Modeling water movement in horizontal columns using fractal theory

Fractal mathematics has been used to characterize water and solute transport in porous media and also to characterize and simulate porous media properties. The objective of this study was to evaluate the correlation between the soil infiltration parameters sorptivity (S) and time exponent (n) and the parameters dimension (D) and the Hurst exponent (H). For this purpose, ten horizontal columns with pure (either clay or loam) and heterogeneous porous media (clay and loam distributed in layers in the column) were simulated following the distribution of a deterministic Cantor Bar with fractal dimension H" 0.63. Horizontal water infiltration experiments were then simulated using Hydrus 2D software. The sorptivity (S) and time exponent (n) parameters of the Philip equation were estimated for each simulation, using the nonlinear regression procedure of the statistical software package SAS®. Sorptivity increased in the columns with the loam content, which was attributed to the relation of S with the capillary radius. The time exponent estimated by nonlinear regression was found to be less than the traditional value of 0.5. The fractal dimension estimated from the Hurst exponent was 17.5 % lower than the fractal dimension of the Cantor Bar used to generate the columns.

Selecting statistical models to study the relationship between soybean yield and soil physical properties

Statistical models allow the representation of data sets and the estimation and/or prediction of the behavior of a given variable through its interaction with the other variables involved in a phenomenon. Among other different statistical models, are the autoregressive state-space models (ARSS) and the linear regression models (LR), which allow the quantification of the relationships among soil-plant-atmosphere system variables. To compare the quality of the ARSS and LR models for the modeling of the relationships between soybean yield and soil physical properties, Akaike's Information Criterion, which provides a coefficient for the selection of the best model, was used in this study. The data sets were sampled in a Rhodic Acrudox soil, along a spatial transect with 84 points spaced 3 m apart. At each sampling point, soybean samples were collected for yield quantification. At the same site, soil penetration resistance was also measured and soil samples were collected to measure soil bulk density in the 0-0.10 m and 0.10-0.20 m layers. Results showed autocorrelation and a cross correlation structure of soybean yield and soil penetration resistance data. Soil bulk density data, however, were only autocorrelated in the 0-0.10 m layer and not cross correlated with soybean yield. The results showed the higher efficiency of the autoregressive space-state models in relation to the equivalent simple and multiple linear regression models using Akaike's Information Criterion. The resulting values were comparatively lower than the values obtained by the regression models, for all combinations of explanatory variables.

Numerical modeling of the effect of variation of boundary conditions on vadose zone hydraulic properties

An accurate estimation of hydraulic fluxes in the vadose zone is essential for the prediction of water, nutrient and contaminant transport in natural systems. The objective of this study was to simulate the effect of variation of boundary conditions on the estimation of hydraulic properties (i.e. water content, effective unsaturated hydraulic conductivity and hydraulic flux) in a one-dimensional unsaturated flow model domain. Unsaturated one-dimensional vertical water flow was simulated in a pure phase clay loam profile and in clay loam interlayered with silt loam distributed according to the third iteration of the Cantor Bar fractal object Simulations were performed using the numerical model Hydrus 1D. The upper and lower pressure heads were varied around average values of -55 cm for the near-saturation range. This resulted in combinations for the upper and lower constant head boundary conditions, respectively, of -50 and -60 cm, -40 and -70 cm, -30 and -80 cm, -20 and -90 cm, and -10 and -100 cm. For the drier range the average head between the upper and lower boundary conditions was set to -550 cm, resulting in the combinations -500 and -600 cm, -400 and -700 cm, -300 and -800 cm, -200 and -900 cm, and -100 and -1,000 cm, for upper and lower boundary conditions, respectively. There was an increase in water contents, fluxes and hydraulic conductivities with the increase in head difference between boundary conditions. Variation in boundary conditions in the pure phase and interlayered one-dimensional profiles caused significant deviations in fluxes, water contents and hydraulic conductivities compared to the simplest case (a head difference between the upper and lower constant head boundaries of 10 cm in the wetter range and 100 cm in the drier range).

