Impact of land use on the hydraulic properties of the topsoil in a small French catchment

The hydraulic properties of the topsoil control the partition of rainfall into infiltration and runoff at the soil surface. They must be characterized for distributed hydrological modelling. This study presents the results of a field campaign documenting topsoil hydraulic properties in a small French suburban catchment (7 km²) located near Lyon, France. Two types of infiltration tests were performed: single ring infiltration tests under positive head and tension‐disk infiltration using a mini‐disk. Both categories were processed using the BEST—Beerkan Estimation of Soil Transfer parameters—method to derive parameters describing the retention and hydraulic conductivity curves. Dry bulk density and particle size data were also sampled. Almost all the topsoils were found to belong to the sandy loam soil class. No significant differences in hydraulic properties were found in terms of pedologic units, but the results showed a high impact of land use on these properties. The lowest dry bulk density values were obtained in forested soils with the highest organic matter content. Permanent pasture soils showed intermediate values, whereas the highest values were encountered in cultivated lands. For saturated hydraulic conductivity, the highest values were found in broad‐leaved forests and small woods. The complementary use of tension‐disk and positive head infiltration tests highlighted a sharp increase of hydraulic conductivity between near saturation and saturated conditions, attributed to macroporosity effect. The ratio of median saturated hydraulic conductivity to median hydraulic conductivity at a pressure of − 20 mm of water was about 50. The study suggests that soil texture, such as used in most pedo‐transfer functions, might not be sufficient to properly map the variability of soil hydraulic properties. Land use information should be considered in the parameterizations of topsoil within hydrological models to better represent in situ conditions, as illustrated in the paper. Copyright © 2010 John Wiley & Sons, Ltd.     

The exponential decline in saturated hydraulic conductivity with depth: a novel method for exploring its effect on water flow paths and transit time distribution

The strong vertical gradient in soil and subsoil saturated hydraulic conductivity is characteristic feature of the hydrology of catchments. Despite the potential importance of these strong gradients, they have proven difficult to model using robust physically based schemes. This has hampered the testing of hypotheses about the implications of such vertical gradients for subsurface flow paths, residence times and transit time distribution. Here we present a general semi‐analytical solution for the simulation of 2D steady‐state saturated‐unsaturated flow in hillslopes with saturated hydraulic conductivity that declines exponentially with depth. The grid‐free solution satisfies mass balance exactly over the entire saturated and unsaturated zones. The new method provides continuous solutions for head, flow and velocity in both saturated and unsaturated zones without any interpolation process as is common in discrete numerical schemes. This solution efficiently generates flow pathlines and transit time distributions in hillslopes with the assumption of depth‐varying saturated hydraulic conductivity. The model outputs reveal the pronounced effect that changing the strength of the exponential decline in saturated hydraulic conductivity has on the flow pathlines, residence time and transit time distribution. This new steady‐state model may be useful to others for posing hypotheses about how different depth functions for hydraulic conductivity influence catchment hydrological response. Copyright © 2016 John Wiley & Sons, Ltd.     

Stochastic analysis of bounded unsaturated flow in heterogeneous aquifers: Spectral/perturbation approach

This paper describes a stochastic analysis of steady state flow in a bounded, partially saturated heterogeneous porous medium subject to distributed infiltration. The presence of boundary conditions leads to non-uniformity in the mean unsaturated flow, which in turn causes non-stationarity in the statistics of velocity fields. Motivated by this, our aim is to investigate the impact of boundary conditions on the behavior of field-scale unsaturated flow. Within the framework of spectral theory based on Fourier–Stieltjes representations for the perturbed quantities, the general expressions for the pressure head variance, variance of log unsaturated hydraulic conductivity and variance of the specific discharge are presented in the wave number domain. Closed-form expressions are developed for the simplified case of statistical isotropy of the log hydraulic conductivity field with a constant soil pore-size distribution parameter. These expressions allow us to investigate the impact of the boundary conditions, namely the vertical infiltration from the soil surface and a prescribed pressure head at a certain depth below the soil surface. It is found that the boundary conditions are critical in predicting uncertainty in bounded unsaturated flow. Our analytical expression for the pressure head variance in a one-dimensional, heterogeneous flow domain, developed using a nonstationary spectral representation approach [Li S-G, McLaughlin D. A nonstationary spectral method for solving stochastic groundwater problems: unconditional analysis. Water Resour Res 1991;27(7):1589–605; Li S-G, McLaughlin D. Using the nonstationary spectral method to analyze flow through heterogeneous trending media. Water Resour Res 1995; 31(3):541–51], is precisely equivalent to the published result of Lu et al. [Lu Z, Zhang D. Analytical solutions to steady state unsaturated flow in layered, randomly heterogeneous soils via Kirchhoff transformation. Adv Water Resour 2004;27:775–84].     

