Scaling soil water retention functions using particle-size distribution

The presented study explores the prediction of soil water retention and its variability from soil texture and bulk density measurements, using a physically-based scaling technique. Specifically, the Arya–Paris (AP) physico-empirical model is applied to two soil datasets that are collected from two catchments located in different areas of Southern Italy. Laboratory-measured soil water retention functions are scaled to characterize soil variability. The laboratory-measured and AP-predicted reference water retention functions are compared by evaluating the lognormal distribution of derived scaling factors, relative to the mean reference retention function. Since the scaling theory assumes geometric similitude for the investigated soils, successful application of using particle-size distribution to estimate soil water retention requires separation of soils with different textures, using variance analysis. We conclude that variability in soil water retention can be determined from limited soil water retention data using the scaling approach when combined with particle-size distribution measurements. This method can potentially be used as an effective tool for identifying soil hydrologic response at catchment scales.     

Functional evaluation of a simplified scaling method for assessing the spatial variability of soil hydraulic properties at the hillslope scale

Abstract

Mapping soil hydraulic parameters with traditional scaling methods that use laboratory-determined hydraulic characteristics (the LAB method) is not always feasible as it involves expensive, time-consuming and sophisticated measurements on soil samples collected in several locations of the study area. An alternative scaling method (the AP method) has been recently proposed to indirectly retrieve the soil hydraulic properties following the Arya-Paris physico-empirical pedotransfer function, which makes use of particle-size distribution and bulk density values. In this synthetic study we verify the performance of the AP method from a functional perspective, by evaluating the differences in the simulated soil water budget through a Monte Carlo approach. Notwithstanding that the AP method can provide soil hydraulic property patterns with faster experimental procedures and minor costs, we observe significant bias in the predicted spatially-averaged soil water budget due to a poor parametric calibration of the AP method and an imprecise identification of the spatial correlation structure of the AP-estimated scaling factors.

Citation Nasta, P., Romano, N., and Chirico, G.B., 2013. Functional evaluation of a simplified scaling method for assessing the spatial variability of soil hydraulic properties at the hillslope scale. Hydrological Sciences Journal, 58 (5), 1059–1071.     

Identification of optimal soil hydraulic functions and parameters for predicting soil moisture

Abstract

The accuracy of six combined methods formed by three commonly-used soil hydraulic functions and two methods to determine soil hydraulic parameters based on a soil hydraulic parameter look-up table and soil pedotransfer functions was examined for simulating soil moisture. A novel data analysis and modelling approach was used that eliminated the effects of evapotranspiration so that specific sources of error among the six combined methods could be identified and quantified. By comparing simulated and observed soil moisture at six sites of the USDA Soil Climate Analysis Network, we identified the optimal soil hydraulic functions and parameters for predicting soil moisture. Through sensitivity tests, we also showed that adjusting only the soil saturated hydraulic conductivity, K_s , is insufficient for representing important effects of macropores on soil hydraulic conductivity. Our analysis illustrates that, in general, soil hydraulic conductivity is less sensitive to K_s than to the soil pore-size distribution parameter.

Editor D. Koutsoyiannis; Associate editor D. Hughes

Citation Pan, F., McKane, R.B. and Stieglitz, M., 2012. Identification of optimal soil hydraulic functions and parameters for predicting soil moisture. Hydrological Sciences Journal, 57 (4), 723–737.     

Unsaturated flows in soils with self-similar hydraulic conductivity distribution

In this article, we are concerned with the statistics of steady unsaturated flow in soils with a fractal hydraulic conductivity distribution. It is assumed that the spatial distribution of log hydraulic conductivity can be described as an isotropic stochastic fractal process. The impact of the fractal dimension of this process, the soil pore-size distribution parameter, and the characteristic length scale on the variances of tension head and the effective conductivity is investigated. Results are obtained for one-dimensional and three-dimensional flows. Our results indicate that the tension head variance is scale-dependent for fractal distribution of hydraulic conductivity. Both tension head variance and effective hydraulic conductivity depend strongly on the fractal dimension. The soil pore-size distribution parameter is important in reducing the variability of the unsaturated hydraulic conductivity and of the fluxes.     

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.     

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].     

