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Cost-effective sampling strategies to understand hydrologic processes in a hillslope are essential to the estimation of hillslope seepage and to the evaluation of slope stability. The objectives of this paper are (a) to introduce a stochastic cross-correlation analysis to hillslope hydrologic processes and stability investigation and (b) to develop a cost-effective sampling strategy to reduce the pore-water pressure uncertainty at the region of our interest. The concept of stochastic representation of spatial variabilities of soil hydraulic properties is introduced first. We then develop a first-order analysis method to determine spatiotemporal distribution of pore-water pressure head (P) variance (unconditional variance or uncertainty) due to spatial variability of saturated hydraulic conductivity (Ks) in a variably saturated hillslope during rainfall. Subsequently, a cross-correlation analysis is presented, which quantifies the spatial correlation between P at a given location and Ks at any part of a hillslope under a transient infiltration event. We afterward formulate a first-order approximation of residual P variance (conditional variance or uncertainty) due to inclusions of Ks measurements. The developed methodology is applied to synthetic, heterogeneous, two-dimensional hillslopes to investigate the effectiveness of several Ks sampling schemes. Results of this investigation show that boreholes and sampling locations should be placed at an interval of one correlation scale. They should be distributed over an area covering several correlation scales, rather than clustered together at the largest cross-correlation region or at regions where prediction uncertainty is large (where our interest and concern are). Further, the results demonstrate that increasing the sampling density is useful but inefficient. Layering structures of hillslopes reduce the number of boreholes and samples required. At last, a cost-effective sampling strategy for study of slope stability based on cross-correlation is suggested, which minimizes the prediction uncertainty of P at critical locations.

Groundwater ridging is the rapid rise of a shallow water table during a rainfall event, in an environment where, in the pre-event period, the capillary fringe extends to the ground surface. Groundwater ridging is widely cited to account for the observed significant appearance of pre-event water in a stream stormflow hydrograph. Various hypotheses have been advanced to explain the groundwater-ridging mechanism; and most recently, from a field study site in South Africa, an energy hypothesis was proposed, which explains that groundwater-ridging water-table rise is a result of rapid introduction and transmission of additional pressure head into the capillary fringe from an intense rainfall at the ground surface. However, there is a need for further analysis and evidence from other field study sites to confirm and support this newly proposed energy hypothesis. The objectives of this paper are, therefore, as follows: to review previous observations on groundwater ridging, from other study sites, in order to deduce evidence of the newly proposed energy hypothesis; to present and evaluate a one-dimensional diffusion mathematical model that can simulate groundwater-ridging water-table rise, based on the newly proposed energy hypothesis; and to evaluate the importance of a capillary fringe in streamflow generation. Analysis of previous observations from other study sites generally indicated that the rate of groundwater-ridging water-table rise is directly related to the rainfall intensity, hence confirming and agreeing with the newly proposed energy hypothesis. Additionally, theoretical results by the mathematical model agreed fairly well with the field results observed under natural rainfall, confirming that the rapidly rainfall-induced energy is diffusively transmitted downwards through pore water, elevating the pressure head at every depth. The results in this study also support the concept of a three-end-member stream stormflow hydrograph and contribute to the explanation of how catchments can store water for long periods but then release it rapidly during storm events. Copyright © 2015 John Wiley & Sons, Ltd.

The solid Earth's surface frequently experience changes in total stresses as a result of periodic loading. When the fluid-saturated porous media deform in response to changes in stress, the induced variations in pore volume affect the pore water pressure. The fluid flow therefore occurs in response to the gradient in the induced excess pore water pressure. This work aims at quantifying the spatial variability in excess pressure head produced by the periodic loading accounting for the variation of log hydraulic conductivity (lnK). It is important for the rational management of groundwater resources. A closed-form expression is developed by the nonstationary spectral approach to analyse the influence of the statistical properties of lnK process, the hydraulic parameters, and the spatial position. The general stochastic framework outlined in this work provides a basis for assessing the impact of statistical properties of input aquifer parameters on the output variability (or uncertainty). Copyright © 2014 John Wiley & Sons, Ltd.