Method to estimate soil macroporosity and microporosity based on sand content and bulk density

Macroporosity is often used in the determination of soil compaction. Reduced macroporosity can lead to poor drainage, low root aeration and soil degradation. The aim of this study was to develop and test different models to estimate macro and microporosity efficiently, using multiple regression. Ten soils were selected within a large range of textures: sand (Sa) 0.07-0.84; silt 0.03-0.24; clay 0.13-0.78 kg kg-1 and subjected to three compaction levels (three bulk densities, BD). Two models with similar accuracy were selected, with a mean error of about 0.02 m³ m-3 (2 %). The model y = a + b.BD + c.Sa, named model 2, was selected for its simplicity to estimate Macro (Ma), Micro (Mi) or total porosity (TP): Ma = 0.693 - 0.465 BD + 0.212 Sa; Mi = 0.337 + 0.120 BD - 0.294 Sa; TP = 1.030 - 0.345 BD 0.082 Sa; porosity values were expressed in m³ m-3; BD in kg dm-3; and Sa in kg kg-1. The model was tested with 76 datum set of several other authors. An error of about 0.04 m³ m-3 (4 %) was observed. Simulations of variations in BD as a function of Sa are presented for Ma = 0 and Ma = 0.10 (10 %). The macroporosity equation was remodeled to obtain other compaction indexes: a) to simulate maximum bulk density (MBD) as a function of Sa (Equation 11), in agreement with literature data; b) to simulate relative bulk density (RBD) as a function of BD and Sa (Equation 13); c) another model to simulate RBD as a function of Ma and Sa (Equation 16), confirming the independence of this variable in relation to Sa for a fixed value of macroporosity and, also, proving the hypothesis of Hakansson & Lipiec that RBD = 0.87 corresponds approximately to 10 % macroporosity (Ma = 0.10 m³ m-3).

Modeling changes in organic carbon stocks for distinct soils in southeastern brazil after four eucalyptus rotations using the century model

Soil organic matter (SOM) plays an important role in carbon (C) cycle and soil quality. Considering the complexity of factors that control SOM cycling and the long time it usually takes to observe changes in SOM stocks, modeling constitutes a very important tool to understand SOM cycling in forest soils. The following hypotheses were tested: (i) soil organic carbon (SOC) stocks would be higher after several rotations of eucalyptus than in low-productivity pastures; (ii) SOC values simulated by the Century model would describe the data better than the mean of observations. So, the aims of the current study were: (i) to evaluate the SOM dynamics using the Century model to simulate the changes of C stocks for two eucalyptus chronosequences in the Rio Doce Valley, Minas Gerais State, Brazil; and (ii) to compare the C stocks simulated by Century with the C stocks measured in soils of different Orders and regions of the Rio Doce Valley growing eucalyptus. In Belo Oriente (BO), short-rotation eucalyptus plantations had been cultivated for 4.0; 13.0, 22.0, 32.0 and 34.0 years, at a lower elevation and in a warmer climate, while in Virginópolis (VG), these time periods were 8.0, 19.0 and 33.0 years, at a higher elevation and in a milder climate. Soil samples were collected from the 0-20 cm layer to estimate C stocks. Results indicate that the C stocks simulated by the Century model decreased after 37 years of poorly managed pastures in areas previously covered by native forest in the regions of BO and VG. The substitution of poorly managed pastures by eucalyptus in the early 1970´s led to an average increase of C of 0.28 and 0.42 t ha-1 year-1 in BO and VG, respectively. The measured C stocks under eucalyptus in distinct soil Orders and independent regions with variable edapho-climate conditions were not far from the values estimated by the Century model (root mean square error - RMSE = 20.9; model efficiency - EF = 0.29) despite the opposite result obtained with the statistical procedure to test the identity of analytical methods. Only for lower soil C stocks, the model over-estimated the C stock in the 0-20 cm layer. Thus, the Century model is highly promising to detect changes in C stocks in distinct soil orders under eucalyptus, as well as to indicate the impact of harvest residue management on SOM in future rotations.

