Search

While hydrological science has made great strides forward during the last 50 years with the advance of computing power and availability of satellite images, much is unknown about the sustainable development of water for irrigation, domestic use, and livestock consumption for millions of households in the developing world. Specifically, quantification of shallow underground water resources for irrigation in highland regions remains challenging. The objective is to better understand the hydrology of highland watersheds with sloping hillside aquifers. Therefore, we present a subsurface flow model for hillside aquifers with recharge that varied from day to day. Recharge to the aquifer was estimated by the Thornthwaite Mather procedure. A characteristic time was identified for travel time of water flowing from the upper part of the hillside to the river or well. Using the method of characteristics, we found that the height of shallow groundwater level can be predicted by determining the total recharge over the characteristic time divided by drainable porosity. We apply the model to farmer‐dug wells in the Ethiopian highlands using observed rainfall, potential evaporation, and a fitted travel time. We find that the model performs well with maximum water table heights being determined by the soil surface and minimum heights by the presence or absence of volcanic dikes downhill. Our application shows that unless the water is ponded behind a natural or artificial barrier, hillslope aquifers are unable to provide a continuous source of water during the long, dry season. This clearly limits any irrigation development in the highlands from shallow sloping groundwater.

An approximation is obtained for the recession of a sloping aquifer. The analytical approximation can provide a useful tool to analyze data and obtain physical properties of the aquifer. In contrast to the case of a horizontal aquifer, when plotting the time derivative of the flux versus the flux on a log scale, the result shows that the flux derivative reaches a minimum value and that the curve can have a slope of unity as often observed. Illustration of the application of the analytical results to the Mahantango Creek data is also discussed.

Parlange and Brutsaert (1987) derived a modified Boussinesq equation to account for the capillary effect on water table dynamics in unconfined aquifers. Barry et al. (1996) solved this equation subject to a periodic boundary condition. Their solution shows significant influence of capillarity on water table fluctuations, which evolve to finite-amplitude standing waves at the high frequency limit. Here we propose a new governing equation for the water table, which considers both horizontal and vertical flows in an unsaturated zone of finite thickness. An approximate analytical solution for periodic water table fluctuations based on the new equation was derived. In agreement with previous results, the analytical solution shows that the unsaturated zone's storage capacity permits water table fluctuations to propagate more readily than predicted by the Boussinesq equation. Furthermore, the new solution reveals a capping effect of the unsaturated zone on both the amplitude and phase of the water table fluctuations as well as the water table overheight. Due to the finite thickness of the unsaturated zone, the capillary effect on water table fluctuations is modified mainly with reduced amplitude damping and phase shift.

The effect of antecedent conditions and specific rock fragment coverage on precipitation-driven soil erosion dynamics through multiple rainfall events was investigated using a pair of 6-m × 1-m flumes with 2.2% slope. Four sequential experiments – denoted E1, E2, E3 and E4, involved 2-h precipitation (rates of 28, 74, 74 and 28 mm h-1, respectively) and 22 h without rainfall – were conducted. In each experiment, one flume was bare while the other had 40% rock fragment coverage. The soil was hand-cultivated and smoothed before the first event (E1) only, and left untouched subsequently. Sediment yields at the flume exit reached steady-state conditions over time scales that increased with sediment size. Experiments were designed such that both steady and non-steady effluent sediment yields were reached at the conclusion of E1. Results from subsequent experiments showed that short-time soil erosion was dependent on whether steady-state erosion was achieved during the preceding event, although consistent steady-state effluent sediment yields were reached for each sediment size class. Steady-state erosion rates were, however, dependent on the rainfall intensity and its duration. If steady-state sediment yields were reached for a particular size class, that class’s effluent sediment yield peaked rapidly in the next rainfall event. The early peak was followed by a gradual decline to the steady-state condition. On the other hand, for size classes in which steady state was not reached at the end of the rainfall event (i.e., E1), in the following event (E2), the sediment yields for those classes increased gradually to steady state, i.e., the sharp peak was not observed. The effect of rock fragment cover (40%) on the soil surface was also found to be significant in terms of the time to reach steady state, i.e., their presence reduced the time for steady conditions to be attained. Effluent sediment yields for the bare and rock fragment-covered flumes (E1) showed steady conditions were reached for the latter, in contrast to the former. We used the Hairsine-Rose (H-R) model to simulate the experimental data as it explicitly models soil particle size classes. Experiments E1 and E2 involved soil compaction by raindrops, and in this case the model predictions were found to be unsatisfactory. However, compaction was effectively completed by the end of experiment E2, and the model provided reasonable predictions for experiments E3 and E4.

