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.     

Influence of heterogeneity on unsaturated hydraulic properties (2) – percentage and shape of heterogeneity

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.     

Effect of mineral reactions on the hydraulic properties of unsaturated soils: Model development and application

The selective radius shift model was used to relate changes in mineral volume due to precipitation/dissolution reactions to changes in hydraulic properties affecting flow in porous media. The model accounts for (i) precipitation/dissolution taking place only in the water-filled part of the pore space and further that (ii) the amount of mineral precipitation/dissolution within a pore depends on the local pore volume. The pore bundle concept was used to connect pore-scale changes to macroscopic soil hydraulic properties. Precipitation/dissolution induces changes in the pore radii of water-filled pores and, consequently, in the effective porosity. In a time step of the numerical model, mineral reactions lead to a discontinuous pore-size distribution because only the water-filled pores are affected. The pore-size distribution is converted back to a soil moisture characteristic function to which a new water retention curve is fitted under physically plausible constraints. The model equations were derived for the commonly used van Genuchten/Mualem hydraulic properties. Together with a mixed-form solution of Richards’ equation for aqueous phase flow, the model was implemented into the geochemical modelling framework PHREEQC, thereby making available PHREEQC’s comprehensive geochemical reactions. Example applications include kinetic halite dissolution and calcite precipitation as a consequence of cation exchange. These applications showed marked changes in the soil’s hydraulic properties due to mineral precipitation/dissolution and the dependency of these changes on water contents. The simulations also revealed the strong influence of the degree of saturation on the development of the saturated hydraulic conductivity through its quadratic dependency on the van Genuchten parameter α. Furthermore, it was shown that the unsaturated hydraulic conductivity at fixed reduced water content can even increase during precipitation due to changes in the pore-size distribution.     

Soil moisture states,lateral flow,and streamflow generation in a semi‐arid,snowmelt‐driven catchment

Hydraulic connectivity on hillslopes and the existence of preferred soil moisture states in a catchment have important controls on runoff generation. In this study we investigate the relationships between soil moisture patterns, lateral hillslope flow, and streamflow generation in a semi‐arid, snowmelt‐driven catchment. We identify five soil moisture conditions that occur during a year and present a conceptual model based on field studies and computer simulations of how streamflow is generated with respect to the soil moisture conditions. The five soil moisture conditions are (1) a summer dry period, (2) a transitional fall wetting period, (3) a winter wet, low‐flux period, (4) a spring wet, high‐flux period, and (5) a transitional late‐spring drying period. Transitions between the periods are driven by changes in the water balance between rain, snow, snowmelt and evapotranspiration. Low rates of water input to the soil during the winter allow dry soil regions to persist at the soil–bedrock interface, which act as barriers to lateral flow. Once the dry‐soil flow barriers are wetted, whole‐slope hydraulic connectivity is established, lateral flow can occur, and upland soils are in direct connection with the near‐stream soil moisture. This whole‐slope connectivity can alter near‐stream hydraulics and modify the delivery of water, pressure, and solutes to the stream. Copyright © 2005 John Wiley & Sons, Ltd.     

Stochastic analysis of unsaturated transport in soils with fractal log-conductivity distribution

Within the framework of stochastic theory and the spectral perturbation techniques, three-dimensional dispersion in partially saturated soils with fractal log hydraulic conductivity distribution is analyzed. Our analysis is focused on the impact of fractal dimension of log hydraulic conductivity distribution, local dispersivity, and unsaturated flow parameters, such as the soil poresize distribution parameter and the moisture distribution parameter, on the spreading behavior of solute plume and the concentration variance. Approximate analytical solutions to the stochastic partial differential equations are derived for the variance of asymptotic solute concentration and asymptotic macrodispersivities.     

Investigation of spatially distributed braided river flows using a two‐dimensional hydraulic model

This paper reports the application of a two‐dimensional hydraulic model to a braided reach of the Avoca River, New Zealand. Field measurements of water surface elevation, depth and velocity obtained at low flow were used to validate the model and to optimize the parameterization of bed friction. The main systematic trends in the measured flow variables are reproduced by the model. However, field data are characterized by greater spatial variability than model output reflecting differences in the scale of processes measured in the field and represented by the model. Additional model runs were conducted to simulate flow patterns within the study reach at five higher discharges. The purpose of these simulations was to evaluate the potential for using two‐dimensional hydraulic models to quantify the reach‐scale hydraulic characteristics of braided rivers and their dependence on discharge. Changes in flow depth and velocity with increasing discharge exhibit trends that are consistent with the results of previous field investigations, although the tendency for the wetted area of the braidplain within particular depth and velocity categories to remain fixed as discharge rises, as has been noted for several braided rivers in New Zealand, was not observed. Modelled shear stress frequency distributions fit gamma functions that incorporate a distribution shape parameter, the value of which follows clear systematic trends with rising discharge. These results illustrate both the problems of, and potential for, using two‐dimensional hydraulic models in braided river applications. This leads to something of a paradox in that while such models provide a means of generating hydraulic information that would be difficult to obtain in the field at an equivalent spatial resolution, they are, due to the problems inherent to data collection, difficult to validate conclusively. Despite this limitation, the application of spatially distributed models to investigate relationships between discharge and reach‐scale form and process variables appears to have considerable potential. Copyright © 2003 John Wiley & Sons, Ltd.     