Chronofunctions of Heilu soil developed from Loess in Luochuan, on the chinese Loess plateau

Soil chronofunctions are an alternative for the quantification of soil-forming processes and underlie the modeling of soil genesis. To establish soil chronofunctions of a Heilu soil profile on Loess in Luochuan, selected soil properties and the 14C ages in the Holocene were studied. Linear, logarithmic, and third-order polynomial functions were selected to fit the relationships between soil properties and ages. The results indicated that third-order polynomial function fit best for the relationships between clay (< 0.002 mm), silt (0.002-0.02 mm), sand (0.02-2 mm) and soil ages, and a trend of an Ah horizon ocurrence in the profile. The logarithmic function indicated mainly variations of soil organic carbon and pH with time (soil age). The variation in CaCO3 content, Mn/Zr, Fe/Zr, K/Zr, Mg/Zr, Ca/Zr, P/Zr, and Na/Zr ratios with soil age were best described by three-order polynomial functions, in which the trend line showed migration of CaCO3 and some elements.

Local influence for spatial analysis of soil physical properties and soybean yield using student's t-distribution

The modeling and estimation of the parameters that define the spatial dependence structure of a regionalized variable by geostatistical methods are fundamental, since these parameters, underlying the kriging of unsampled points, allow the construction of thematic maps. One or more atypical observations in the sample data can affect the estimation of these parameters. Thus, the assessment of the combined influence of these observations by the analysis of Local Influence is essential. The purpose of this paper was to propose local influence analysis methods for the regionalized variable, given that it has n-variate Student's t-distribution, and compare it with the analysis of local influence when the same regionalized variable has n-variate normal distribution. These local influence analysis methods were applied to soil physical properties and soybean yield data of an experiment carried out in a 56.68 ha commercial field in western Paraná, Brazil. Results showed that influential values are efficiently determined with n-variate Student's t-distribution.

Soil infiltration based on bp neural network and grey relational analysis

Soil infiltration is a key link of the natural water cycle process. Studies on soil permeability are conducive for water resources assessment and estimation, runoff regulation and management, soil erosion modeling, nonpoint and point source pollution of farmland, among other aspects. The unequal influence of rainfall duration, rainfall intensity, antecedent soil moisture, vegetation cover, vegetation type, and slope gradient on soil cumulative infiltration was studied under simulated rainfall and different underlying surfaces. We established a six factor-model of soil cumulative infiltration by the improved back propagation (BP)-based artificial neural network algorithm with a momentum term and self-adjusting learning rate. Compared to the multiple nonlinear regression method, the stability and accuracy of the improved BP algorithm was better. Based on the improved BP model, the sensitive index of these six factors on soil cumulative infiltration was investigated. Secondly, the grey relational analysis method was used to individually study grey correlations among these six factors and soil cumulative infiltration. The results of the two methods were very similar. Rainfall duration was the most influential factor, followed by vegetation cover, vegetation type, rainfall intensity and antecedent soil moisture. The effect of slope gradient on soil cumulative infiltration was not significant.

Soil thermal diffusivity estimated from data of soil temperature and single soil component properties

Under field conditions, thermal diffusivity can be estimated from soil temperature data but also from the properties of soil components together with their spatial organization. We aimed to determine soil thermal diffusivity from half-hourly temperature measurements in a Rhodic Kanhapludalf, using three calculation procedures (the amplitude ratio, phase lag and Seemann procedures), as well as from soil component properties, for a comparison of procedures and methods. To determine thermal conductivity for short wave periods (one day), the phase lag method was more reliable than the amplitude ratio or the Seemann method, especially in deeper layers, where temperature variations are small. The phase lag method resulted in coherent values of thermal diffusivity. The method using properties of single soil components with the values of thermal conductivity for sandstone and kaolinite resulted in thermal diffusivity values of the same order. In the observed water content range (0.26-0.34 m³ m-3), the average thermal diffusivity was 0.034 m² d-1 in the top layer (0.05-0.15 m) and 0.027 m² d-1 in the subsurface layer (0.15-0.30 m).