A new general method has been obtained to solve the physically-based equations describing the dynamics of sediment adjustment through time following erosion on a plane soil surface. This method is based on exploiting differences in behavior between smaller and larger sediment particles in their ability to form a protective layer by net deposition of previously eroded sediment. The utility of this approximate solution was verified by comparison with a numerical solution, for the particular case when a steady over land flow of water is the cause of the erosion.

Detailed analyses of hydrological and water quality variables are very important to study the dynamic processes in a river basin. In this study, we have further modified the Enhanced Soil and Water Assessment Tool (ESWAT) model by incorporating hourly evapotranspiration and overland flow routing modules. Results from comparison of the performances by two ESWAT versions indicate that the modified version performed better than the original model. The modified ESWAT model has reasonably reproduced observed time series runoff and most commonly collected water quality data. In addition, input data availability at required spatial and temporal resolutions is the major bottleneck in implementing many detailed hydrological models. In this paper, we have also developed a robust methodology to successfully disaggregate daily rainfall data into hourly datasets. Furthermore, we have assessed the implications of such daily rainfall disaggregation schemes on subsequent simulation of hydrological and water quality variables at river basin level. The outcomes suggest that the multivariate rainfall disaggregation scheme better reproduced observed rainfall and runoff data.

A nonlinear model for single-phase fluid flow in slightly compressible porous media is presented and solved approximately. The model assumes state equations for density, porosity, viscosity and permeability that are exponential functions of the fluid (either gas or liquid) pressure. The governing equation is transformed into a nonlinear diffusion equation. It is solved for a semi-infinite domain for either constant pressure or constant flux boundary conditions at the surface. The solutions obtained, although approximate, are extremely accurate as demonstrated by comparisons with numerical results. Predictions for the surface pressure resulting from a constant flux into a porous medium are compared with published experimental data.

Effective water resources management programs have always incorporated detailed analyses of hydrological and water quality processes in the upland watershed and downstream waterbody. We have integrated two powerful hydrological and water quality models (SWAT and CE-QUAL-W2) to simulate the combined processes of water quantity and quality both in the upland watershed and downstream waterbody. Whereas the SWAT model outputs water quality variables in its entirety, the CE-QUAL-W2 model requires inputs in various pools of organic matter contents. An intermediate program was developed to extract outputs from SWAT at required subbasin and reach outlets and converts them into acceptable CE-QUAL-W2 inputs. The CE-QUAL-W2 model was later calibrated for various hydrodynamic and water quality simulations in the Cedar Creek Reservoir, TX, USA. The results indicate that the two models are compatible and can be used to assess and manage water resources in complex watersheds comprised of upland watershed and downstream waterbodies.

An existing capillarity correction for free surface groundwater flow as modelled by the Boussinesq equation is re-investigated. Existing solutions, based on the shallow flow expansion, have considered only the zeroth-order approximation. Here, a second-order capillarity correction to tide-induced watertable fluctuations in a coastal aquifer adjacent to a sloping beach is derived. A new definition of the capillarity correction is proposed for small capillary fringes, and a simplified solution is derived. Comparisons of the two models show that the simplified model can be used in most cases. The significant effects of higher-order capillarity corrections on tidal fluctuations in a sloping beach are also demonstrated.

Over the past decade there have been a variety of exact solutions developed for one-dimensional two-phase flow, however when higher dimensions are considered there is a distinct scarcity of solutions. In this paper we consider the problem of radially symmetric two-phase flow, into an infinite medium of uniform initial saturation, subject to a constant flux V from a line source at the origin. We show that in the absence of gravity and when the two-phase diffusivity D is related to the fraction flow function f by βD = V df/dθ, where θ is the water content and β is a constant of proportionality, a new class of exact solutions can be found. In particular, when β = 2, we show that the solution is given by a simple quadrature for arbitrary D, and is fully integrable for specific functional forms of D. It has been shown by Weeks et al. [Weeks SW, Sander GC, Parlange J-Y. n-Dimensional first integral and similarity solutions for two-phase flow. ANZIAM J 2003;44:365–80] that when D obeys the above relation, a saturated zone does not grow around the line of injection, consequently we find for β = 1, the flow equation maps to one-dimensional single-phase flow under a saturated boundary condition. Consequently solutions developed for one-dimensional single-phase flow (exact or approximate) apply to radially symmetric two-phase flow. Solutions for β = 1 or 2 can be derived for either a wetting fluid displacing a non-wetting fluid, or a non-wetting fluid displacing a wetting fluid, however for arbitrary β numerical methods are required.

