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.     

Testing a conceptual hillslope recession model based on the storage–discharge relationship with the Richards equation

The conceptual recession model based on the storage–discharge relationship was proposed to account for the unsaturated–saturated water storage interaction. The recession model was formulated by combining the constitutive storage–discharge relationship with the integral balance equation for unsaturated and saturated water storage. The functional form of the constitutive storage–discharge relationship was determined from the spatial integration of the Richards equation. The performance of the recession model was tested by comparing with the solution of the Richards equation for different simulation geometric shapes and soil types. The conceptual recession model incorporating the unsaturated–saturated water storage interaction was in good agreement with the recession response of the Richards equation. However, the recession model that neglected the unsaturated–saturated water storage interaction was comparable to the Richards equation only for soils with the weak interaction between unsaturated water storage and saturated water storage. This result suggests the important role of the unsaturated–saturated water storage interaction in the formulation of the recession process when the derivative of the functional relationship between the unsaturated water storage and saturated water storage becomes significant. Copyright © 2007 John Wiley & Sons, Ltd.     

非饱和土的固结与水力特性研究

采用平均土骨架应力代替Bishop的非饱和土的有效应力,基于分析体积变形连续性条件建立了简化的一维非饱和土固结方程,分析计算了非饱和土在固结过程中孔隙压力、平均土骨架应力、饱和度的变化情况。同时建立了耦合水力特性的非饱和土本构模型和屈服方程。算例计算结果表明本文提出的非饱和土简化固结理论和耦合水力特性的非饱和土应力应变本构模型的有效性。     

Water percolation process studies in a Mediterranean karst area

To investigate processes of water percolation, the drip response of stalactites in a karstic cave below a 143 m² sprinkling plot was measured. The experiment was conducted in Mount Carmel, Israel, at the end of the dry season and intended to simulate a series of two high‐intensity storms on dry and wet soils. In addition to hydrometric measurements (soil moisture, surface runoff, stalactite dripping rates), two types of tracers (electrical conductivity and bromide) were used to study recharge processes, water origin and mixing inside a 28‐m vadose zone. Results suggested that slow, continuous percolation through the rock matrix is of minor importance and that percolating water follows a complicated pattern including vertical and horizontal flow directions. While bromide tracing allowed identification of quick direct flow paths at all drips with maximum flow velocities of 4·3 m/h, mixing analysis suggested that major water fractions were mobilized by piston flow, pushing out water stored in the unsaturated zone above the cave. Under dry preconditions, 80 mm of artificial rainfall applied in less than 7 h was not enough to initiate significant downward water percolation. Most water was required to fill uppermost soil and rock storages. Under wet preconditions during the second day sprinkling, higher water contents in soils and karst cavities facilitated piston flow effects and a more intense response of the cave drips. Results indicate that in Mediterranean karst regions, filling of the unsaturated zone, including soil and rock storages, is an important precondition for the onset of significant water percolation and recharge. This results in a higher seasonal threshold for water percolation than for the generation of surface runoff. Copyright © 2010 John Wiley & Sons, Ltd.     

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     

A new saturated/unsaturated model for stormwater infiltration systems

Infiltration systems are widely used as an effective urban stormwater control measure. Most design methods and models roughly approximate the complex physical flow processes in these systems using empirical equations and fixed infiltration rates to calculate emptying times from full. Sophisticated variably saturated flow models are available, but rarely applied owing to their complexity. This paper describes the development and testing of an integrated one‐dimensional model of flow through the porous storage of a typical infiltration system and surrounding soils. The model accounts for the depth in the storage, surrounding soil moisture conditions and the interaction between the storage and surrounding soil. It is a front‐tracking model that innovatively combines a soil‐moisture‐based solution of Richard's equation for unsaturated flow with piston flow through a saturated zone as well as a reservoir equation for flow through a porous storage. This allows the use of a simple non‐iterative numerical solution that can handle ponded infiltration into dry soils. The model is more rigorous than approximate stormwater infiltration system models and could therefore be valuable in everyday practice. A range of test cases commonly used to test soil water flow models for infiltration in unsaturated conditions, drainage from saturation and infiltration under ponded conditions were used to test the model along with an experiment with variable depth in a porous storage over saturated conditions. Results show that the model produces a good fit to the observed data, analytical solutions and Hydrus. Copyright © 2008 John Wiley & Sons, Ltd.     