Fuzzy logic applied to the modeling of water dynamics in an Oxisol in northeastern Brazil

Modeling of water movement in non-saturated soil usually requires a large number of parameters and variables, such as initial soil water content, saturated water content and saturated hydraulic conductivity, which can be assessed relatively easily. Dimensional flow of water in the soil is usually modeled by a nonlinear partial differential equation, known as the Richards equation. Since this equation cannot be solved analytically in certain cases, one way to approach its solution is by numerical algorithms. The success of numerical models in describing the dynamics of water in the soil is closely related to the accuracy with which the water-physical parameters are determined. That has been a big challenge in the use of numerical models because these parameters are generally difficult to determine since they present great spatial variability in the soil. Therefore, it is necessary to develop and use methods that properly incorporate the uncertainties inherent to water displacement in soils. In this paper, a model based on fuzzy logic is used as an alternative to describe water flow in the vadose zone. This fuzzy model was developed to simulate the displacement of water in a non-vegetated crop soil during the period called the emergency phase. The principle of this model consists of a Mamdani fuzzy rule-based system in which the rules are based on the moisture content of adjacent soil layers. The performances of the results modeled by the fuzzy system were evaluated by the evolution of moisture profiles over time as compared to those obtained in the field. The results obtained through use of the fuzzy model provided satisfactory reproduction of soil moisture profiles.

Plant-available soil water capacity: estimation methods and implications

The plant-available water capacity of the soil is defined as the water content between field capacity and wilting point, and has wide practical application in planning the land use. In a representative profile of the Cerrado Oxisol, methods for estimating the wilting point were studied and compared, using a WP4-T psychrometer and Richards chamber for undisturbed and disturbed samples. In addition, the field capacity was estimated by the water content at 6, 10, 33 kPa and by the inflection point of the water retention curve, calculated by the van Genuchten and cubic polynomial models. We found that the field capacity moisture determined at the inflection point was higher than by the other methods, and that even at the inflection point the estimates differed, according to the model used. By the WP4-T psychrometer, the water content was significantly lower found the estimate of the permanent wilting point. We concluded that the estimation of the available water holding capacity is markedly influenced by the estimation methods, which has to be taken into consideration because of the practical importance of this parameter.

Assessment of pedotransfer functions for estimating soil water retention curves for the amazon region

Knowledge of the soil water retention curve (SWRC) is essential for understanding and modeling hydraulic processes in the soil. However, direct determination of the SWRC is time consuming and costly. In addition, it requires a large number of samples, due to the high spatial and temporal variability of soil hydraulic properties. An alternative is the use of models, called pedotransfer functions (PTFs), which estimate the SWRC from easy-to-measure properties. The aim of this paper was to test the accuracy of 16 point or parametric PTFs reported in the literature on different soils from the south and southeast of the State of Pará, Brazil. The PTFs tested were proposed by Pidgeon (1972), Lal (1979), Aina & Periaswamy (1985), Arruda et al. (1987), Dijkerman (1988), Vereecken et al. (1989), Batjes (1996), van den Berg et al. (1997), Tomasella et al. (2000), Hodnett & Tomasella (2002), Oliveira et al. (2002), and Barros (2010). We used a database that includes soil texture (sand, silt, and clay), bulk density, soil organic carbon, soil pH, cation exchange capacity, and the SWRC. Most of the PTFs tested did not show good performance in estimating the SWRC. The parametric PTFs, however, performed better than the point PTFs in assessing the SWRC in the tested region. Among the parametric PTFs, those proposed by Tomasella et al. (2000) achieved the best accuracy in estimating the empirical parameters of the van Genuchten (1980) model, especially when tested in the top soil layer.