Applications of the axisymmetric Boussinesq equation to groundwater hydrology and reservoir engineering have long been recognised. An archetypal example is invasion by drilling fluid into a permeable bed where there is initially no such fluid present, a circumstance of some importance in the oil industry. It is well known that the governing Boussinesq model can be reduced to a nonlinear ordinary differential equation using a similarity variable, a transformation that is valid for a certain time-dependent flux at the origin. Here, a new analytical approximation is obtained for this case. The new solution,, which has a simple form, is demonstrated to be highly accurate.

The solution to the Green and Ampt infiltration equation is expressible in terms of the Lambert W−1 function. Approximations for Green and Ampt infiltration are thus derivable from approximations for the W−1 function and vice versa. An infinite family of asymptotic expansions to W−1 is presented. Although these expansions do not converge near the branch point of the W function (corresponds to Green–Ampt infiltration with immediate ponding), a method is presented for approximating W−1 that is exact at the branch point and asymptotically, with interpolation between these limits. Some existing and several new simple and compact yet robust approximations applicable to Green–Ampt infiltration and flux are presented, the most accurate of which has a maximum relative error of 5 × 10−5%. This error is orders of magnitude lower than any existing analytical approximations.

Free surface flow of groundwater in aquifers has been studied since the early 1960s. Previous investigations have been based on the Boussinesq equation, derived from the non-linear kinematic boundary condition. In fact, the Boussinesq equation is the zeroth-order equation in the shallow-water expansion. A key assumption in this expansion is that the mean thickness of the aquifer is small compared with a reference length, normally taken to be the linear decay length. In this study, we re-examine the expansion scheme for free surface groundwater flows, and propose a new expansion wherein the shallow-water assumption is replaced by a steepness assumption. A comparison with experimental data shows that the new model provides a better prediction of water table levels than the conventional shallow-water expansion. The applicable ranges of the two expansions are exhibited.

A simple modeling and laboratory investigation was carried out to investigate the raindrop effects on both sediment detachment and chemical transport from soil–water into runoff. Solute movement between soil–water and runoff is usually modeled as either a mixing model or as a diffusion-like process, both of which ignore the important roles of raindrop impact on the transport process. We hypothesized a process-based chemical transport model that incorporated both rain-drop induced mixing and diffusion and tested it using a small-scale experiment in which simulated rainfall fell on soil, pre-saturated with chloride (Cl K ) laden water. We simultaneously observed sediment and Cl K runoff concentrations trends and the evolution of the ‘shield’ layer composed of relatively heavy particles that resettle after each raindrop-impact. Using recently published and directly measured parameters, the model results generally agreed very well with measured concentrations. The exception was for the early (!5 min) Cl K transport, which was faster than the model predicted, suggesting that an additional process needs to be added to our model. Even with this deficiency, the model developed here described our experimental results better than popular ‘mixing-layer’ and ‘diffusion’ models. This study provides a new approach to chemical transport modeling by linking the rain-controlled processes with similar soil erosion processes. q 2004 Elsevier B.V. All rights reserved.

Image calibration is central to extending the capabilities of neutron radiography beyond mere visualization. However, the effects of scattered neutrons and variations in background image intensity adversely affect quantitative radiography. We describe the calibration of a real-time neutron radiography system that limits these effects and which is applicable to systems with variable digitizer gain and offset. A neutron image intensifier tube coupled to a vidicon camera with a capture rate of 30 frames/s was used. The system could account for 10 ml of water entering the field of view to within 2% and could measure the variation in thickness of a graphite wedge to within 2.3%. The spatial resolution was 450 /spl mu/m for a field of view of 410 cm/sup 2/. The image persistence half life was /spl sim/0.3 s and the system was functional for quantitative radiography with neutron fluxes above /spl sim/5*10/sup 5/n/cm/sup 2//s.

Capillary rise in porous media is frequently modeled using the Washburn equation. Recent accurate measurements of advancing fronts clearly illustrate its failure to describe the phenomenon in the long term. The observed underprediction of the position of the front is due to the neglect of dynamic saturation gradients implicit in the formulation of the Washburn equation. We consider an approximate solution of the governing macroscopic equation, which retains these gradients, and derive new analytical formulae for the position of the advancing front, its speed of propagation, and the cumulative uptake. The new solution properly describes the capillary rise in the long term, while the Washburn equation may be recovered as a special case.