Copyright © 2014 John Wiley & Sons, Ltd. Introduction In hillslopes with soils characterized by deep regoliths, such as Ultisols, Oxisols, and Alfisols, interflow occurs episodically over impeding layers near and parallel to the soil surface such as low-conductivity B horizons (e.g. Newman et al., 1998; Buttle andMcDonald, 2002; Du et al., In Review), till layers (McGlynn et al., 1999; Bishop et al., 2004), hardpans (McDaniel et al., 2008), C horizons (Detty and McGuire, 2010), and permeable bedrock (Tromp van Meerveld et al., 2007). As perched saturation develops within and above these impeding but permeable horizons, flow moves laterally downslope, but the perched water also continues to percolate through the impeding horizon to the unsaturated soils and saprolite below. Perched water and solutes will eventually traverse the zone of perched saturation above the impeding horizon and then enter and percolate through the impeding horizon. In such flow situations, only lower hillslope segments with sufficient downslope travel distance will deliver water to the riparian zone within the time scale of a storm. Farther up the slope, lateral flow within the zone of perched saturation will act mainly to shift the point of percolation (location where a water packet leaves the downslope flow zone in the upper soil layer and enters the impeding layer) down the hillslope from the point of infiltration. In flatter parts of the hillslope or in areas with little contrast between the conductivities of the upper and impeding soil layers, lateral flow distances will be negligible. From Darcy’s law, we can estimate the downslope travel distance for quasi-steady-state conditions within the saturated layer assuming Boussinesq (slope parallel) flow above the restrictive layer and normal flow (perpendicular to the slope) through the restrictive layer to unsaturated soils below (Figure 1). Using a downslope flow vector, we must employ an orthogonal normal vector and avoid Harr’s (1977) mistake of adding non-orthogonal and non-independent gradient vectors in calculating flow directions. Weassume that each layer is isotropic, and the impeding layer is saturated or nearly so and drains freely to an unsaturated layer below (pressure head equals zero at the base of the impeding layer). We assume diffuse porosity within the impeding layer so percolation is not restricted to randomly spaced discontinuities. With these assumptions generally applicable to hillslopes with deep regoliths and a low conductivity layer paralleling the soil surface, we will calculate downslope travel distances for reasonable combinations of slopes, conductivities, and impeding layer thicknesses; evaluate these distances with respect to typical slope lengths;map the downslope travel distances on watersheds with soil and slope conditions matching these assumptions; and discuss how couplingBoussinesq downslope flow and percolation affect our understanding of the potential zonation of lateral flow processes.

The pore water pressure head that builds in the soil during storms is a critical factor for the prediction of potential slope instability. We report findings from a 3-year study of pressure head in 83 piezometers distributed within a 13-ha forested catchment on the northern coast of California. The study's primary objective was to observe the seasonal and storm-based dynamics of pressure head at a catchment scale in relation to observed rainfall characteristics and in situ topography to better understand landscape patterns of pressure head. An additional goal was to determine the influence of the interaction between rainfall and forest canopy in altering delivery of water and pressure head during the large storms necessary to induce landsliding. We found that pressure head was highly variable in space and time at the catchment scale. Pore pressures peaked close to maximum rainfall intensity during the largest storms measured. The difference between rainfall and throughfall delivered through the canopy was negligible during the critical landslide-producing peak rainfall periods. Pore pressure was spatially variable within the catchment and did not strongly correlate with surficial topographic features. Only 23% of the piezometers located in a variety of slope positions were found to be highly responsive to rainfall. Topographic index statistically explained peak pressure head at responsive locations during common storms, but not during the larger storms with potential to produce landslides. Drainage efficiency throughout the catchment increased significantly in storms exceeding 2 to 7 months peak pressure head return period indicated by slowing or cessation of the rate of increase of pressure head with increasing storm magnitude. This asymptotic piezometric pattern persisted through the largest storm measured during the study. Faster soil drainage suppressed pressure head response in larger storms with important process implications for pore pressure development and landslide hazard modelling. Copyright © 2012 John Wiley & Sons, Ltd.

The deformation of the solid matrix affects the fluid pore pressure and flow by altering the pore volume. Such interaction in turn affects the storage of groundwater in the void space. Obviously, this subject is of interest in groundwater hydrology. This paper describes an investigation of the effect of aquifer heterogeneity on the variability of the fluid pressure head and solid's volume strain, where the assumption of a constant vertical total stress leads to a relatively simple relationship between changes in solid's volume strain and fluid pressure head. To solve the problem analytically, focus is placed on the one-dimensional models. It is found from our closed-form solutions that the variance and correlation length of the log hydraulic conductivity are important in increasing the variability of pressure head and solid's volume strain. It is hoped that our findings will provide a basic framework for understanding and quantifying field-scale volume strain processes and be useful in stimulating further research in this area. Copyright © 2011 John Wiley & Sons, Ltd.