Local‐ and field‐scale infiltration into vertically non‐uniform soils with spatially‐variable surface hydraulic conductivities

We studied the problem of local‐ and field‐scale infiltration over a particular class of heterogeneous soils. At the local scale, the soils are described as being vertically non‐uniform, with the saturated hydraulic conductivity continuously decreasing with depth according to a power law function. Analogous to the Green–Ampt model, analytical expressions are first developed for local‐scale infiltration using a sharp front approximation, and model results are compared with numerical solutions of the Richards equation. These results show that saturation does not occur from below in soils with such vertical non‐uniformity, thereby allowing for the use of a sharp front approximation. Because of vertical non‐uniformity, ponding conditions are achieved locally even for rainfall rates less than the surface saturated hydraulic conductivity. Furthermore, infiltration rates asymptotically approach zero at long times. To determine field‐scale infiltration properties, the spatial variability in the surface saturated hydraulic conductivity is represented by a log‐normal random field. Using cumulative infiltration as the independent variable, expressions are developed for the ensemble mean of field‐scale infiltration and the expected time for a given depth of water to infiltrate over the field. Surface horizontal heterogeneity is found to control field‐scale infiltration at small times, whereas local vertical non‐uniformity exerts a strong control at long times. Copyright © 2011 John Wiley & Sons, Ltd.     

Inverse upscaling of hydraulic parameters during constant flux infiltration using borehole radar

Modeling unsaturated flow in porous media requires constitutive relations that describe the soil water retention and soil hydraulic conductivity as a function of either potential or water content. Often, the hydraulic parameters that describe these relations are directly measured on small soil cores, and many cores are needed to upscale to the entire heterogeneous flow field. An alternative to the forward upscaling method using small samples are inverse upscaling methods that incorporate soft data from geophysical measurements observed directly on the larger flow field. In this paper, we demonstrate that the hydraulic parameters can be obtained from cross borehole ground penetrating radar by measuring the first arrival travel time of electromagnetic waves (represented by raypaths) from stationary antennae during a constant flux infiltration experiment. The formulation and coupling of the hydrological and geophysical models rely on a constant velocity wetting front that causes critical refraction at the edge of the front as it passes by the antennae. During this critical refraction period, the slope of the first arrival data can be used to calculate (1) the wetting velocity and (2) the hydraulic conductivity of the wet (or saturated) soil. If the soil is undersaturated during infiltration, then an estimate of the saturated water content is needed before calculating the saturated hydraulic conductivity. The hydraulic conductivity value is then used in a nonlinear global optimization scheme to estimate the remaining two parameters of a Broadbridge and White soil.     

Vadose Zone Characterization of Low-Permeability Sediments Using Field Permeameters

Measurement of the saturated hydraulic conductivity of material in the unsaturated zone beneath proposed surface impoundments is important for predicting seepage rates of water and contaminants. Hazardous waste disposal facilities are commonly sited on the basis of the low permeability of the geologic materials beneath the site. Field measurement of the saturated hydraulic conductivity of low-permeability materials may be accomplished using air-entry permeameters and borehole permeameters. The results of a coordinated field and laboratory investigation of low-permeability materials at a hazardous waste facility are presented. The different methods of testing and analysis are compared and discussed. In general, air-entry permeameters and borehole permeameters are useful for measuring the saturated hydraulic conductivity of low-permeability materials.     

A geostatistically based inverse model for three-dimensional variably saturated flow

We present a geostatistically based inverse model for characterizing heterogeneity in parameters of unsaturated hydraulic conductivity for three-dimensional flow. Pressure and moisture content are related to perturbations in hydraulic parameters through cross-covariances, which are calculated to first-order. Sensitivities needed for covariance calculations are derived using the adjoint state sensitivity method. Approximations of the conditional mean parameter fields are then obtained from the cokriging estimator. Correlation between parameters and pressure – moisture content perturbations is seen to be strongly dependent on mean pressure or moisture content. High correlation between parameters and pressure data was obtained under saturated or near saturated flow conditions, providing accurate estimation of saturated hydraulic conductivity, while moisture content measurements provided accurate estimation of the pore size distribution parameter under unsaturated flow conditions.     