An approximate analytical solution is obtained for a physically based model of soil erosion on a gentle slope driven by rainfall impact in which there is inflow of clear or nearly clear water to the top of the soil bed. Comparison of the approximate analytical and numerical solutions shows very good agreement, except for the first few minutes of an erosion event. The approximate analytic solution is applied using data from an illustrative experiment to explore its physical features. The importance of adequately defining the soil's settling velocity characteristic through the use of a sufficient number of sediment size classes, especially for prediction at short times, is illustrated. The temporal variation in sediment concentration, except at short times, is shown to be more significant than the spatial variation down the eroding surface. Solution of the equations allows visualization of the rate of convective transport of sediment down the eroding surface, this rate decreasing as sediment size increased due to more frequent return of such particles to the soil surface in deposition.

Dynamic changes take place in the nature of sediment eroded from bare soil at low slopes by rainfall impact when there is no inflow of water at the top of the eroding slope. This relates initially to fine soil sediment not settling back onto the soil after the rainfall impact. Coupled partial differential equations describing such dynamic changes have been solved numerically for a bed of soil, bounded at its upper end, and subject to a constant rainfall rate. This solution allows prediction of the change with time and downslope distance in the concentration and settling velocity (or size) characteristics of eroding sediment, allowing critical evaluation of the assumption of space-independent sediment characteristics made in prior approximate analytical solutions of the equations involved. Following the determination of as yet unpredictable soil-related parameters in the equations, the solution was tested by comparison with experimented data on two soils of contrasting structural stability, namely a vertosol [The Australian Soil Classification (1996)] and a aridisol. Investigations included the determination of a minimum number of sediment size classes required to adequately describe the settling velocity characteristics, based on the shape of the underlying basic settling velocity characteristic, which is used to predict the dynamics of sediment deposition. The effect on the solution of observed structural breakdown in soil aggregation due to rainfall impact was investigated, leading to more accurate predictions of the settling velocity characteristics of eroded sediment. Other sources of discrepancy between theory and observation remain to be determined.

Keywords: TRANSIENT STREAM/AQUIFER INTERACTION Note: 56(1): 113-116 Reference EFLUM-ARTICLE-2004-008doi:10.1023/B:TIPM.0000018431.90320.e3 URL: http://www.springerlink.com/content/100342/ Record created on 2005-09-08, modified on 2016-08-08

Recent research suggests that evapotranspiration (ET) rates have changed over the past 50 years; however, some studies conclude ET has increased, and others conclude that it has decreased. These studies were indirect, using long-term observations of air temperature, cloud cover, and pan evaporation as indices of potential and actual ET. This study considers the hydrological cycle more directly and uses published precipitation and stream discharge data for several large basins across the conterminous United States to show that ET rates have increased over the past 50 years. These results suggest that alternative explanations should be considered for environmental changes that previously have been interpreted in terms of decreasing large-scale ET rates.

Few methods exist for measuring rapidly changing fluid contents at the pore scale that simultaneously allow whole flow field visualization. We present a method for using real-time neutron radiography to measure rapidly changing moisture profiles in porous media. The imaging technique monitors the attenuation of a thermal neutron beam as it traverses a flow field and provides measurements every 30 ms with an image area .410 cm 2 and a spatial resolution , 0.05 cm. The technique is illustrated by measuring the variation in moisture content across a wetting front moving at constant velocity through SiO2 sand. The relative contributions of the hydraulic conductivity and diffusivity terms in Richards’ equation to the total fluid flux within the wetting front region were also measured. The diffusivity was found to rise from zero to a peak value within the wetting front region before falling off while the conductivity was found to rise monotonically. The reliability of the technique was checked via mass balance. q 2003 Elsevier B.V. All rights reserved.

The St Venant equation is used to model the steady flow of water on a low slope through a grass buffer strip represented by beds of nails of various densities. The analytical solution is obtained both for flow upstream and within the buffer strip. Solution only requires the boundary conditions far upstream to be given and no curve fitting of parameters. The sensitivity of the solution to uncertainty in the measured boundary conditions and the effect of the theoretical resistive flow equation used are explored. Differences are observed between experimental observations and the theory but these are likely to be due to the presence of turbulent waves at the surface of the flow which are not part of the model.

