Pedotransfer functions estimating soil hydraulic properties using different soil parameters

Estimates of soil hydraulic properties using pedotransfer functions (PTF) are useful in many studies such as hydrochemical modelling and soil mapping. The objective of this study was to calibrate and test parametric PTFs that predict soil water retention and unsaturated hydraulic conductivity parameters. The PTFs are based on neural networks and the Bootstrap method using different sets of predictors and predict the van Genuchten/Mualem parameters. A Danish soil data set (152 horizons) dominated by sandy and sandy loamy soils was used in the development of PTFs to predict the Mualem hydraulic conductivity parameters. A larger data set (1618 horizons) with a broader textural range was used in the development of PTFs to predict the van Genuchten parameters. The PTFs using either three or seven textural classes combined with soil organic mater and bulk density gave the most reliable predictions of the hydraulic properties of the studied soils. We found that introducing measured water content as a predictor generally gave lower errors for water retention predictions and higher errors for conductivity predictions. The best of the developed PTFs for predicting hydraulic conductivity was tested against PTFs from the literature using a subdata set of the data used in the calibration. The test showed that the developed PTFs gave better predictions (lower errors) than the PTFs from the literature. This is not surprising since the developed PTFs are based mainly on hydraulic conductivity data near saturation and sandier soils than the PTFs from the literature. Copyright © 2007 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.     

A concise parameterization of the hydraulic conductivity of unsaturated soils

The parameter n in the well-known expression for hydraulic conductivity K=K₀S_eⁿ (where K₀ is its value at satiation and S_e the effective saturation) is determined as a function of the exponent in the power form of the soil–water retention relationship. The result is validated with an extensive experimental database comprising some 43 soils, collected by Mualem.     

A comparative study of closed-form hydraulic conductivity prediction models

The Mualem and the Burdine hydraulic conductivity prediction models are considered in combination with the van Genuchten analytical retention curve, as well as the Brooks and Corey prediction model. An equivalence is presented between the retention curves of these models. A comparative study follows between hydraulic conductivities that are based on equivalent retention curves. A unified presentation of prediction models provides a framework for the whole analysis. The treatment of the equivalence problem consists in a minimization procedure characterized by uncoupling of the parameters and analytical evaluation of the objective function. Exact analytical equivalence relations are given for significant parts of the parameter ranges, and, for the remaining parts, analytical approximations are proposed. The comparisons between hydraulic conductivities are carried out via an inequality analysis. It is shown that the hydraulic conductivity of the Burdine model is less than that of the other models for extended ranges of equivalent parameters.     

Consistent parameter constraints for soil hydraulic functions

Parameters of functions to describe soil hydraulic properties are derived from measurements by means of parameter estimation. Of crucial importance here is the choice of correct constraints in the parameter space. Often, the parameters are mere shape parameters without physical meaning, giving flexibility to the model. A fundamental requirement is that the hydraulic functions are monotonic: the retention function and the conductivity function can only decrease as the capillary suction increases. A stricter physical requirement for the conductivity function is that its decrease with respect to saturation is at least linear. This linear decrease would occur if all pores of a capillary bundle had an equal radius. In the first part of this contribution, we derive constraints for the so-called tortuosity parameter of the Mualem conductivity model, which allow highest possible flexibility on one hand and guarantee physical consistency on the other hand. In combination with the retention functions of Brooks and Corey, van Genuchten, or Durner, such a constraint can be expressed as a function of the pore-size distribution parameters. In the second part, we show that a common modification of retention models, which is applied to reach zero water content at finite suction, can lead to the physically unrealistic case of increasing water content with increasing suction. We propose a solution for this problem by slightly modifying these models and introducing a correct parameter constraint.     

Hydraulic properties of peat soils along a bulk density gradient—A meta study

Our understanding of hydraulic properties of peat soils is limited compared with that of mineral substrates. In this study, we aimed to deduce possible alterations of hydraulic properties of peat soils following degradation resulting from peat drainage and aeration. A data set of peat hydraulic properties (188 soil water retention curves [SWRCs], 71 unsaturated hydraulic conductivity curves [UHCs], and 256 saturated hydraulic conductivity [K_s] values) was assembled from the literature; the obtained data originated from peat samples with an organic matter (OM) content ranging from 23 to 97 wt% (weight percent; and according variation in bulk density) representing various degrees of peat degradation. The Mualem‐van Genuchten model was employed to describe the SWRCs and UHCs. The results show that the hydraulic parameters of peat soils vary over a wide range confirming the pronounced diversity of peat. Peat decomposition significantly modifies all hydraulic parameters. A bulk density of approximately 0.2 g cm^?3 was identified as a critical threshold point; above and below this value, macroporosity and hydraulic parameters follow different functions with bulk density. Pedotransfer functions based on physical peat properties (e.g., bulk density and soil depth) separately computed for bog and fen peat have significantly lower mean square errors than functions obtained from the complete data set, which indicates that not only the status of peat decomposition but also the peat‐forming plants have a large effect on hydraulic properties. The SWRCs of samples with a bulk density of less than 0.2 g cm^?3 could be grouped into two to five classes for each peat type (botanical composition). The remaining SWRCs originating from samples with a bulk density of larger than 0.2 g cm^?3 could be classified into one group. The Mualem‐van Genuchten parameter values of α can be used to estimate K_s if no K_s data are available. In conclusion, the derived pedotransfer functions provide a solid instrument to derive hydraulic parameter values from easily measurable quantities; however, additional research is required to reduce uncertainty.     