A geostatistically based inverse model for three-dimensional variably saturated flow

We present a geostatistically based inverse model for characterizing heterogeneity in parameters of unsaturated hydraulic conductivity for three-dimensional flow. Pressure and moisture content are related to perturbations in hydraulic parameters through cross-covariances, which are calculated to first-order. Sensitivities needed for covariance calculations are derived using the adjoint state sensitivity method. Approximations of the conditional mean parameter fields are then obtained from the cokriging estimator. Correlation between parameters and pressure – moisture content perturbations is seen to be strongly dependent on mean pressure or moisture content. High correlation between parameters and pressure data was obtained under saturated or near saturated flow conditions, providing accurate estimation of saturated hydraulic conductivity, while moisture content measurements provided accurate estimation of the pore size distribution parameter under unsaturated flow conditions.     

Infiltration model in sloping layered soils and guidelines for model parameter estimation

A Green-Ampt type model for sloping layered soils (GASLS) was developed to investigate infiltration processes. We introduced a factor c, which is the same for all layers and represents the ratio of effective hydraulic conductivity over saturated hydraulic conductivity. Guidelines to estimate the factor c were established based on 234 scenarios under various conditions. The model with the estimated factor c can describe infiltration processes better than that with c = 1. For fine soils, or layered formations with finer soils on the top, c is smaller than 1. The factor c for coarse soils, or layer formations with coarse soils on the top is close to 1. Comparison with laboratory experiments on a sloping surface indicated that the GASLS model with a slope factor that is adjusted by the sine of the slope angle can represent the sloping surface effects. The GASLS model can incorporate any slope factor.     

Impact of fractal characteristics on evaporation and infiltration in unsaturated heterogeneous soils

ABSTRACT

In this study, an approach is developed to investigate the impact of fractal characteristics of unsaturated soil between the water table and land surface on the steady-state evaporation and infiltration across a heterogeneous landscape. The soil domain is conceptualized as a collection of stream tubes of soils and the particle diameters in various stream tubes follow a fractal distribution. The saturated hydraulic conductivity of each stream tube is related to the representative particle diameter in the tube. The effective specific discharge is then integrated from the specific discharge for each stream tube and the fractal distribution. The effective evaporation and infiltration in unsaturated soils increase with the fractal dimension. The ratio of minimum over maximum diameters does not significantly affect the specific discharge in the fractal soil. The specific discharge in unsaturated fractal soils calculated by using the simple average particle diameter mostly over-predicts the actual effective specific discharge.     

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.     

A peridynamic model of flow in porous media

This paper presents a nonlocal, derivative free model for transient flow in unsaturated, heterogeneous, and anisotropic soils. The formulation is based on the peridynamic model for solid mechanics. In the proposed model, flow and changes in moisture content are driven by pairwise interactions with other points across finite distances, and are expressed as functional integrals of the hydraulic potential field. Peridynamic expressions of the rate of change in moisture content, moisture flux, and flow power are derived, as are relationships between the peridynamic and the classic hydraulic conductivities; in addition, the model is validated. The absence of spacial derivatives makes the model a good candidate for flow simulations in fractured soils and lends itself to coupling with peridynamic mechanical models for simulating crack formation triggered by shrinkage and swelling, and assessing their potential impact on a wide range of processes, such as infiltration, contaminant transport, and slope stability.     

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.     

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     

Estimation of soil hydraulic properties and their uncertainty through the Beerkan infiltration experiment

The Beerkan method based on in situ single‐ring water infiltration experiments along with the relevant specific Beerkan estimation of soil transfer parameters (BEST) algorithm is attractive for simple soil hydraulic characterization. However, the BEST algorithm may lead to erroneous or null values for the saturated hydraulic conductivity and sorptivity especially when there are only few infiltration data points under the transient flow state, either for sandy soil or soils in wet conditions. This study developed an alternative algorithm for analysis of the Beerkan infiltration experiment referred to as BEST‐generalized likelihood uncertainty estimation (GLUE). The proposed method estimates the scale parameters of van Genuchten water retention and Brooks–Corey hydraulic conductivity functions through the GLUE methodology. The GLUE method is a Bayesian Monte Carlo parameter estimation technique that makes use of a likelihood function to measure the goodness‐of‐fit between modelled and observed data. The results showed that using a combination of three different likelihood measurements based on observed transient flow, steady‐state flow and experimental steady‐state infiltration rate made the BEST‐GLUE procedure capable of performing an efficient inverse analysis of Beerkan infiltration experiments. Therefore, it is more applicable for a wider range of soils with contrasting texture, structure, and initial and saturated water content. Copyright © 2015 John Wiley & Sons, Ltd.     