The theory of water movement in high shrink/swell soils has experienced consistent revision since Haines first presented the topic in 1923. Several aspects of the infiltration process in cracking soils have proven to be difficult to measure; seal/crust formation and properties, crack network patterns, preferential flow zones and contributions, and soil moisture determinations within the profile (near crack and near center of prismatic column) to name a few. Here, we used simulated rainstorms, laser measurements of surface elevation, needle-penetrometer measurements, and mass measurements of infiltrating water over a 206- and 145-d period to examine water movement and cracking patterns in a large sample box filled with a swelling clay soil. Water movement was restricted to the neighborhood of the crack zone, since the formation of a surface seal/crust prohibited infiltration into the surface of the prismatic columns of soil between cracks. Also, the location of cracks was observed to alternate between rainstorms. The alternating crack pattern led to more uniform wetting with depth as time increased and the number of rainstorms increased, thereby reducing the extent of preferential flow.

One-dimensional drying of a porous building material is modelled as a nonlinear diffusion process. The most difficult case of strong surface drying when an internal drying front is created is treated in particular. Simple analytical formulae for the drying front and moisture profiles during second stage drying are obtained when the hydraulic diffusivity is known. The analysis demonstrates the origin of the constant drying front speed observed elsewhere experimentally. Application of the formulae is illustrated for an exponential diffusivity and applied to the drying of a fired clay brick.

The absorption of fluid by unsaturated, rigid porous materials may be characterized by the sorptivity. This is a simple parameter to determine and is increasingly being used as a measure of a material's resistance to exposure to fluids (especially moisture and reactive solutes) in aggressive environments. The complete isothermal absorption process is described by a nonlinear diffusion equation, with the hydraulic diffusivity being a strongly nonlinear function of the degree of saturation of the material. This diffusivity can be estimated from the sorptivity test. In a typical test the cumulative absorption is proportional to the square root of time. However, a number of researchers have observed deviation from this behaviour when the infiltrating fluid is water and there is some potential for chemo-mechanical interaction with the material. In that case the current interpretation of the test and estimation of the hydraulic diffusivity is no longer appropriate. Kuntz and Lavallee (2001) discuss the anomalous behaviour and propose a non-Darcian model as a more appropriate physical description. We present an alternative Darcian explanation and theory that retrieves the earlier advantages of the simple sorptivity test in providing parametric information about the material's hydraulic properties and allowing simple predictive formulae for the wetting profile to be generated.

Mixed confined and unconfined groundwater flow occurs in a bounded initially dry aquifer when the hydraulic head at the side boundary suddenly rises above the elevation of the aquifer's top boundary. The flow problem as modelled by the Boussinesq equation is non-trivial because of the involvement of two moving boundaries. The transformed equation (based on a similarity transformation) can, however, be dealt with more easily. Here, we present an approximate analytical solution for this flow problem. The approximate solution is compared with an 'exact' numerical solution and found to be a very accurate description for describing the mixed confined and unconfined flow in the confined aquifer. (C) 2002 Elsevier Science B.V. All rights reserved.

This paper considers similarity solutions of the multi-dimensional transport equation for the unsteady flow of two viscous incompressible fluids. We show that in plane, cylindrical and spherical geometries, the flow equation can be reduced to a weakly-coupled system of two first-order nonlinear ordinary differential equations. This occurs when the two phase diffusivity D(θ) satisfies (D/D′)′ = 1/α and the fractional flow function f (θ) satisfies df/dθ = kDn/2, where n is a geometry index (1, 2 or 3), α and k are constants and primes denote differentiation with respect to the water content θ. Solutions are obtained for time dependent flux boundary conditions. Unlike single-phase flow, for two-phase flow with n = 2 or 3, a saturated zone around the injection point will only occur provided the two conditions and f′(1) ≠ 0 are satisfied. The latter condition is important due to the prevalence of functional forms of f (θ) in oil/water flow literature having the property f′(1) = 0.

Motion of a single fluid sphere is described by two theories, each characterized by different levels of Hill's vortex circulation within the sphere. An existing experimental data set giving measurements of vertical velocity along the major axis of the sphere is re-examined. Contrary to published discussions of that experiment, we find that the theory of Parlange agrees better with the laboratory data than that of Harper & Moore. This agreement supports the key difference between the two theories, i.e. that the fluid within the sphere is unlikely to have a singular (infinite) velocity as it moves upwards towards the stagnation region at the top of the sphere.

The Green and Ampt infiltration formula, as well as the Talsma and Parlange formula, are two-parameter equations that are both expressible in terms of Lambert W-functions. These representations are used to derive explicit, simple and accurate approximations for each case. The two infiltration formulas are limiting cases that can be deduced from an existing three-parameter infiltration equation, the third parameter allowing for interpolation between the limiting cases. Besides the limiting cases, there is another case for which the three-parameter infiltration equation yields an exact solution. The three- parameter equation can be solved by fixed-point iteration, a scheme which can be exploited to obtain a sequence of increasingly complex explicit infiltration equations. For routine use, a simple, explicit approximation to the three- parameter infiltration equation is derived. This approximation eliminates the need to iterate for most practical circumstances.