Factors influencing the growth of miniature ice lenses

Experiments involving six soil types indicated that the production of miniature ice lenses is dependent on soil moisture content and grain size with lenses being produced in finer-grained soils at lower moisture contents than is possible in coarser soils. Explanation of the results involves consideration of the unsaturated hydraulic conductivity of the unfrozen soil through which water migrated to the freezing plane to allow ice lens growth.     

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.     

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.     

The erodibility of upland soils and the design of preafforestation drainage networks in the United Kingdom

Hydraulic thresholds for erosion of fourteen upland mineral and organic soils were determined in a hydraulic flume. These soils are from areas to be afforested in the United Kingdom. Some of the group are erosion resistant but others are susceptible to erosion once denuded of vegetation; for example, by preafforestation ploughing. These threshold data were required to calibrate a hydraulic model for effective design of preafforestation drainage networks on a variety of soils. However, simple field measures of soil properties indicative of erosion potential would be of value to the forestry industry for management purposes. Consequently, hydraulic threshold data were related by linear regression methods to basic soil properties, including organic content, grain size, bulk density, compression strength and penetration resistance. The investigation concluded that four peat soils are not eroded by clear water velocities up to 5·7 m s⁻¹, although a mineral bedload might induce erosion at lesser current speeds. Penetration resistance is a good field indicator of the degree of humification of the peat soils. Although selected physical parameters contribute resistance to water erosion, an increased organic content is pre-eminent in reducing erosion susceptibility in both organic and mineral soils. Although compressive strength was not indicative of soil erodibility, field measurements of penetration resistance on a variety of soils could be related to hydraulic thresholds of erosion; albeit through the construction of discriminant functions interpolated by eye. Consequently, organic content (laboratory) or penetration resistance (field) might form the basis of classifying upland soils in terms of erodibility. Mineral soils differ widely in terms of their erodibility, so that subject to further consideration, the use of ploughing for forestry cultivation might be appropriate in wider circumstances than presently recommended by the Forests and Water Guidelines. Ploughing should be acceptable on deep peat providing the underlying mineral soil is not exposed in the bottom of the furrow, and furrows are not led from mineral soils on to deep peat. © 1997 John Wiley & Sons, Ltd.     

Continuum percolation theory for pressure–saturation characteristics of fractal soils: extension to non-equilibrium

Systematic experimental deviations from theoretical predictions derived for water retention characteristics of fractal porous media have previously been interpreted in terms of continuum percolation theory (at low moisture contents, below the critical volume fraction of water, α_c capillary flow ceases). In other work, continuum percolation theory was applied to find the hydraulic conductivity as a function of saturation for saturations high enough to guarantee percolation of capillary flow. Now these two problems are further linked, using percolation theory to estimate non-equilibrium water retention at matric potential values such that the equilibrium water content is too low for percolation of capillary flow paths. In particular, a procedure for developing a time-dependent moisture content is developed for experimental time scales long enough that film flow can provide an alternate mechanism for equilibrating when continuous capillary flow is not possible. The time scales are defined in terms of moisture-dependent length scales and film flow and capillary flow hydraulic conductivities. Imbibition is treated in the extreme case of no film-flow contribution to equilibration. In another application at higher matric potentials, recursive relations are derived for the water content of porous media during drying when external pressures are changed at rates too rapid for equilibrium to be attained by capillary flow.     

Influence of antecedent soil moisture on hydraulic conductivity in a series of texture‐contrast soils

Antecedent soil moisture significantly influenced the hydraulic conductivity of the A1, A2e and B21 horizons in a series of strong texture‐contrast soils. Tension infiltration at six supply potentials demonstrated that in the A1 horizon, hydraulic conductivity was significantly lower in the ‘wet’ treatment than in the ‘dry’ treatment. However in the A2e horizon, micropore and mesopore hydraulic conductivity was lower in the ‘dry’ treatment than the ‘wet’ treatment, which was attributed to the precipitation of soluble amorphous silica. In the B21 horizon, desiccation of vertic clays resulted in the formation of shrinkage cracks which significantly increased near‐saturated hydraulic conductivity and prevented the development of subsurface lateral flow in the ‘dry’ treatment. In the ‘wet’ treatment, the difference between the hydraulic conductivity of the A1 and B21 horizons was reduced; however, lateral flow still occurred in the A1 horizon due to difficulty displacing existing soil water further down the soil profile. Results demonstrate the need to account for temporal variation in soil porosity and hydraulic conductivity in soil‐water model conceptualisation and parameterisation. Copyright © 2011 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.     

