Walter J. Rawls

Fractal models for predicting soil hydraulic properties: a review

Modern hydrological models require information on hydraulic conductivity and soil-water retention characteristics. The high cost and large spatial variability of measurements makes the prediction of these properties a viable alternative. Fractal models describe hierarchical systems and are suitable to model soil structure and soil hydraulic properties. Deterministic fractals are often used to model porous media in which scaling of mass, pore space, pore surface and the size-distribution of fragments are all characterized by a single fractal dimension. Experimental evidence shows fractal scaling of these properties between upper and lower limits of scale, but typically there is no coincidence in the values of the fractal dimensions characterizing different properties. This poses a problem in the evaluation of the contrasting approaches used to model soil-water retention and hydraulic conductivity. Fractal models of the soil-water retention curve that use a single fractal dimension often deviate from measurements at saturation and at dryness. More accurate models should consider scaling domains each characterized by a fractal dimension with different morphological interpretations. Models of unsaturated hydraulic conductivity incorporate fractal dimensions characterizing scaling of different properties including parameters representing connectivity. Further research is needed to clarify the morphological properties influencing the different scaling domains in the soil-water retention curve and unsaturated hydraulic conductivity. Methods to functionally characterize a porous medium using fractal approaches are likely to improve the predictability of soil hydraulic properties.

Generalized Richards' equation to simulate water transport in unsaturated soils

Simulations of water transport in soil are ubiquitous, and the Richards’ equation introduced in 1931 is the main tool for that purpose. For experiments on water transport in soil horizontal columns, Richards’ equation predicts that volumetric water contents should depend solely on the ratio (distance)/(time) q where q ¼ 0:5: Substantial experimental evidence shows that value of q is significantly less than 0.5 in some cases. Donald Nielsen and colleagues in 1962 related values of q , 0.5 to ‘jerky movements’ of the wetting front, i.e. occurrences of rare large movements. The physical model of such transport is the transport of particles being randomly trapped and having a power law distribution of waiting periods. The corresponding mathematical model is a generalized Richards’ equation in which the derivative of water content on time is a fractional one with the order equal or less than one. We solved this equation numerically and fitted the solution to data on horizontal water transport. The classical Richards’ equation predicted a decrease of the soil water diffusivity for the same water content as infiltration progressed whereas the generalized Richards’ equation described all observations well with a single diffusivity function. Validity of the generalized Richards’ equation indicates presence of memory effects in soil water transport phenomena and may help to explain scale-dependence and variability in soil hydraulic conductivity encountered by researchers who applied classical Richards’ equation. Published by Elsevier Science B.V.

Using field topographic descriptors to estimate soil water retention

In field-, watershed-, and regional-scale projects, soil water retention is often estimated from soil textural classes shown in soil maps. The textural classes are relatively broad, often only the dominating textural class is shown, cartographers routinely use error-prone field judgments of soil texture, and soil texture is known to vary along slopes and to depend on the land surface shape. We, therefore, hypothesized that including topographic information in water retention estimation would increase accuracy. To test this hypothesis, we extracted data on 216 soil pedons for soils of moderate and large extent from the Natural Resources Conservation Service (NRCS) soil characterization database. Textural classes, genetic horizon numbers, slopes, position on the slope classes, and land surface shape classes were the field descriptors that we used to estimate water retention at −33 and −1500 kPa potentials for each horizon in each pedon. Because our input variables were both categorical and continuous, regression trees were used for subdividing the samples into the smallest number of the most homogeneous groups, which we tentatively called topotextural groups (TTG). The jackknife cross-validation was used to prune the regression trees to prevent overparameterization. Ten or fewer TTGs were defined for both the −33 and the −1500 kPa retention. The TTGs were different for the two matric potential levels. Using topographic variables and soil horizon seemed to be the most accurate way to make up for errors made in field determination of texture. For the A horizon, the topotextural grouping resulted in estimates that were more accurate than those using laboratory textures only. Although most of the topographic variables in this work are categorical, those variables seemed to be useful for improving estimates of water retention.