Geotechnical centrifuge testing is used to examine the preferential (fingered) flow of a nonaqueous phase liquid (NAPL) in a uniform dry sand. The results of nine experiments, containing a total of 87 observations of NAPL finger behavior, are analyzed. The observed finger tip velocities range from 0.01 to 0.3 cm/s, while the observed finger widths range from 0.3 to 3.6 cm. From the experimental data it is concluded that, asymptotically, the NAPL fingers are not fully saturated. For comparison, the behavior of water fingers is examined using the same experimental setup. In contrast to the NAPL fingers, and in agreement with other work reported in the literature, the water fingers are found to be fully saturated. In addition, it is confirmed that the water finger properties can be well predicted from known porous medium and fluid properties. A scaling analysis is presented that allows the NAPL finger properties to be inferred from models developed to describe water finger properties. The analysis predicts NAPL finger velocities to within 15% and NAPL finger, widths to within 50% if both finger types are assumed saturated. By adjusting the analysis to account for the fact that the NAPL fingers are not fully saturated, NAPL finger widths can be predicted within to 10%, and NAPL finger velocities to within 30%.

The interaction of the wetting front, described by the Boussinesq equation, with an impervious wall is considered using a superposition principle. A number of approximate solutions are compared with the numerical solution of the Boussinesq equation. The results show that the superposition approach provides an excellent method for obtaining an approximate solution.

Centrifuge experiments modeling single-phase flow in prototype porous media typically use the same porous medium and permeant. Then, well-known scaling laws are used to transfer the results to the prototype. More general scaling laws that relax these restrictions are presented. For permeants that are immiscible with an accompanying gas phase, model-prototype (i.e., centrifuge model experiment–target system) scaling is demonstrated. Scaling is shown to be feasible for Miller-similar (or geometrically similar) media. Scalings are presented for a more general class, Lisle-similar media, based on the equivalence mapping of Richards' equation onto itself. Whereas model-prototype scaling of Miller-similar media can be realized easily for arbitrary boundary conditions, Lisle-similarity in a finite length medium generally, but not always, involves a mapping to a moving boundary problem. An exception occurs for redistribution in Lisle- similar porous media, which is shown to map to spatially fixed boundary conditions. Complete model-prototype scalings for this example are derived.

Most three-phase flow models lack rigorous validation because very few methods exist that can measure transient fluid contents of the order of seconds of whole flow fields. The objective of this study was to develop a method by which fluid content can be measured rapidly in three-phase systems. The method uses the hue and intensity of light transmitted through a slab chamber to measure fluid contents. The water is colored blue with CuSO4. The light transmitted by high-frequency light bulbs is recorded with a color video camera in red, green, and blue and then converted to hue, saturation, and intensity. Calibration of hue and intensity with water, oil, and air is made using cells filled with different combinations of the three fluids. The results show that hue and water content are uniquely related over a large range of fluid contents. Total liquid content is a function of both hue and light intensity. The air content is obtained by subtracting the liquid content from the porosity. The method was tested with static and transient experiments. Measurements made with the light transmission method (LTM) and synchrotron X rays of the static experiment agreed well. In the transient experiments, fingers were formed by dripping water on the surface in a two-dimensional slab chamber with partially oil-saturated sand. The LTM is able to capture the spatial resolution of the fluid contents and can provide new insights in rapidly changing, three-phase flow systems.

A simple experiment was used to test the development of a “shield” over the original soil and associated changes in sediment concentrations as described in the mechanistic Rose erosion model. The Rose model, developed for rain-induced erosion and sediment transport on hillslopes (J. Hydrol., 217 (1999) 149; Trends Hydrol., 1 (1994) 443), was applied to a simple experimental set-up, consisting of a small horizontal soil surface (7×7 cm2) under constant shallow (5 mm) overland flow with raindrop impact. The soil consisted of two particle size classes, clay and sand, greatly simplifying the analytical solution of the Rose model by reducing the unknown system parameters to one, the soil detachability. Photographic documentation of shield formation corroborated the conceptual validity of the Rose model. Using a single, best-fit value for the soil detachability, quantitative agreement between modeled and experimental results is excellent (R2=0.9). This research provides lucidity to the primary processes enveloped in the Rose model and these mechanisms can be extrapolated to more complicated or realistic systems in which the individual processes may be more difficult to recognize.