In subsurface porous media, the soil water retention curve (WRC) and unsaturated hydraulic conductivity curve (UHC) are two important soil hydraulic property curves. Spatial heterogeneity is ubiquitous in nature, which may significantly affect soil hydraulic property curves. The main theme of this paper is to investigate how spatial heterogeneities, including their arrangements and amounts in soil flumes, affect soil hydraulic property curves. This paper uses a two-dimensional variably saturated flow and solute transport finite element model to simulate variations of pressure and moisture content in soil flumes under a constant head boundary condition. To investigate the behavior of soil hydraulic property curves owing to variations of heterogeneities and their arrangements as well, cases with different proportions of heterogeneities are carried out. A quantitative evaluation of parameter variations in the van Genuchten model (VG model) resulting from heterogeneity is presented. Results show that the soil hydraulic properties are strongly affected by variations of heterogeneities and their arrangements. If the pressure head remains at a specific value, the soil moisture increases when heterogeneities increase in the soil flumes. On the other hand, the unsaturated hydraulic conductivity decreases when heterogeneities increase in the soil flumes under a constant pressure head. Moreover, results reveal that parameters estimated from both WRC and UHC also are affected by shapes of heterogeneity; this indicates that the parameters obtained from the WRC are not suitable for predicting the UHC of different shapes in heterogeneous media. Copyright © 2011 John Wiley & Sons, Ltd.

Macropores are important preferential pathways for the migration of water and contaminants through the vadose zone. The objective of this study was to examine small-scale preferential flow processes during infiltration in macroporous, low permeability soils. A series of tension infiltration tests were conducted using Brilliant Blue dye tracer at two field sites in southwestern Ontario, Canada. The maximum applied pressure head was varied for each test and the resulting dye stain patterns and macropore networks were characterized by excavation, mapping, photography, and image analysis. Worm burrows were the dominant macropore type, with average macropore densities exceeding 400 m−2 and peak densities of more than 750 m−2 at 30 cm depth at both sites. Flow in macropores became significant at infiltration pressures > − 3 cm, with corresponding increases in infiltration rate, soil water content variability (spatially and temporally), and depth of dye staining. The results demonstrated clear evidence for partially saturated macropore flow under porewater tension conditions and the associated importance of macropore–matrix interaction in controlling this flow. Field observations of transient infiltration showed that film and rivulet flow along macropores yielded vertical flow velocities exceeding 40 m d−1. Simple calculations showed that film flow along the walls and corners of irregularly shaped macropores could explain the observed results. Copyright © 2009 John Wiley & Sons, Ltd.

Column and field experiments have shown that the hydrologic response to increases in rainfall rates can be more rapid than expected from simple estimates. Physics-based hydrologic response simulation, with the Integrated Hydrology Model (InHM), is used here to investigate rapid hydrologic response, within the variably saturated near surface, to temporal variations in applied flux at the surface boundary. The factors controlling the speed of wetting front propagation are discussed within the Darcy-Buckingham conceptual framework, including kinematic wave approximations. The Coos Bay boundary-value problem is employed to examine simulated discharge, pressure head, and saturation responses to a large increase in applied surface flux. The results presented here suggest that physics-based simulations are capable of representing rapid hydrologic response within the variably saturated near surface. The new InHM simulations indicate that the temporal discretization and measurement precision needed to capture the rapid subsurface response to a spike increase in surface flux, necessary for both data-based analyses and evaluation of physics-based models, are smaller than the capabilities of the instrumentation deployed at the Coos Bay experimental catchment.

A method is proposed for calculating the equivalent hydraulic conductivity (EHC) within a finite difference block (FDB). Application of the constant-flux assumption of Darcy's Law, the EHC equals to the integration of effective hydraulic conductivity (Kw) as a function of pressure head (hw) divided by the head difference at the ends of the FDB. Error analysis show that the constant-flux (CF) EHC estimates are better than those computed by the commonly used arithmetic-mean (AM), geometric-mean (GM), and harmonic-mean (HM) techniques. CF EHC results are even more superior at larger interblock head difference situations. Simulations of water infiltration experiments show that simulations using the CF EHC or AM or GM weighting technique have only slight difference while applying the Neumann type boundary condition at the ground surface. In case of the Dirichlet type boundary condition, however, the CF EHC is superior to the other two in correctly estimating the depth of infiltration while enlarging the grid size. Therefore, it is recommended to adopt the CF EHC with a larger grid size to the more stable and more efficient results. Copyright © 2007 John Wiley & Sons, Ltd.