Estimation of water saturation dependence of dispersion in unsaturated porous media: experiments and modelling analysis

In the dispersion theory, a linear relationship has been verified between the coefficient of hydrodynamic dispersion and water velocity, both in saturated and in unsaturated porous media. But for unsaturated soils the variability of flow directions and microscopic velocities can be larger than in saturated soils because of the lower degree of water saturation. This leads to an increased dispersion. Therefore, relationships between water content and relative water velocity fluctuations and water content together with the coefficient of dispersivity in unsaturated porous media respectively have been investigated systematically by displacement experiments in glass beads and coarse-textured sandy soil columns. The breakthrough curves (BTCs) of chloride showed that an increase of solute mixing with a decrease of water content was caused by an increase of flow velocity fluctuations for different pathways. In order to explain the observed tailing effect in unsaturated flow, two mathematical models were used to fit theoretically derived nonlinear functions of water content dependent dispersivities for both porous media. The close agreement between the observed and computed results suggests that the theoretical model of hydrodynamic dispersion can be extended to transport in unsaturated porous media, providing that BTCs of the effluent water are used to estimate representative dispersivity parameters of soils.     

A quasi three-dimensional model for flow and transport in unsaturated and saturated zones: 1. Implementation of the quasi two-dimensional case

A quasi three-dimensional (QUASI 3-D) model is presented for simulating the subsurface water flow and solute transport in the unsaturated and in the saturated zones of soil. The model is based on the assumptions of vertical flow in the unsaturated zone and essentially horizontal groundwater flow. The 1-D Richards equation for the unsaturated zone is coupled at the phreatic surface with the 2-D flow equation for the saturated zone. The latter was obtained by averaging 3-D flow equation in the saturated zone over the aquifer thickness. Unlike the Boussinesq equation for a leaky-phreatic aquifer, the developed model does not contain a storage term with specific yield and a source term for natural replenishment. Instead it includes a water flux term at the phreatic surface through which the Richards equation is linked with the groundwater flow equation. The vertical water flux in the saturated zone is evaluated on the basis of the fluid mass balance equation while the horizontal fluxes, in that equation, are prescribed by Darcy law. A 3-D transport equation is used to simulate the solute migration. A numerical algorithm to solve the problem for the general quasi 3-D case was developed. The developed methodology was exemplified for the quasi 2-D cross-sectional case (QUASI2D). Simulations for three synthetic problems demonstrate good agreement between the results obtained by QUASI2D and two fully 2-D flow and transport codes (SUTRA and 2DSOIL). Yet, simulations with the QUASI2D code were several times faster than those by the SUTRA and the 2DSOIL codes.     

Free surface and saturated-unsaturated analyses of borehole infiltration tests above the water table

Constant head borehole infiltration tests are widely used for the in situ evaluation of saturated hydraulic conductivities of unsaturated soils above the water table. The formulae employed in analysing the results of such tests disregard the fact that some of the infiltrating water may flow under unsaturated conditions. Instead, these formulae are based on various approximations of the classical free surface theory which treats the flow region as if it were fully saturated and enclosed within a distinct envelope, the so-called ‘free surface’. A finite element model capable of solving free surface problems is used to examine the mathematical accuracy of the borehole infiltration formulae. The results show that in the hypothetical case where unsaturated flow does not exist, the approximate formulae are reasonably accurate within·a practical range of borehole conditions. To see what happens under conditions closer to those actually encountered in the field, the effect of unsaturated flow on borehole infiltration is investigated by means of two different numerical models: a mixed explicit-implicit finite element model, and a mixed explicit-implicit integrated finite difference model. Both of these models give nearly identical results; however, the integrated finite difference model is considerably faster than the finite element model. The relatively low computational efficiency of the finite element scheme is attributed to the large number of operations required in order to re-evaluate the conductivity (stiffness) matrix at each iteration in this highly non-linear saturated-unsaturated flow problem. The saturated-unsaturated analysis demonstrates that the classical free surface approach provides a distorted picture of the flow pattern in the soil. Contrary to what one would expect on the basis of this theory, only a finite region of the soil in the immediate vicinity of the borehole is saturated, whereas a significant percentage of the flow takes place under unsaturated conditions. As a consequence of disregarding unsaturated flow, the available formulae may underestimate the saturated hydraulic conductivity of fine grained soils by a factor of two, three, or more. Our saturated-unsaturated analysis leads to an improved design of borehole infiltration tests and a more accurate method for interpreting the results of such tests. The analysis also shows how one can predict the steady state rate of infiltration from data collected during the early transient period of the test.     