The Parlange hysteresis model is reformulated as a pair of recurrence relations to provide relationships between wetting and drying phases to any order. The model is applied to the classical van Genuchten model for soil water retention used as the main wetting curve. The nonphysical behaviour of these retention curves is related to the existence of a point of inflection in the van Genuchten model when it is used for the wetting boundary. Where the van Genuchten form is used as the main drying curve, the Parlange hysteresis model provides an ordinary differential equation describing the main wetting curve. A number of simple analytical solutions, relating to particular values of the parameters of the van Genuchten model, then provide forms for the main wetting curve. In general, a numerical integration is required to generate the main wetting curve, for general values of the parameters of the van Genuchten model. The recurrence relations for the hysteresis cycling are still applicable, even when the main wetting curve is only known numerically. The new main wetting curves do not have inflection points and there is no nonphysical behaviour. The model is then applied to the experimental data of Viaene et al. (1994)

A recent method based on a specific power-law relationship between the matric potential head and the Boltzmann variable was presented by Prevedello et. al. (2008). Here, this relationship was generalized to a range of powers, and the solution extended to include the saturated zone. As a result, the new solution satisfies the Bruce and Klute equation exactly.

The mechanistic Rose model for rain-induced erosion and sediment transport on hillslopes was tested for a simple experimental study, consisting of a small horizontal soil surface under constant shallow overland flow with raindrop impact. The soil consisted of two particle size classes, clay and sand, greatly simplifying the analytical solution of the Rose model reducing the unknown system parameters to one, the soil detachability. Photographic documentation of shield formation corroborated the conceptual validity of the Rose model and illustrated very clearly the primary processes involved.

Modeling solutes under field conditions is cumbersome due to presence of preferential flow paths and the input data needed to describe these paths. We propose a simple equation that can predict the breakthrough of solutes without excessive data requirements. Conceptually the soil is divided in a distribution layer and a conveyance zone. The distribution zone act as a linear reservoir resulting in an exponential loss of solutes from this zone. In the conveyance zone the transport of solutes is described with the convective dispersive equation. Input data required are apparent water content of the distribution zone and solute velocity and dispersion in the conveyance zone. The model with these three parameters was able to describe the breakthrough of solutes through undisturbed columns.

Tidal water table fluctuations in a coastal aquifer are driven by tides on a moving boundary that varies with the beach slope. One-dimensional models based on the Boussinesq equation are often used to analyse tidal signals in coastal aquifers. The moving boundary condition hinders analytical solutions to even the linearised Boussinesq equation. This paper presents a new perturbation approach to the problem that maintains the simplicity of the linearised one-dimensional Boussinesq model. Our method involves transforming the Boussinesq equation to an ADE (advection-diffusion equation) with an oscillating velocity. The perturbation method is applied to the propagation of spring-neap tides (a bichromatic tidal system with the fundamental frequencies wt and wt) in the aquifer. The results demonstrate analytically, for the first time, that the moving boundary induces interactions between the two primary tidal oscillations, generating a slowly damped water table fluctuation of frequency omega(1) - omega(2), i.e., the spring-neap tidal water table fluctuation. The analytical predictions are found to be consistent with recently published field observations. (C) 2000 Elsevier Science Ltd. All rights reserved.

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

A method for developing wetting front profiles for the one-dimensional Richards' equation is given. The method is obtained by simplifying and extending a recent approximate solution and brings together features from several different studies. Difficulties associated with profile development are discussed by applying the method to several examples, providing a deeper understanding of the solutions of Richards' equation. For simplicity, we illustrate the improvements for soil-water diffusivities and conductivities which have a power law dependence on the water content although they should apply in general, and the appropriate generalization is given in the conclusion.

Similarity transforms of the Boussinesq equation in a semi-infinite medium are available when the boundary conditions are a power of time. The Boussinesq equation is reduced from a partial diAerential equation to a boundary-value problem. Chen et al. [Trans Porous Media 1995;18:15‐36] use a hodograph method to derive an integral equation formulation of the new diAerential equation which they solve by numerical iteration. In the present paper, the convergence of their scheme is improved such that numerical iteration can be avoided for all practical purposes. However, a simpler analytical approach is also presented which is based on Shampine’s transformation of the boundary value problem to an initial value problem. This analytical approximation is remarkably simple and yet more accurate than the analytical hodograph approximations. ” 2000 Elsevier Science Ltd. All rights reserved.