Factors affecting soil moisture spatial variability for a humid forest hillslope

Soil moisture is an important variable in explaining hydrological processes at hillslope scale. The distribution of soil moisture along a hillslope is related to the spatial distribution of the soil properties, the topography, the soil depth, and the vegetation. In order to investigate the factors affecting soil moisture, various environmental data were collected from a humid forest hillslope in this study. Several factors (the wetness index; the contributing area; the local slope; the soil depth; the composition of sand, silt, and clay; the scaling parameter; the hydraulic conductivity; the tree diameter at breast height; and the total weighted basal area) were evaluated for their effect on soil moisture and its distribution over the hillslope at depths of 10, 30, and 60 cm. Both linear correlation analysis and empirical orthogonal function analysis indicated that the soil texture was a dominant factor in soil moisture distribution. The impact of soil hydraulic conductivity was important for all soil moisture ranges at a depth of 30 cm, but those at 10 and 60 cm were limited to very wet and dry conditions, respectively. The relationships of the various factors with the spatial variability of soil moisture indicated the existence of a threshold soil moisture that is related to the composition of the soil and the factors related to the distribution of water in the study area.     

Similarity analysis and scaling: An application to soil infiltration properties

Similarity and scaling theory are applied to soil physics, specifically to several parameters of unsaturated soil water movement. Following a dimensional analysis of Richards' equation, a mechanical similarity criterion of the hydraulic parameters is developed. Dimensionless factors which conform to assumptions of kinematic and dynamic mechanical similarity in the flow system are converted to relations using the scale factor a derived under the assumption of geometric similarity. As an example, the infiltration process is assessed through scaling of the parameters in Philip's equation, using experimental data from double-ring infiltration measurements at 54 locations in a study catchment as the scaling test.     

Vulnerability of three spatially variable soil groups for solute leaching

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.     

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.     

Temporal stability of soil water content as affected by climate and soil hydraulic properties: a simulation study

Temporal stability of soil water content (TS SWC) is an often‐observed phenomenon, which characterization finds multiple applications. Climate and variability in soil properties are usually mentioned as factors of TS SWC, but their effects are far from clear. The objective of this work was to use SWC modeling to evaluate the effects of climate and soil hydraulic properties on the TS of soil water at different measurement schedules. We selected four representative climates found in USA and simulated the multiyear SWC dynamics for sandy loam, loam, and silty clay loam soils, all having the lognormal spatial distribution of the saturated hydraulic conductivity. The CLIMGEN and the HYDRUS6 codes were used to generate weather patterns and to simulate SWC, respectively. Four different methods were applied to select the representative location (RL). The low probability of having the same variability of mean relative differences of soil water under different climates was found in most of the cases. The probability that the variance of mean relative differences depended on sampling frequency was generally higher than 91% for the three soils. The interannual difference in mean relative differences variation from short and intensive summer campaigns was highly probable for all climates and soils. The RLs changed as climate and measurement scheduling changed, and they were less pronounced for coarse‐textured soils. The RL selection methods based solely on bias provided more consistency as compared with other methods. The TS appears to be the result of the interplay between climate, soil properties, and survey protocols. One implication of this factor interaction effect on TS SWC is that a simulation study can be useful to decide on the feasibility of including a search for TS‐based RLs for a specific site. Copyright © 2013 John Wiley & Sons, Ltd.     

Use of practical aspects of soil behaviour to evaluate different methods to generate soil hydraulic functions

Soil hydraulic functions can be obtained with methods that range from complex and costly to simple and cheap. Decisions as to which is the most appropriate method for a specific application have to be based on a comparison of generated hydraulic functions. This comparison should preferably be based on a statistical comparison of practical applications calculated with the different hydraulic functions rather than on a statistical comparison of the functions themselves. In this study four different methods were used to generate hydraulic functions: (A) direct on-site measurement, (B) measurement in soil horizons in the area, (C) use of a national data set, and (D) use of Van Genuchten parameters correlated with soil texture and organic matter content. The four methods were compared by their effect on two practical aspects of soil behaviour: (1) evapotranspiration deficit and (2) flux through a plane at 30 cm below soil surface. These two aspects are highly relevant for agricultural and environmental use. However, direct measurement is not feasible. A validated simulation model was used for the calculations and results obtained with method A were taken as a reference. Calculations were performed for three soil profiles for a period of seven years. Deficits and fluxes, calculated with the four methods to generate hydraulic functions, were not significantly different using the data of the seven-year period. However, methods were significantly different when rainfall deficits were used as a covariable. This is true with the exception of downward fluxes in the period October until March which are most important for leaching of pollutants. The user has to decide whether differences between methods are sufficiently large to justify repeated, expensive on-site measurements (method A) or whether an investment will be made to make standard series of curves to be used everywhere (methods C and D).     