Unsaturated hydraulic properties of xerophilous mosses: towards implementation of moss covered soils in hydrological models

Evaporation from mosses and lichens can form a major component of the water balance, especially in ecosystems where mosses and lichens often grow abundantly, such as tundra, deserts and bogs. To facilitate moss representation in hydrological models, we parameterized the unsaturated hydraulic properties of mosses and lichens such that the capillary water flow through moss and lichen material during evaporation could be assessed. We derived the Mualem‐van Genuchten parameters of the drying retention and the hydraulic conductivity functions of four xerophilous moss species and one lichen species. The shape parameters of the retention functions (2.17 < n < 2.35 and 0.08 < α < 0.13 cm^?1) ranged between values that are typical for sandy loam and loamy sand. The shapes of the hydraulic conductivity functions of moss and lichen species diverged from those of mineral soils, because of strong negative pore‐connectivity parameters (?2.840 < l < ?2.175) and low hydraulic conductivities at slightly negative pressure heads (0.016 < K₀ < 0.280 cm/d). These K₀ values are surprisingly low, considering that mosses are very porous. However, during evaporation, large pores and voids were air filled and did not participate in capillary water flow. Small K₀ values cause mosses and lichens to be conservative with water during wet conditions, thus tempering evaporation compared to mineral soils. On the other hand, under dry conditions, mosses and lichens are able to maintain a moisture supply from the soil, leading to a higher evaporation rate than mineral soils. Hence, the modulating effect of mosses on evaporation possibly differs between wet and dry climates. Copyright © 2013 John Wiley & Sons, Ltd.     

Comparison of relative permeability-saturation-pressure parametric models for infiltration and redistribution of a light nonaqueous-phase liquid in sandy porous media

To test and evaluate the ability of commonly used constitutive relations for multifluid flow predictions, results of numerical flow and transport simulations are compared to experimental data. Three quantitative experiments were conducted in 1-m-long vertical columns. The columns were filled with either a uniform sand, a sand with a broad particle-size distribution, or with a layered system where a layer of a course-textured uniform sand was placed in an otherwise finer-textured uniform sand. After establishing variably water-saturated conditions, a pulse of a light nonaqueous-phase liquid (LNAPL) was injected uniformly at a constant rate. Water and LNAPL saturations were measured as a function of time and elevation with a dual-energy gamma-radiation system. The infiltration and redistribution of the LNAPL were simulated with nonhysteretic and hysteretic parametric relative permeability-saturation-pressure (k-S-P) models. The models were calibrated using two-phase air-water retention data and an established scaling theory. The nonhysteretic Brooks-Corey k-S-P model, which utilizes the Burdine relative permeability model, yielded predictions that closely matched the experimental data. Use of the nonhysteretic and hysteretic k-S-P models, based on the van Genuchten S-P relations and k-S relations derived from the Mualem relative permeability model, did not agree as well with the experimental data as those obtained with the Brooks-Corey k-S-P model. Explanations for the differences in performance of the three tested parametric k-S-P models are proposed.     

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.     

Inverse modelling techniques for determining hydraulic properties of coarse-textured porous media by transient outflow methods

A series of multi-step outflow experiments was carried out to identify the unsaturated hydraulic properties of two homogeneous coarse-textured porous media (glass beads and sand). Because of the measured sharp fronts of water content decrease during these experiments the hydraulic functions are assumed to be represented by the complete van Genuchten–Mualem closed-form expressions with variable coefficients α, n, m and θ_r. The values of θ_s and K_s were measured directly. A sensitivity analysis with respect to α, n, and m shows that conditions of local identifiability are satisfied if measurements of water content at some inner points inside the column are considered. The inverse modelling technique consists of two steps: first, computation of objective function values based on water content data responses to obtain initial parameter estimations, and second, a more detailed parameter determination using a Levenberg–Marquardt scheme. In both steps a numerical model incorporating the hydraulic functions is utilized to simulate theoretical pressure head and water content distributions along the column. For both porous media unique solutions of the inverse problem could be obtained, and afterwards, the corresponding hydraulic functions were verified from additional drainage experiments.©1998 Elsevier Science Limited. All rights reserved     