A two‐dimensional model of hydraulic performance of stormwater infiltration systems

Stormwater infiltration systems are a popular method for urban stormwater control. They are often designed using an assumption of one‐dimensional saturated outflow, although this is not very accurate for many typical designs where two‐dimensional (2D) flows into unsaturated soils occur. Available 2D variably saturated flow models are not commonly used for design because of their complexity and difficulties with the required boundary conditions. A purpose‐built stormwater infiltration system model was thus developed for the simulation of 2D flow from a porous storage. The model combines a soil moisture–based model for unsaturated soils with a ponded storage model and uses a wetting front‐tracking approach for saturated flows. The model represents the main physical processes while minimizing input data requirements. The model was calibrated and validated using data from laboratory 2D stormwater infiltration trench experiments. Calibrations were undertaken using five different combinations of calibration data to examine calibration data requirements. It was found that storage water levels could be satisfactorily predicted using parameters calibrated with either data from laboratory soils tests or observed water level data, whereas the prediction of soil moistures was improved through the addition of observed soil moisture data to the calibration data set. Copyright © 2012 John Wiley & Sons, Ltd.     

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.     

An infiltration model based on flow variability in macropores: development, sensitivity analysis and applications

Simulating infiltration in soils containing macropores still provides unsatisfactory results, as existing models seem not to capture all relevant processes. Recent studies of macropore flow initiation in natural soils containing earthworm channels revealed a distinct flow rate variability in the macropores depending on the initiation process. When macropore flow was initiated at the soil surface, most of the macropores received very little water while a few macropores received a large proportion of the total inflow. In contrast, when macropore flow was initiated from a saturated or nearly saturated soil layer, macropore flow rate variation was much lower. The objective of this study was to develop, evaluate, and test a model, which combines macropore flow variability with several established approaches to model dual permeability soils. We then evaluate the INfiltration–INitiation–INteraction Model (IN³M) to explore the influence of macropore flow variability on infiltration behavior by performing a sensitivity analysis and applying IN³M to sprinkling and dye tracer experiments at three field sites with different macropore and soil matrix properties. The sensitivity analysis showed that the flow variability in macropores reduces interaction between the macropores and the surrounding soil matrix and thus increases bypass flow, especially for surface initiation of macropore flow and at higher rainfall intensities. The model application shows reasonable agreement between IN³M simulations and field data in terms of water balance, water content change, and dye patterns. The influence of macropore flow variability on the hydrological response of the soil was considerable and especially pronounced for soils where initiation occurs at the soil surface. In future, the model could be applied to explore other types of preferential flow and hence to get a generally better understanding of macropore flow.     

A process‐based transfer function approach to model tile‐drain hydrographs

Tile‐drain response to rainfall events is determined by unsaturated vertical flow to the water table, followed by horizontal saturated water movement. In this study, unsaturated vertical movement from the redistribution of water is modelled using a sharp‐front approximation, and the saturated horizontal flow is modelled by an approximate solution to the Boussinesq equation. The unsaturated flow component models the fast response that is associated with the presence of preferential flow paths. By convoluting the responses of the two components, a transfer function is developed that predicts tile‐drain response to unit amounts of infiltrated water. It is observed that the unsaturated flow component can be cast in a form that is linear in a power function of the infiltrated depth. Since the approach is process based, model parameter definitions are easily identified with soil properties at the field scale. Furthermore, it is demonstrated that the transfer function model parameters can be estimated from moment analysis. Using superposition, the transient tile‐drain response to arbitrary amounts of infiltrated water can be constructed. Comparison with data measured from the Water Quality Field Station show that this approach provides a promising method for generating tile‐drain response to rainfall events. Copyright © 2006 John Wiley & Sons, Ltd.     

Temporal variability of solute transport under vadose zone conditions

The heterogeneity of the solute flux field in the horizontal plane at the field scale has been documented in several field studies. On the other hand, little information is available on the persistence of certain solute transport scenarios over consecutive infiltration cycles. This study was initiated to analyse the recurrence of solute leaching behaviour as estimated in two soil column tests emphasizing the preferential flow phenomenon. Twenty-four small-sized soil samples were subjected to two consecutive unsaturated steady-state flow leaching experiments with bromide as tracer. Observed breakthrough curves (BTCs) were analysed by the method of moments and by the advection–dispersion equation (ADE) to classify solute behaviour. Frequency distributions of the parameters indicating the solute velocity were heavily skewed or bimodal, reflecting the broad variability of the leaching scenarios, including some with pronounced preferential solute breakthrough. Exclusion of the preferential flow columns from our calculations revealed an average amount of 37% of immobile water. The large-scale BTCs derived from assembling the individual concentration courses of each run showed similar features, such as an early bromide breakthrough. However, two distinct apices, viz. one preferential and one matrix, were observed only in the first run, whereas the concentration decrease between the peaks was missing from the second run. A change in soil structure with continuous leaching was presumed to modify the interplay of the various flow domains, thereby altering the spreading of the BTCs. Correlation analysis between parameters of both tests suggests that preferential transport conditions are likely to occur at the same locations in the field over several infiltration cycles, whereas the ‘classical’ or expected matrix flow is time variant and therefore seems to be hardly predictable. © 1998 John Wiley & Sons, Ltd.     