The validation of soil water balance models and the evaluation of the quality of the model predictions at field-scale require time-series of in situ measured model outputs. In our study, we have validated such a model using a 6-year period with time-series of automatically recorded, daily volumetric soil water contents measured with the time-domain reflectometry with intelligent microelements (TRIME) method and daily pressure heads measured with tensiometers. The comparisons of simulated with measured soil water contents and pressure heads were analysed using the modelling efficiency index (IA) and the square root of the mean square error (RMSE) in order to evaluate the prediction quality of the model. In our study, IA and RMSE, obtained either from the comparison of simulated with measured soil water contents or the comparison of calculated with observed pressure heads, in some cases lead to different results regarding the evaluation of the simulation quality of the soil water balance model. For example, a good fit between simulated and observed soil water contents does not necessarily result in a comparably good fit between the corresponding calculated and measured pressure heads. Therefore, a combined use of both measurement techniques, which takes into account their respective advantages and disadvantages, gives a more complete overview on the simulation quality of the soil water balance model than the single use of one of those techniques. Copyright © 2004 John Wiley & Sons, Ltd.

Relationships between gravimetric soil moisture content (w) and matric potential (ϕ), and between volumetric soil moisture content (θv) and pressure head (h) were approximated for the unsaturated zone on Long Island, New York. Soil samples were collected from two sites using a hand auger. The soil moisture content was determined using the filter-paper (wf) and gravimetric (w) methods, respectively. The wf was then used in an empirical equation to estimate ϕm. Each set of ϕm and w was combined with a straight-line empirical model to obtain a w(ϕm) relationship. Soil ϕm was converted to h, and w to the volumetric moisture content θv, in order to produce a θv(h) curve. Graphical and statistical comparison showed that the resulting θv(h) curves fell within one order of magnitude of similar curves generated by a more sophisticated non-linear model developed previously. The simplicity and low cost of the filter-paper approach described in this study recommends it for preliminary studies of hydraulic properties in the unsaturated zone. Copyright © 2000 John Wiley & Sons, Ltd.

A tension infiltrometer technique was used to characterize differences in hydraulic conductivity (K) in two rain-fed hillsides (north-facing and south-facing) in central Chile. For the north-facing locations, smaller values of K (at a range of supply water pressure heads ψ) compared with south-facing locations were found, with accentuated differences close to saturation (zero pressure head). The differences were attributed to differences in texture and organic matter contents observed for the two sites. Furthermore, K(ψ) had a tendency to increase with increasing slope gradient. This tendency was to an extent explained by the deviation from requirements of measurements on level ground. The differences found in K(ψ) between different slope gradients were explained by the differences in the vertical and lateral hydraulic conductivity and by the occurrence of surface sealing in low slope plots. Copyright © 2000 John Wiley & Sons, Ltd.

Surface run-off may be generated when rainfall intensity exceeds infiltration capacity, or when the soil profile is saturated. Both types of overland flow may occur in hilly agricultural loess regions. It was shown with pressure head and run-off measurements that Hortonian overland flow occurs during summer rain events. A two-dimensional water flow model could simulate pressure head changes and run-off. Simulated potential run-off for the transect studied was three times as high. This indicates effects of surface ponding and the probable location of this particular transect in a region with high run-off production.

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.

Solute leaching in unsaturated soil is influenced by the variability in hydraulic functions (water retention and conductivity) that govern the flow process. Variability in measured soil hydraulic functions of a coarse-, medium- and fine-textured soil group was quantified with the scaling theory of similar media. Solute leaching in these soils was calculated with Monte Carlo simulation assuming, successively, hydraulic conductivity, K, volumetric water content, 0, and pressure head, h, to be constant. In addition to variability in hydraulic functions, variability in the solute retardation factor was also taken into account. To examine this effect five solutes were considered: a conservative solute (chloride), a non-retarded solute subject to decay (nitrate), a retarded solute that does not decay (cadmium) and two organic solutes which are retarded but have different sorption and decay parameters (the pesticide atrazine and a chlorinated hydrocarbon). The numerical results obtained with Monte Carlo simulation were in a number of instances verified with analytical solutions. The three soil groups distinguished showed considerable differences in vulnerability for leaching of the five solutes, emphasizing the importance of the effect of variability in soil hydraulic functions when studying solute leaching. Numerical and analytical results showed good agreement. Therefore, in relatively simple situations analytical solutions are attractive. However, in complicated situations, analytical solutions are cumbersome and numerical solutions are the only realistic alternative.