Evaluation of site‐dependent constant‐damage design spectra for reinforced concrete structures

An investigation on the validity of the conventional design approach known as constant displacement ductility is carried out. The hysteretic behaviour described by the Modified Takeda model is taken to represent the characteristics of reinforced concrete structural systems. The results presented in the form of seismic damage spectra indicate that the conventional design approach may not be valid because cumulative damage is excessively high. The inelastic design spectra based on the constant‐damage concept are proposed in terms of simplified expressions. The expressions are derived from constant‐damage design spectra computed by non‐linear response analysis for SDOF systems subjected to ground motions recorded on rock sites, alluvium deposits, and soft‐soil sites. The proposed expressions, which are dependent on the local soil conditions, are functions of target seismic damage, displacement ductility ratio and period of vibration. The seismic damage of structures that have been designed based on this new design approach is also checked by a design‐and‐evaluation approach. The results are found to be satisfactory. Copyright © 2004 John Wiley & Sons, Ltd.     

Determination of soil hydrophysical characteristics in the Ivankovo Reservoir watershed

The capillary-sorption potential and the unsaturated hydraulic conductivity of soils as functions of soil water content are derived for forest, meadow, and agricultural ecosystems of the Ivankovo Reservoir watershed. The parameters of van Genuchten-Mualem equations were determined for the same soils based on data on soil particle size distribution and density. Computer code HYDRUS-1D and the obtained data were used to calculate the values of field capacity of soils in forest, meadow, and agricultural ecosystems in the drainage basin of the Ivankovo Reservoir.     

An effective scale-dependent dispersivity deduced from a purely convective flow field

Abstract

In the case of straight flow but with hydraulic conductivity varying in a transverse direction, the distribution of hydraulic conductivity has been determined for which the breakthrough curve due to convection only will have the same analytical form as the onedimensional convection/dispersion equation solution at the outlet end of a porous medium. That distribution is found exactly and it is very similar to the lognormal distribution. This result is significant since field evidence indicates that the logarithm of hydraulic conductivity is normally distributed. For the case considered, a simple relation between dispersivity and the coefficient of variation of hydraulic conductivity is found. One can thus determine very simply dispersivity in terms of the parameters of the distribution of hydraulic conductivity. This is particularly useful to estimate dispersivity in various cells of finite difference or finite element models when the distribution of hydraulic conductivity is not stationary, i.e. varies in space.     

ESTABLISHING TEMPORALLY AND SPATIALLY VARIABLE SOIL HYDRAULIC DATA FOR USE IN A RUNOFF SIMULATION IN A LOESS REGION OF THE NETHERLANDS

Soil hydraulic functions for runoff simulation were collected in three catchments in a loess region of The Netherlands. To obtain these functions each soil horizon was sampled and water retention and hydraulic conductivity characteristics were determined. A simulation with the computer program SWMS_2D was used to quantify runoff generation during standard rain events. Based on the simulation outcome, soil horizons were merged. This resulted in a database of 25 soil hydraulic functions, each representing a soil horizon or a specific condition of the top layer. Maps showing the soil physical composition of the area were constructed using these soil physical building blocks. The maps can be used as input for soil and water erosion models to be applied on the catchment scale. Comparison of potential runoff figures with measured data showed that the soil physical schematization appeared to be appropriate. The soil physical schem-atization in the areas studied was based on structural rather than on textural differences of the top soil.     

The scaling characteristics of soil parameters: From plot scale heterogeneity to subgrid parameterization

The variation in soil texture, surface moisture or vertical soil moisture gradient in larger scale atmospheric models may lead to significant variations in simulated surface fluxes of water and heat. The parameterization of soil moisture fluxes at spatial scales compatible with the grid size of distributed hydrological models and mesoscale atmospheric models ( 100 km²) faces principal problems which relate to the underlying microscopic or field scale heterogeneity in soil characteristics.