Comparing the artificial neural network with parcial least squares for prediction of soil organic carbon and pH at different moisture content levels using visible and near-infrared spectroscopy

Visible and near infrared (vis-NIR) spectroscopy is widely used to detect soil properties. The objective of this study is to evaluate the combined effect of moisture content (MC) and the modeling algorithm on prediction of soil organic carbon (SOC) and pH. Partial least squares (PLS) and the Artificial neural network (ANN) for modeling of SOC and pH at different MC levels were compared in terms of efficiency in prediction of regression. A total of 270 soil samples were used. Before spectral measurement, dry soil samples were weighed to determine the amount of water to be added by weight to achieve the specified gravimetric MC levels of 5, 10, 15, 20, and 25 %. A fiber-optic vis-NIR spectrophotometer (350-2500 nm) was used to measure spectra of soil samples in the diffuse reflectance mode. Spectra preprocessing and PLS regression were carried using Unscrambler® software. Statistica® software was used for ANN modeling. The best prediction result for SOC was obtained using the ANN (RMSEP = 0.82 % and RPD = 4.23) for soil samples with 25 % MC. The best prediction results for pH were obtained with PLS for dry soil samples (RMSEP = 0.65 % and RPD = 1.68) and soil samples with 10 % MC (RMSEP = 0.61 % and RPD = 1.71). Whereas the ANN showed better performance for SOC prediction at all MC levels, PLS showed better predictive accuracy of pH at all MC levels except for 25 % MC. Therefore, based on the data set used in the current study, the ANN is recommended for the analyses of SOC at all MC levels, whereas PLS is recommended for the analysis of pH at MC levels below 20 %.

BEYOND THE “LEAST LIMITING WATER RANGE”: RETHINKING SOIL PHYSICS RESEARCH IN BRAZIL

As opposed to objective definitions in soil physics, the subjective term “soil physical quality” is increasingly found in publications in the soil physics area. A supposed indicator of soil physical quality that has been the focus of attention, especially in the Brazilian literature, is the Least Limiting Water Range (RLL), translated in Portuguese as "Intervalo Hídrico Ótimo" or IHO. In this paper the four limiting water contents that define RLLare discussed in the light of objectively determinable soil physical properties, pointing to inconsistencies in the RLLdefinition and calculation. It also discusses the interpretation of RLL as an indicator of crop productivity or soil physical quality, showing its inability to consider common phenological and pedological boundary conditions. It is shown that so-called “critical densities” found by the RLL through a commonly applied calculation method are questionable. Considering the availability of robust models for agronomy, ecology, hydrology, meteorology and other related areas, the attractiveness of RLL as an indicator to Brazilian soil physicists is not related to its (never proven) effectiveness, but rather to the simplicity with which it is dealt. Determining the respective limiting contents in a simplified manner, relegating the study or concern on the actual functioning of the system to a lower priority, goes against scientific construction and systemic understanding. This study suggests a realignment of the research in soil physics in Brazil with scientific precepts, towards mechanistic soil physics, to replace the currently predominant search for empirical correlations below the state of the art of soil physics.

Surface Complexation Modeling in Variable Charge Soils: Charge Characterization by Potentiometric Titration

ABSTRACT Intrinsic equilibrium constants of 17 representative Brazilian Oxisols were estimated from potentiometric titration measuring the adsorption of H+ and OH− on amphoteric surfaces in suspensions of varying ionic strength. Equilibrium constants were fitted to two surface complexation models: diffuse layer and constant capacitance. The former was fitted by calculating total site concentration from curve fitting estimates and pH-extrapolation of the intrinsic equilibrium constants to the PZNPC (hand calculation), considering one and two reactive sites, and by the FITEQL software. The latter was fitted only by FITEQL, with one reactive site. Soil chemical and physical properties were correlated to the intrinsic equilibrium constants. Both surface complexation models satisfactorily fit our experimental data, but for results at low ionic strength, optimization did not converge in FITEQL. Data were incorporated in Visual MINTEQ and they provide a modeling system that can predict protonation-dissociation reactions in the soil surface under changing environmental conditions.