show that the 30 year lag in rejuvenation comes from return flow of groundwater at a subsurface discharge zone that evolves along the interface between two soil types. By comparing the observed groundwater age stratification with a simple analytical approximation, we show that the observed lag in rejuvenation can be a powerful indicator of the extent and structure of the subsurface discharge zone, while the vertical gradient of the age-depth-relationship can still be used as a proxy of the overall aquifer recharge even when sampled in the discharge zone. The single age stratification profile measured in the discharge zone, close to the aquifer outlet, can reveal the main structure of the groundwater flow pattern from recharge to discharge. This groundwater flow pattern provides information on the participation of groundwater in the hydrological cycle and indicates the lower boundary of hydrological connectivity.     

Forecasting changes of water resources in large rivers following land drainage / Méthode de prévision des modifications des ressources en eau des grands fleuves sous l'effet du drainage

ABSTRACT

Techniques are described for annual forecasts of the water balance after drainage of large river basins. In the development of these techniques precipitation was assumed to be constant and unaffected by drainage. It is shown that the effect of drainage upon the annual runoff of the improved basins is to decrease the groundwater and swamp water resources which leads to evaporation changes. According to experimental data on the hydrophysical properties of peats, mineral soils and subsoils and how they change after drainage, the decrease in the groundwater resources was estimated for each per cent of the basin drained. This allowed account to betaken of this effect while making forecasts of runoff changes. Evaporation changes are computed as the difference between the maximum possible evaporation (potential evaporation) from cultivated areas and that from undisturbed swamps.     

Towards the representation of groundwater in the Joint UK Land Environment Simulator

Groundwater is an important component of the hydrological cycle with significant interactions with soil hydrological processes. Recent studies have demonstrated that incorporating groundwater hydrology in land surface models (LSMs) considerably improves the prediction of the partitioning of water components (e.g., runoff and evapotranspiration) at the land surface. However, the Joint UK Land Environment Simulator (JULES), an LSM developed in the United Kingdom, does not yet have an explicit representation of groundwater. We propose an implementation of a simplified groundwater flow boundary parameterization (JULES-GFB), which replaces the original free drainage assumption in the default model (JULES-FD). We tested the two approaches under a controlled environment for various soil types using two synthetic experiments: (1) single-column and (2) tilted-V catchment, using a three-dimensional (3-D) hydrological model (ParFlow) as a benchmark for JULES’ performance. In addition, we applied our new JULES-GFB model to a regional domain in the UK, where groundwater is the key element for runoff generation. In the single-column infiltration experiment, JULES-GFB showed improved soil moisture dynamics in comparison with JULES-FD, for almost all soil types (except coarse soils) under a variety of initial water table depths. In the tilted-V catchment experiment, JULES-GFB successfully represented the dynamics and the magnitude of saturated and unsaturated storage against the benchmark. The lateral water flow produced by JULES-GFB was about 50% of what was produced by the benchmark, while JULES-FD completely ignores this process. In the regional domain application, the Kling-Gupta efficiency (KGE) for the total runoff simulation showed an average improvement from 0.25 for JULES-FD to 0.75 for JULES-GFB. The mean bias of actual evapotranspiration relative to the Global Land Evaporation Amsterdam Model (GLEAM) product was improved from −0.22 to −0.01 mm day⁻¹. Our new JULES-GFB implementation provides an opportunity to better understand the interactions between the subsurface and land surface processes that are dominated by groundwater hydrology.     

Drainage water temperature as a basis for verifying drainage runoff composition on slopes

Tile drainage water temperatures and discharge rates were measured in five highland watersheds of which most are underlain by acid crystalline rock. One of them, Dehtá?e in the Bohemo‐Moravian highland (Czech Republic), was studied in greater detail. The aim was to evaluate water temperature monitoring as a means of determining the source and pathway of drainage runoff during high‐flow events. Rapid increase in drainage discharge was accompanied by rapid change in water temperature. In winter, the rising limb of the hydrograph was accompanied by a decrease in temperature, and the falling limb was associated with a corresponding temperature increase. In summer, the trends were reversed. These data suggest that the water temperature changes are caused by the fastest component of drainage runoff, water from a precipitation event or snowmelt, which can be separated from the remainder of the hydrograph. Measurements of hydraulic conductivity, soil moisture content, soil temperature, and groundwater table level indicate that the major portion of the event water causing this effect infiltrates in the watershed recharge zone where soils are permeable, enters the weathered bedrock, flows preferentially and rapidly down the slope along disjoint fissures in the bedrock, finally emerging as ascending springs, and is, for the most part, intercepted by the tile drainage systems. Copyright © 2011 John Wiley & Sons, Ltd.