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.

Invariant Solutions of Richards' Equation for Water Movement in Dissimilar Soils

Scaling methods allow a single solution to Richards' equation (RE) to suffice for numerous specific cases of water flow in unsaturated soils. During the past half-century, many such methods were developed for similar soils. In this paper, a new method is proposed for scaling RE for a wide range of dissimilar soils. Exponential-power (EP) functions are used to reduce the dependence of the scaled RE on the soil hydraulic properties. To evaluate the proposed method, the scaled RE was solved numerically considering two test cases: infiltration into relatively dry soils having initially uniform water content distributions, and gravity-dominant drainage occurring from initially wet soil profiles. Although the results for four texturally different soils ranging from sand to heavy clay (adopted from the UNSODA database) showed that the scaled solution were invariant for a wide range of flow conditions, slight deviations were observed when the soil profile was initially wet in the infiltration case or deeply wet in the drainage case. The invariance of the scaled RE makes it possible to generalize a single solution of RE to many dissimilar soils and conditions. Such a procedure reduces the numerical calculations and provides additional opportunities for solving the highly nonlinear RE for unsaturated water flow in soils.

Water levels in selected wells and directions of ground-water movement near Fort Hall, Fort Hall Indian Reservation, Southeastern Idaho /

Mode of access: Internet.

Ground water movement in a rectangular aquifer bounded by four canals /

Mode of access: Internet.

FRACTAL CHARACTERISTICS OF THE HORIZONTAL MOVEMENT OF WATER IN SOILS

Observed deviations from traditional concepts of soil-water movement are considered in terms of fractals. A connection is made between this movement and a Brownian motion, a random and self-affine type of fractal, to account for the soil-water diffusivity function having auxiliary time dependence for unsaturated soils. The position of a given water content is directly proportional to t(n), where t is time, and exponent n for distinctly unsaturated soil is less than the traditional 0.50. As water saturation is approached, n approaches 0.50. Macroscopic fractional Brownian motion is associated with n < 0.50, but shifts to regular Brownian motion for n = 0.50.

Extraction of soil water by plants: development and validation of a model

A quantitative model of water movement within the immediate vicinity of an individual root is developed and results of an experiment to validate the model are presented. The model is based on the assumption that the amount of water transpired by a plant in a certain period is replaced by an equal volume entering its root system during the same time. The model is based on the Darcy-Buckingham equation to calculate the soil water matric potential at any distance from a plant root as a function of parameters related to crop, soil and atmospheric conditions. The model output is compared against measurements of soil water depletion by rice roots monitored using γ-beam attenuation in a greenhouse of the Escola Superior de Agricultura "Luiz de Queiroz"/Universidade de São Paulo(ESALQ/USP) in Piracicaba, State of São Paulo, Brazil, in 1993. The experimental results are in agreement with the output from the model. Model simulations show that a single plant root is able to withdraw water from more than 0.1 m away within a few days. We therefore can assume that root distribution is a less important factor for soil water extraction efficiency.

Contribution of macroporosity to water flux of a soil under different tillage systems

In view of the importance of the macroporosity for the water transport properties of soils, its quantitative assessment is a challenging task. Measurements of hydraulic conductivity (K) at different soil water tensions and the quantification of water-conducting macropores (θM) of a soil under different tillage systems could help understand the effects on the soil porous system and related hydraulic properties. The purpose of this study was to assess the effects of Conventional Tillage (CT), Chisel Plow (CP) and No Tillage (NT) on θM and on K; and to quantify the contribution of macroporosity to total water flux in a loam soil. A tension disc infiltrometer was used at two soil water pressure heads (-5 cm, and 0) to infer θM and K, during fallow. Macroporosity was determined based on the flow contribution between 0 and -5 cm water potentials (K0, K5, respectively), according to the Hagen-Poiseuille equation. The K0 values were statistically higher for CT than for NT and CP. The K5 values did not differ statistically among treatments. The mean K values varied between 0.20 and 3.70 cm/h. For CT, θM was significantly greater than for CP and NT, following the same trend as K0. No differences in θM were detected between CP and NT. With CT, the formation of water-conducting macropores with persistence until post-harvest was possible, while under CP preparation, the water-conducting macropores were not persistent. These results support the idea that tillage affects the soil water movement mainly by the resulting water-conducting macropores. Future studies on tillage effects on water movement should focus on macroporosity.

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.

Evaluation of a computer model to simulate water table response to subirrigation

The objective of this work was to evaluate the water flow computer model, WATABLE, using experimental field observations on water table management plots from a site located near Hastings, FL, USA. The experimental field had scale drainage systems with provisions for subirrigation with buried microirrigation and conventional seepage irrigation systems. Potato (Solanum tuberosum L.) growing seasons from years 1996 and 1997 were used to simulate the hydrology of the area. Water table levels, precipitation, irrigation and runoff volumes were continuously monitored. The model simulated the water movement from a buried microirrigation line source and the response of the water table to irrigation, precipitation, evapotranspiration, and deep percolation. The model was calibrated and verified by comparing simulated results with experimental field observations. The model performed very well in simulating seasonal runoff, irrigation volumes, and water table levels during crop growth. The two-dimensional model can be used to investigate different irrigation strategies involving water table management control. Applications of the model include optimization of the water table depth for each growth stage, and duration, frequency, and rate of irrigation.