Statistical properties of soil moisture images revisited

Data from passive microwave remote sensing with an ESTAR L-band radiometer, deployed on an aircraft, were used to produce soil moisture images over the area of the Little Washita watershed in Oklahoma in 1992. This area was revisited during the Southern Great Plains 1997 Hydrology Experiment. This offered an opportunity to evaluate the time-specificity of the conclusions, relating to scaling of the surface soil moisture, that have been reported for 1992. The objective of this work was to compare scaling properties of soil moisture fields observed in 1992 and 1997. We analyzed one 1992 data set and three 1997 data sets, each covering several days of continuous drydown. Different resolutions were introduced by aggregating the pixels of original 200-m resolution into bigger square cells. Scaling in dependencies on resolution was observed for the variance of moisture content, for the within-cell variance, and for the first six moments about zero, the latter indicating multiscaling. Parameters of the scaling equations differed among four drying periods studied. However, once a scaling dependency on resolution was established in the beginning of a drying period, its shape was maintained during the drydown both in 1992 and 1997. Slopes of the dependencies changed only slightly, whereas the intercepts decreased as the drying progressed. Having constant slopes and intercepts dependent on average area water contents gives an opportunity to reduce the volume of observations needed to predict scaling of surface soil moisture during drydowns.

Scaling properties of saturated hydraulic conductivity in soil

Abstract Variability of saturated hydraulic conductivity, k sat , increases when sample size decreases implying that saturated water flow might be a scaling process. The moments of scaling distributions observed at different resolutions can be related by a power-law function, with the exponent being a single value (simple scaling) or a function (mutiscaling). Our objective was to investigate scaling characteristics of k sat using the method of the moments applied to measurements obtained with different sample sizes. We analyzed three data sets of k sat measured in: (1) cores with small diameter and increasing length spanning a single soil horizon, (2) columns with increasing cross sectional area and constant length, and (3) columns with increasing cross sectional area and length, the longest column spanning three soil horizons. Visible porosity (macroporosity) was traced on acetate transparency sheets prior to measurement of k sat in situation (2). Six moments were calculated assuming that observations followed normal ( k sat , macroporosity) and/or log-normal ( k sat ) distributions. Scaling of k sat was observed in all three data sets. Simple scaling was only found when flux occurred in small cross sectional areas of a simple soil horizon (data set (1)). Multiscaling of k sat distributions was found when larger soil volumes were involved in the flux process (data sets (2) and (3)). Moments of macroporosity distributions showed multiscaling characteristics, with exponents similar to those from ln k sat distributions. The scaling characteristics of k sat reported in this paper agree with similar results found at larger scales using semivariograms. Scaling exponents from the semivariogram and the moment techniques could be complemented, as demonstrated by the agreement between macroporosity scaling exponents found with both techniques.

Software data news: Software to estimate -33 and -1500kPa soil water retention using the non-parametric k-Nearest Neighbor technique

A computer tool has been developed that uses a k-Nearest Neighbor (k-NN) lazy learning algorithm to estimate soil water retention at -33 and -1500kPa matric potentials and its uncertainty. The user can customize the provided source data collection to accommodate specific local needs. Ad hoc calculations make this technique a competitive alternative to publish pedotransfer equations, as re-development of such equations is not needed when new data become available.

Impact of roots on ground water quality

Preferential flow is perhaps the major chemical transport process influencing the rapid and typically unexpected movement of agricultural chemicals to ground water. Plant roots are a major contributor to preferential flow mechanics as they form spatial voids which can be used as preferential flow pathways. Chemical transport of atrazine, deethylatrazine, and bromide solutions concentrations under tilled and no-tilled corn fields was evaluated below the active root zone. Additionally, the impact of roots on flow pathways was visualized using a soluble dye (Brilliant Blue FCF). Pictures of the dye-stained pattern were subsequently digitized to determine the cross-sectional area used for transport as a function of depth. Bromide transit times through the field soils were not influenced by tillage practice, whereas atrazine transport was strongly influenced by tillage practice. Under no-till field conditions, atrazine was rarely detected but deethylatrazine concentrations were greater than those observed under tilled field conditions. Visual observation indicated that the dye under no-tillage was more predominant in the corn row, indicative of transport through void root channels. No-tillage practices may decrease the likelihood of ground water contamination through leaching due to the formation of stable root channels where an organic carbon source and microbial population are preferentially located to degrade pesticides.