Effects of experimental uncertainty on the calculation of hillslope flow paths

Measurement uncertainty is a key hindrance to the quantification of water fluxes at all scales of investigation. Predictions of soil‐water flux rely on accurate or representative measurements of hydraulic gradients and field‐state hydraulic conductivity. We quantified the potential magnitude of errors associated with the parameters and variables used directly and indirectly within the Darcy – Buckingham soil‐water‐flux equation. These potential errors were applied to a field hydrometric data set collected from a forested hillslope in central Singapore, and their effect on flow pathway predictions was assessed. Potential errors in the hydraulic gradient calculations were small, approximately one order of magnitude less than the absolute magnitude of the hydraulic gradients. However, errors associated with field‐state hydraulic conductivity derivation were very large. Borehole (Guelph permeameter) and core‐based (Talsma ring permeameter) techniques were used to measure field‐saturated hydraulic conductivity. Measurements using these two approaches differed by up to 3\9 orders of magnitude, with the difference becoming increasingly marked within the B horizon. The sensitivity of the shape of the predicted unsaturated hydraulic conductivity curve to ±5% moisture content error on the moisture release curve was also assessed. Applied moisture release curve error resulted in hydraulic conductivity predictions of less than ±0\2 orders of magnitude deviation from the apparent conductivity. The flow pathways derived from the borehole saturated hydraulic conductivity approach suggested a dominant near‐surface flow pathway, whereas pathways calculated from the core‐based measurements indicated vertical percolation to depth. Direct tracer evidence supported the latter flow pathway, although tracer velocities were approximately two orders of magnitude smaller than the Darcy predictions. We conclude that saturated hydraulic conductivity is the critical hillslope hydrological parameter, and there is an urgent need to address the issues regarding its measurement further. Copyright © 2000 John Wiley & Sons, Ltd.     

Unified macroscopic model for unsaturated water flow in soils of bimodal porosity

Abstract

Natural soils very often contain micro- and macropores, having different hydraulic properties. At the macroscopic scale, the unsaturated flow in such soils can be described with various models, depending on the hydraulic diffusivity ratio of the components and the connectivity of the most conductive component. Three macroscopic models recently derived by the homogenization method are discussed. The limit passages between the models are studied. A unified model suitable for the entire range of the hydraulic diffusivity ratio is proposed. A numerical example shows the application of the model to macroscopically one-dimensional infiltration in a porous medium containing inclusions. A parametric study for varying conductivity (diffusivity) ratio is performed.     

Water and solute movement in a coarse-textured water-repellent field soil

Unstable water flow in water-repellent unsaturated soils can significantly affect the processes of infiltration and soil water redistribution. A field experiment was carried out to study the effect of water-repellency on water and bromide movement in a coarse-textured soil in the southwestern part of The Netherlands. The field data were analyzed using a relatively simple numerical model based on the standard Richards' equation for unsaturated water flow and the Fickian-based convection-dispersion equation for solute transport. Water-repellency was accounted for by multiplying the water content and the unsaturated hydraulic conductivity of the soil with F, a factor equal to the volumetric fraction of soil occupied by preferential flow paths resulting from the unstable flow process. The good comparison of simulated and measured bromide concentrations suggests that the model provides a viable method for simulating unstable water flow in water-repellent soils.     

REPORT ON THE ACTIVITIES OF THE INTERNATIONAL COMMISSION ON SNOW AND ICE FOR THE PERIOD 1971–1975

ABSTRACT

An infiltration model based on the Green-Ampt assumptions is developed for a class of non-uniform soils in which saturated hydraulic conductivity decreases as an exponential function of depth, and the storage-suction factor C = ΔθΔΨ is a constant. An analysis of measured hydraulic conductivity and porosity data suggests that the model may be useful in some soils where the changes of hydraulic characteristics with depth are of this form. A method for using the model with time variable rainfall rates is given. The model is applied to simulate the experimental results of Childs &; Bybordi (1969) who measured infiltration into layered sand profiles. Agreement was satisfactory even for this case.     

Sensitivity analysis on processes affecting bypass flow

Bypass flow in structured soils is dominated by soil hydrological processes, such as rain intensity, initial pressure head of the soil, surface storage of rain, horizontal contact area and absorption rate, and hydraulic conductivity of the soil matrix. This study was conducted to determine the relative impact of these processes in different soil types. A quasi 3-dimensional simulation model was used to calculate the effects of these soil hydrological input parameters on surface infiltration, macropore flow (with related horizontal absorption) and drainage. For light textured soils, surface infiltration was the most important term in the water balance. Heavy textured soils, in contrast, had drainage as the main term. In the latter soils bypass flow, when occurring, was almost equal to the amount of rain applied, indicating that absorption processes were strongly reduced. Lateral absorption on macropore walls was a minor fraction in the total mass balances, due to limited contact area and relatively weak diffusivity forces. Surface infiltration is a crucial parameter in bypass flow and is mainly dependent on rain intensity, initial pressure head and conductivity of the soil matrix. This requires measurement methods for hydraulic conductivity that specifically consider the effect of macropores.