Lateral water flux in the unsaturated zone: A mechanism for the formation of spatial soil heterogeneity in a headwater catchment

Measurements of soil water potential and water table fluctuations suggest that morphologically distinct soils in a headwater catchment at the Hubbard Brook Experimental Forest in New Hampshire formed as a result of variations in saturated and unsaturated hydrologic fluxes in the mineral soil. Previous work showed that each group of these soils had distinct water table fluctuations in response to precipitation; however, observed variations in soil morphology also occurred above the maximum height of observed saturation. Variations in unsaturated fluxes have been hypothesized to explain differences in soil horizon thickness and presence/absence of specific horizons but have not been explicitly investigated. We examined tensiometer and shallow groundwater well records to identify differences in unsaturated water fluxes among podzols that show distinct morphological and chemical differences. The lack of vertical hydraulic gradients at the study sites suggests that lateral unsaturated flow occurs in several of the soil units. We propose that the variations in soil horizon thickness and presence/absence observed at the site are due in part to slope‐parallel water flux in the unsaturated portion of the solum. In addition, unsaturated flow may be involved in the translocation of spodic material that primes those areas to contribute water with distinct chemistry to the stream network and represents a potential source/sink of organometallic compounds in the landscape.     

Using bromide data tracer and HYDRUS-1D to estimate groundwater recharge and evapotranspiration under film-mulched drip irrigation in an arid Inland Basin,Northwest China

Accurate estimation of groundwater recharge (GR) and evapotranspiration (ET) are essential for sustainable management of groundwater resources, especially in arid and semi-arid regions. In the Manas River Basin (MRB), water shortage is the main factor restricting sustainable development of irrigated agriculture, which relies heavily on groundwater. Film-mulched drip irrigation significantly changes the pattern and dominant processes of water flow in the unsaturated zone, which increases the difficulty of GR and ET estimation. To better estimate GR and ET under film-mulched drip irrigation in the MRB, bromide tracer tests and soil lithologic investigation were conducted at 12 representative sites. A one-dimensional variably saturated flow model (HYDRUS-1D) was calibrated at each site using soil evaporation data inferred from the bromide tracer tests. The results showed that average annual soil evaporation in uncultivated lands calculated from bromide trace tests was 25.55 mm. The annual GR ranged from 5.5 to 37.0 mm under film-mulched drip irrigation. The annual ET ranged from 507.0 to 747.1 mm, with soil evaporation between 35.7 and 117.0 mm and transpiration between 460.9 and 642.3 mm. Soil evaporation represented 7% to 16% of the total ET and more than 70% of precipitation and irrigation water was used by cotton plants. Spatial variations of soil lithology, water table depth and initial soil water content led to the spatial differences of GR and ET in the MRB. Our study indicated that bromide tracer tests are useful for inferring ET in the arid and semi-arid oases. The combination of bromide tracer tests and HYDRUS-1D enhances reliability for estimation of GR and ET under film-mulched drip irrigation in the MRB and shows promise for other similar arid inland basins around the world.     

Finite-element analysis of the transport of water and solutes in title-drained soils

The finite-element method based on a Galerkin technique was used to formulate the problem of simulating the two-dimensional (cross-sectional) transient movement of water and solute in saturated or partially saturated nonuniform porous media. The numerical model utilizes linear triangular elements. Nonreactive, as well as reactive solutes whose behaviour can be described by a distribution coefficient or first-order reaction term were considered. The flow portion of the model was tested by comparison of the model results with experimental and finite-difference results for transient flow in an unsaturated sand column and the solute transport portion of the model was tested by comparison with analytical solution results. The model was applied to a hypothetical case involving movement of water and solutes in tile-drained soils. The simulation results showed the development of distinct solute leaching patterns in the soil as drainage proceeded. Although applied to a tile drainage problem in this study, the model should be equally useful in the study of a wide range of two-dimensional water and solute migration problems.