Influence of heterogeneity on unsaturated hydraulic properties: (1) local heterogeneity and scale effect

Spatial heterogeneity is ubiquitous in nature, which may significantly affect the soil hydraulic property curves. The models of a closed‐form functional relationship of soil hydraulic property curves (e.g. VG model or exponential model) are valid at point or local scale based on a point‐scale hydrological process, but how do scale effects of heterogeneity have an influence on the parameters of these models when the models are used in a larger scale process? This paper uses a two‐dimensional variably saturated flow and solute transport finite element model (VSAFT2) to simulate variations of pressure and moisture content in the soil flume under a constant head boundary condition. By changing different numerical simulation block sizes, a quantitative evaluation of parameter variations in the VG model, resulting from the scale effects, is presented. Results show that the parameters of soil hydraulic properties are independent of scale in homogeneous media. Parameters of α and n in homogeneous media, which are estimated by using the unsaturated hydraulic conductivity curve (UHC) or the soil water retention curve (WRC), are identical. Variations of local heterogeneities strongly affect the soil hydraulic properties, and the scale affects the results of the parameter estimations when numerical experiments are conducted. Furthermore, the discrepancy of each curve becomes considerable when moisture content becomes closer to a dry situation. Parameters estimated by UHC are totally different from the ones estimated by WRC. Copyright © 2012 John Wiley & Sons, Ltd.     

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.     

Lateral flow thresholds for aspen forested hillslopes on the Western Boreal Plain,Alberta, Canada

To predict the long‐term sustainability of water resources on the Boreal Plain region of northern Alberta, it is critical to understand when hillslopes generate runoff and connect with surface waters. The sub‐humid climate (P ≤ ET) and deep glacial sediments of this region result in large available soil storage capacity relative to moisture surpluses or deficits, leading to threshold‐dependent rainfall‐runoff relationships. Rainfall simulation experiments were conducted using large magnitude and high intensity applications to examine the thresholds in precipitation and soil moisture that are necessary to generate lateral flow from hillslope runoff plots representative of Luvisolic soils and an aspen canopy. Two adjacent plots (areas of 2·95 and 3·4 m²) of contrasting antecedent moisture conditions were examined; one had tree root uptake excluded for two months to increase soil moisture content, while the second plot allowed tree uptake over the growing season resulting in drier soils. Vertical flow as drainage and soil moisture storage dominated the water balances of both plots. Greater lateral flow occurred from the plot with higher antecedent moisture content. Results indicate that a minimum of 15–20 mm of rainfall is required to generate lateral flow, and only after the soils have been wetted to a depth of 0·75 m (C‐horizon). The depth and intensity of rainfall events that generated runoff > 1 mm have return periods of 25 years or greater and, when combined with the need for wet antecendent conditions, indicate that lateral flow generation on these hillslopes will occur infrequently. Copyright © 2008 John Wiley & Sons, Ltd.     

Ecohydrological modelling in a deciduous boreal forest: Model evaluation for application in non-stationary climates

Soil moisture is an important driver of growth in boreal Alaska, but estimating soil hydraulic parameters can be challenging in this data-sparse region. Parameter estimation is further complicated in regions with rapidly warming climate, where there is a need to minimize model error dependence on interannual climate variations. To better identify soil hydraulic parameters and quantify energy and water balance and soil moisture dynamics, we applied the physically based, one-dimensional ecohydrological Simultaneous Heat and Water (SHAW) model, loosely coupled with the Geophysical Institute of Permafrost Laboratory (GIPL) model, to an upland deciduous forest stand in interior Alaska over a 13-year period. Using a Generalized Likelihood Uncertainty Estimation parameterisation, SHAW reproduced interannual and vertical spatial variability of soil moisture during a five-year validation period quite well, with root mean squared error (RMSE) of volumetric water content at 0.5 m as low as 0.020 cm³/cm³. Many parameter sets reproduced reasonable soil moisture dynamics, suggesting considerable equifinality. Model performance generally declined in the eight-year validation period, indicating some overfitting and demonstrating the importance of interannual variability in model evaluation. We compared the performance of parameter sets selected based on traditional performance measures such as the RMSE that minimize error in soil moisture simulation, with one that is designed to minimize the dependence of model error on interannual climate variability using a new diagnostic approach we call CSMP, which stands for Climate Sensitivity of Model Performance. Use of the CSMP approach moderately decreases traditional model performance but may be more suitable for climate change applications, for which it is important that model error is independent from climate variability. These findings illustrate (1) that the SHAW model, coupled with GIPL, can adequately simulate soil moisture dynamics in this boreal deciduous region, (2) the importance of interannual variability in model parameterisation, and (3) a novel objective function for parameter selection to improve applicability in non-stationary climates.