Subsurface drip irrigation emitter spacing effects on soil water redistribution, corn yield and water productivity

Emitter spacings of 0.3 to 0.6 m are commonly used for subsurface drip irrigation (SDI) of corn on the deep, silt loam soils of the U.S. Great Plains. Subsurface drip irrigation emitter spacings of 0.3, 0.6, 0.9 and 1.2 m were examined for the resulting differences in soil water redistribution, corn grain yield, yield components, seasonal water use, and water productivity in a 4‐year field study (2005 through 2008) at the Kansas State University Northwest Research‐Extension Center, Colby, Kansas. The results indicate that there is increased preferential water movement along the dripline (parallel) as compared to perpendicular to the dripline and that this phenomenon partially compensates for wider emitter spacings in terms of soil water redistribution. Corn yield and water productivity (WP) were not significantly affected by the emitter spacing with application of a full irrigation regime

Subsurface drip irrigation emitter spacing effects on soil water redistribution, corn yield and water productivity

Emitter spacings of 0.3 to 0.6 m are commonly used for subsurface drip irrigation (SDI) of corn on the deep, silt loam soils of the U.S. Great Plains. Subsurface drip irrigation emitter spacings of 0.3, 0.6, 0.9 and 1.2 m were examined for the resulting differences in soil water redistribution, corn grain yield, yield components, seasonal water use, and water productivity in a 4‐year field study (2005 through 2008) at the Kansas State University Northwest Research‐Extension Center, Colby, Kansas. The results indicate that there is increased preferential water movement along the dripline (parallel) as compared to perpendicular to the dripline and that this phenomenon partially compensates for wider emitter spacings in terms of soil water redistribution. Corn yield and water productivity (WP) were not significantly affected by the emitter spacing with application of a full irrigation regime

An easily implemented agro-hydrological procedure with dynamic root simulation for water transfer in the crop-soil system: validation and application

Models for water transfer in the crop-soil system are key components of agro-hydrological models for irrigation, fertilizer and pesticide practices. Many of the hydrological models for water transfer in the crop-soil system are either too approximate due to oversimplified algorithms or employ complex numerical schemes. In this paper we developed a simple and sufficiently accurate algorithm which can be easily adopted in agro-hydrological models for the simulation of water dynamics. We used a dual crop coefficient approach proposed by the FAO for estimating potential evaporation and transpiration, and a dynamic model for calculating relative root length distribution on a daily basis. In a small time step of 0.001 d, we implemented algorithms separately for actual evaporation, root water uptake and soil water content redistribution by decoupling these processes. The Richards equation describing soil water movement was solved using an integration strategy over the soil layers instead of complex numerical schemes. This drastically simplified the procedures of modeling soil water and led to much shorter computer codes. The validity of the proposed model was tested against data from field experiments on two contrasting soils cropped with wheat. Good agreement was achieved between measurement and simulation of soil water content in various depths collected at intervals during crop growth. This indicates that the model is satisfactory in simulating water transfer in the crop-soil system, and therefore can reliably be adopted in agro-hydrological models. Finally we demonstrated how the developed model could be used to study the effect of changes in the environment such as lowering the groundwater table caused by the construction of a motorway on crop transpiration. (c) 2009 Elsevier B.V. All rights reserved.

Water transport in complex, non-wetting porous layers with applications to water management in low temperature fuel cells

An experimental setup was designed to visualize water percolation inside the porous transport layer, PTL, of proton exchange membrane, PEM, fuel cells and identify the relevant characterization parameters. In parallel with the observation of the water movement, the injection pressure (pressure required to transport water through the PTL) was measured. A new scaling for the drainage in porous media has been proposed based on the ratio between the input and the dissipated energies during percolation. A proportional dependency was obtained between the energy ratio and a non-dimensional time and this relationship is not dependent on the flow regime; stable displacement or capillary fingering. Experimental results show that for different PTL samples (from different manufacturers) the proportionality is different. The identification of this proportionality allows a unique characterization of PTLs with respect to water transport. This scaling has relevance in porous media flows ranging far beyond fuel cells. In parallel with the experimental analysis, a two-dimensional numerical model was developed in order to simulate the phenomena observed in the experiments. The stochastic nature of the pore size distribution, the role of the PTL wettability and morphology properties on the water transport were analyzed. The effect of a second porous layer placed between the porous transport layer and the catalyst layer called microporous layer, MPL, was also studied. It was found that the presence of the MPL significantly reduced the water content on the PTL by enhancing fingering formation. Moreover, the presence of small defects (cracks) within the MPL was shown to enhance water management. Finally, a corroboration of the numerical simulation was carried out. A threedimensional version of the network model was developed mimicking the experimental conditions. The morphology and wettability of the PTL are tuned to the experiment data by using the new energy scaling of drainage in porous media. Once the fit between numerical and experimental data is obtained, the computational PTL structure can be used in different types of simulations where the conditions are representative of the fuel cell operating conditions.

Improving simulation of soil water balance using lysimeter observations in a semiarid climate.

Water balance simulation in cropping systems is a very useful tool to study how water can be used efficiently. However this requires that models simulate an accurate water balance. Comparing model results with field observations will provide information on the performance of the models. The objective of this study was to test the performance of DSSAT model in simulating the water balance by comparing the simulations with observed measurements. The soil water balance in DSSAT uses a one dimensional ?tipping bucket? soil water balance approach where available soil water is determined by the drained upper limit (DUL), lower limit (LL) and saturated water content (SAT). A continuous weighing lysimeter was used to get the observed values of drainage and evapotranspiration (ET). An automated agrometeorological weather station close to the lisymeter was also used to record the climatic data. The model simulated accurately the soil water content after the optimization of the soil parameters. However it was found the inability of the model to capture small changes in daily drainage and ET. For that reason simulated cumulative values had larger errors as the time passed by. These results suggested the need to compare outputs of DSSAT and some hydrological model that simulates soil water movement with a more mechanistic approach. The comparison of the two models will allow us to find which mechanism can be modified or incorporated in DSSAT model to improve the simulations.