Comparing hydraulic properties of different forest floors

The forest floor plays an important role in runoff rate, soil erosion and soil infiltration capacity by protecting mineral soils from the direct impact of falling raindrops. Forest floor consists of different kinds of litter with different hydraulic properties. In this study, the inverse method was used to estimate the hydraulic properties of three kinds of forest floor (broad‐leaved, needle‐leaved and mixed‐stand) at three replications in a completely random design. Forest floor samples were collected from the Gilan Province, Iran. The samples were piled up to make long columns 40.88 cm high with an inner diameter of 18.1 cm. Artificial rainfall experiments were conducted on top of the columns, and free drainage from the bottom of the columns was measured in the laboratory. Saturated hydraulic conductivity (K_s), saturated water content and water retention curve parameters (van Genuchten equation) were estimated by the inverse method. The results showed that the K_s of needle‐leaved samples differed significantly (p < 0.05) from those of broad‐leaved and mixed‐stand samples, whereas the latter two did not differ in this regard. No significant differences emerged in the water retention function parameters of van Genuchten (θ_r, β and α) in the three forest floor samples. The saturated water content of mixed‐stand samples was significantly different (p < 0.05) from that of broad‐leaved and needle‐leaved treatments with the latter two samples showing no significant difference. The good agreement between simulated and observed free drainage for all forest floor samples in the validation period indicates that the estimated hydraulic properties efficiently characterize the unsaturated water flow in the forest floor. Copyright © 2013 John Wiley & Sons, Ltd.     

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.     

On the Relation Between Saturated Conductivity and Capillary Retention Characteristics

Abstract. A simple closed-form expression relating saturated hydraulic conductivity to the van Genuchten capillary retention model parameters is derived. Application of this equation to an experimental data set shows reasonable agreement between measured and predicted saturated conductivity values. The proposed equation provides a consistent theoretical basis for estimating both saturated and unsaturated hydraulic conductivity from statistical pore structure models.     

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.     

Maximum-likelihood estimation of unsaturated hydraulic parameters

Maximum-likelihood estimators properly represent measurement error, thus provide a statistically sound basis for evaluating the adequacy of a model fit and for finding the multivariate parameter confidence region. We demonstrate the advantages of using maximum-likelihood estimators rather than simple least-squares estimators for the problem of finding unsaturated hydraulic parameters. Inversion of outflow data given independent retention data can be treated by an extension to a Bayesian estimator. As an example, we apply the methodology to retention and transient unsaturated outflow observations, both obtained on the same medium sand sample. We found the van Genuchten expression to be adequate for the retention data, as the best fit was within measurement error. The Cramer–Rao confidence bound described the true parameter uncertainty approximately. The Mualem–van Genuchten expression was, however, inadequate for our outflow observations, suggesting that the parameters (, n) may not always be equivalent in describing both retention and unsaturated conductivity.     

Using a pore‐scale model to quantify the effect of particle re‐arrangement on pore structure and hydraulic properties

A pore‐scale model based on measured particle size distributions has been used to quantify the changes in pore space geometry of packed soil columns resulting from a dilution in electrolyte concentration from 500 to 1 mmol l^?1 NaCl during leaching. This was applied to examine the effects of particle release and re‐deposition on pore structure and hydraulic properties. Two different soils, an agricultural soil and a mining residue, were investigated with respect to the change in hydraulic properties. The mining residue was much more affected by this process with the water saturated hydraulic conductivity decreasing to 0·4% of the initial value and the air‐entry value changing from 20 to 50 cm. For agricultural soil, there was little detectable shift in the water retention curve but the saturated hydraulic conductivity decreased to 8·5% of the initial value. This was attributed to localized pore clogging (similar to a surface seal) affecting hydraulic conductivity, but not the microscopically measured pore‐size distribution or water retention. We modelled the soil structure at the pore scale to explain the different responses of the two soils to the experimental conditions. The size of the pores was determined as a function of deposited clay particles. The modal pore size of the agricultural soil as indicated by the constant water retention curve was 45 µm and was not affected by the leaching process. In the case of the mining residue, the mode changed from 75 to 45 µm. This reduction of pore size corresponds to an increase of capillary forces that is related to the measured shift of the water retention curve. Copyright © 2007 John Wiley & Sons, Ltd.     

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.     

Development of pedotransfer functions for soil hydraulic properties in the critical zone on the Loess Plateau,China

Soil hydraulic properties (SHPs) including the soil water retention curve and saturated soil hydraulic conductivity (Ks) are crucial input data for simulations of soil water and solute transport in the Earth's critical zone. However, obtaining direct measurements of SHPs at a wide range of scales is time consuming and expensive. Pedotransfer functions (PTFs) are employed as an alternative method for indirectly estimating these parameters based on readily measured soil properties. However, PTFs for SHPs for the deep soil layer in the Earth's critical zone are lacking. In this study, we developed new PTFs in the deep soil profile for Ks and soil water retention curve on the Loess Plateau, China, which were fitted with the van Genuchten equation. In total, 206 data sets comprising the hydraulic and basic soil properties were obtained from three typical sites. Samples were collected from the top of the soil profile to the bedrock by soil core drilling. PTFs were developed between the SHPs and basic soil properties using stepwise multiple linear regression. The PTFs obtained the best predictions for Ks (R_adj² = 0.561) and the worst for van Genuchten α (R_adj² = 0.474). The bulk density and sand content were important input variables for predicting Ks, α, and θs, and bulk density, clay content, and soil organic carbon were important for n. The PTFs developed in this study performed better than existing PTFs. This study contains the first set of PTFs of SHPs to be developed for the deep profile on the Loess Plateau, and they may be applicable to other regions.