Effect of soil organic carbon on soil hydraulic properties

Publisher Summary The primary soil hydraulic properties that soil organic carbon affects are porosity, soil water retention, and hydraulic conductivity. This chapter discusses the effect of organic carbon or organic matter on these properties and explains the way these effects can be incorporated into pedotransfer functions (PTFs). The sensitivity of water retention to changes in organic carbon content decreases as the initial organic carbon content increases. A similar conclusion can be drawn from the equations presented for water retention of soils amended with the organic waste in soils in the United States, England, India, and Germany. In a study discussed in the chapter, the reduction of the effect of increasing organic carbon content on water content at −5 kPa with the increase in the original value of the organic carbon content was reported. Water retention of peat soils presents a limit case for the increase of organic carbon content in samples. Soil-survey databases contain data on soils in natural ecosystems and on agricultural soils showing similar responses of soil water retention to changes in organic carbon content. Modeling of the changes of organic carbon content in soils and related changes in ecosystem productivity attracts significant attention with regard to climate changes and management changes. Existing models lack the feedback effect of organic carbon content accumulation on water retention and saturated hydraulic conductivity. Results presented in the chapter can be used in those models to improve their predictive ability.

SOIL TEXTURE AND PARTICLE-SIZE DISTRIBUTION AS INPUT TO ESTIMATE SOIL HYDRAULIC PROPERTIES

Publisher Summary This chapter provides an overview on the way soil texture can be characterized and described, the way those data are considered in different pedotransfer functions (PTFs), and the methods that can be used to fill in missing data required by some PTFs. It also presents a study that compares different representations of soil particle-size distribution (PSD) in estimating soil water retention. Textural classification of soils is based on particle-size analyses in most parts of the world. A number of standards exist internationally for the description of soil PSD and particle-size classes. Soil texture classes are defined based on sand, silt, and clay content limits and are usually displayed in soil texture diagrams. Even when the same particle-size class system is used, texture class definitions may differ. Soil-texture-class information is primarily used as input to class PTFs. A class PTF does not use detailed particle-size data as input but gives calculated, usually averaged, values of the output variable in a tabular format for each soil class/unit. Detailed PSD and/or parameters derived from it are used in almost all PTFs. The chapter compares the usefulness of some of the most common representations of PSD in estimating water retention at -−10, −33, and −1500 kPa and the available water content (AWC) of the soil, which is defined as the difference between water contents at −33 and −1500 kPa matric potentials. To relate the above soil hydraulic properties to soil texture, a number of PTFs are developed using three databases and the group method of data handling (GMDH). The GMD and its standard deviation are also used as predictors.

Prediction of A pore distribution factor from soil textural and mechanical parameters

Soil-water retention properties (WRC) are required for modeling purposes, but data availability is restricted by the high cost of measurements. Prediction of WRC from particle size distribution (PSD) is a useful approach that could be improved by accounting for soil structure. Mechanical parameters can characterize soil structure in situ. Our objective was to use mechanical and PSD parameters to estimate a pore distribution factor, λ, from a power-law model of WRC. Samples for WRC and PSD determinations were taken in pre-wetted horizons after characterization of soil structure with multiple measurements of a single-vane shear test (SB) and penetration resistance (PR). Mechanical parameters were the mean, M, and standard deviation, σ, of SB and PR. Parameters characterizing a PSD were the power exponent of a cumulative exponential function, β; the geometric mean, μ(r) = eμln(r) and standard deviation, σln(r), of a log-normal distribution; and clay content. Models of λ were built with the Group Method of Data Handling (GMDH) first using textural and mechanical parameters separately and then using each textural variable with all mechanical parameters. Both μ(r) and σln(r) were consistently selected as the best textural estimators of λ. The best mechanical estimators were log(MSB) and σSB. In models that included textural and mechanical parameters, σPR was selected consistently regardless of the textural parameter used. Textural parameters were better predictors than mechanical parameters, even though the latter alone provided a reasonable estimate of λ. Mechanical parameters improved textural estimates of λ only when clay content was used to characterize a PSD.