The most widely used parameterization in soil hydrology, the Darcy-Richards (DR) equation, is gaining increasing importance in mesoscale and climate modelling. This is mainly due to the need to introduce plant-interactive soil water depletion and stomatal conductance parameterizations and to improve the calculation of deep percolation and runoff. Covering a grid of several hundreds of square kilometres, the DR parameterization in soil-vegetation-atmosphere-transfer schemes (SVATs) is assumed to be scale-invariant. The parameters describing the non-linear, area-average soil hydraulic functions in this scale-invariant DR-equation should be treated as calibration-parameters, which do not necessarily have a physical meaning. The saturated hydraulic conductivity is one of the soil parameters to which the models show very high sensitivity. It is shown that saturated hydraulic conductivity can be scaled in both vertical and horizontal directions for large flow domains.

In this paper, a distinction is made between effective and aggregated soil parameters. Effective parameters are defined as area-average values or distributions over a domain with a single, distinct textural soil type. They can be obtained by scaling or inverse modelling. Aggregated soil parameters represent grid-domains with several textural soil types. In soil science dimensional methods have been developed to scale up soil hydraulic characteristics. With some specific assumptions, these techniques can be extrapolated from classical field-scale problems in soil heterogeneity to larger domains, compatible with the grid-size of large scale models. Particularly promising is the estimation of effective soil hydraulic parameters from area averaging measurements through inverse modelling of the unsaturated flow.

Techniques to scale and aggregate the soil characteristics presented in this paper qualify for direct or indirect use in large scale meteorological models. One of the interesting results is the effective behaviour of the reference curve, which can be obtained from similar media scaling. If the conclusions of this paper survive further studies, a relatively simple method will become available to parameterize soil variability at large scales. The inverse technique is found to provide effective soil parameters which perform well in predicting both the area-average evaporation and the area-average soil moisture fluxes, such as subsurface runoff. This is not the case for aggregated soil parameters. Obtained from regression relationships between soil textural composition and hydraulic characteristics, these aggregated parameters predict evaporation fluxes well, but fail to predict water balance terms such as percolation and runoff. This is a serious drawback which could eventually hamper the improvement of the representation of the hydrological cycle in mesoscale atmospheric models and in GCMs.     

On the consistency of the indirect lognormal correction

The indirect lognormal correction is a change-of-support model commonly used in geostatistical applications when dealing with additive variables, for which the upscaling amounts to arithmetic averaging. It was designed as a generalization of the lognormal correction that states the permanence of lognormality, but so far its internal consistency has not been proven in the general case. After a recall of the theoretical conditions that change-of-support models must honor, the concept of conventional income is introduced and used to establish the mathematical consistency of the indirect lognormal correction. However, the suitability of this model is questionable in many situations, in particular when the support effect is important or when the point-support distribution presents a zero effect, is not continuous or not positively skewed.Tel.: +56-2-672-3504, +56-2-678-4498     

A heuristic probabilistic approach to estimating size-dependent mobility of nonuniform sediment

This paper presents a heuristic probabilistic approach to estimating the size-dependent mobilities of nonuniform sediment based on the pre- and post-entrainment particle size distributions (PSDs), assuming that the PSDs are lognormally distributed. The approach fits a lognormal probability density function to the pre-entrainment PSD of bed sediment and uses the threshold particle size of incipient motion and the concept of sediment mixture to estimate the PSDs of the entrained sediment and post-entrainment bed sediment. The new approach is simple in physical sense and significantly reduces the complexity and computation time and resource required by detailed sediment mobility models. It is calibrated and validated with laboratory and field data by comparing to the size-dependent mobilities predicted with the existing empirical lognormal cumulative distribution function approach. The novel features of the current approach are: (1) separating the entrained and non-entrained sediments by a threshold particle size, which is a modified critical particle size of incipient motion by accounting for the mixed-size effects, and (2) using the mixture-based pre- and post-entrainment PSDs to provide a continuous estimate of the size-dependent sediment mobility.