Laboratory experiments related to gravity-driven unstable flows in water repellent porous media contained in two-dimensional chambers have been reported [Bauters, T.W.J., DiCarlo, D.A., Steenhuis, T.S., Parlange, J.-Y., 1998. Preferential flow in water-repellent sands. Soil Sci. Soc. Am. J. 62, 1185–1190]. These experiments demonstrate that water repellency has a significant impact on the stability of flow. As a follow up to these experiments, numerical solutions of the Richards equation for a two-dimensional domain are derived to examine the effect of water repellency on flow characteristics. Of particular interest is the development of gravity-driven unstable flow conditions caused by water repellency. The degree of water repellency of the porous medium is manifested in the water saturation—capillary pressure and water saturation—hydraulic conductivity relationships for the porous medium. To derive the numerical solutions, parameters closely representing the flow domain boundary conditions and the porous medium properties in the experiments of Bauters et al., were employed. In this paper we present the results of simulations for two cases: a water wettable sand and an extremely water repellent sand. The numerical solution for the water wettable sand led to a stable flow condition, while for the water-repellent sand the flow was unstable as manifested by the development of a single finger of flow. A new feature of these modeling results, in comparison to previous modeling results for gravity-driven unstable flow, is that the water pressure inside the finger core is positive. In testing the numerical solutions we compared the solution results to the laboratory results in terms of flow patterns, water pressure at a single reference point, and wetting front velocity. The degree of agreement between the laboratory results and the numerical solutions in terms of these measures is quite good.

The initial soil water content affects wetting front instability. A series of experiments were conducted where water was infiltrated into a 20/30 sand with initial volumetric water contents of 0, 0.005, 0.01, 0.015, 0.02, 0.03, 0.04 and 0.047 cm3/cm3. Both water content and matric potential were measured. Water content was measured with Synchrotron X-rays at the Cornell High Energy Synchrotron Source (CHESS) and matric potential with fast responding tensiometers. The flow field changed gradually from unstable fingered flow at 0% initial water content to a wetting pattern that can be described with Richards’ equation without hysteresis. For unstable flow, the matric potential and water content decreased a short distance behind the wetting front. Except in the initially dry soil, the finger pattern began to widen immediately after infiltration. The pressure and water content of the wetting front were hyperbolically related to the initial water content. In general, this research showed that in coarse soils when an unstable wetting front occurs both the matric potential and water content drop behind the wetting front while, when a stable Richards’ type wetting front forms, the matric potential and water content increase (slightly) behind the wetting front.

Artificial capillary barriers are being used to divert water away from sensitive underground regions. Conversely, funneled flow over natural capillary barriers may increase the danger of groundwater contamination by decreasing the travel time and contact area. There have been relatively few experimental studies of capillary barrier flow patterns. In this study, water was applied uniformly across the top surface of a backlit tilting chamber, 1 cm thick, 110 cm high, and 180 cm long, in which a coarse sand layer was imbedded in a fine sand. Bedding slope and water application rates were varied between 0° and 12° and 1 and 3 cm h−1, respectively. After attaining steady state, matric potential was measured along the textural interface, and photos of dye traces were taken in order to visualize streamlines. The funneled flow was characterized by three discrete regions: an initial capillary diversion, a breakthrough region, and a toe diversion. The breakthrough region consisted of a significant zone of partial breakthrough where the vertical flux into the coarse layer was less than the water application rate. The lateral distance of the capillary diversion was explained well by previously published relationships when the water entry value at the textural interface was replaced by lower, observed matric potential at which breakthrough occurred at the most upslope point. The length of the capillary diversion was overpredicted using the air entry value. Finally, the toe of the coarse layer had significant, observed effects on funneled flow patterns, which have previously received little, if any, attention. The results of this study imply that the slope of the coarse layer and infiltration rate will largely govern the effectiveness of capillary barriers and that capillary barriers are less effective than previously assumed.

A partial analysis of the stream-aquifer interaction problem at steady state for a semi-infinite unconfined aquifer was presented by Bear (1979). This analysis was restricted to the case of influent boundary condition where the water flux is directed from the boundary into the aquifer. Here, we extend the analysis to provide analytical solutions for both influent and effluent conditions. Comparisons with numerical solutions are also presented for further validation.

In this note, we provide an analytical approximation to the exponential integral valid for all values of its argument. The approximation is constructed by interpolation between the exponential integral's small and large asymptotes. The interpolation contains an unknown function, which is determined using the minimax criterion. The maximum error in the approximation is less than 0.07%, making it useful for routine hydrological applications.