Moisture Flow Equation Research Articles

Effects of Gravity on Evaporation for Soil‐Limited Conditions

AbstractThis manuscript systematically investigates the effects of gravity during soil‐limited (Stage 2) evaporation from bare soil. Analytical and numerical solutions to the one‐dimensional Richards soil moisture flow equation are developed based on simplified hydraulic functions that depend exponentially on soil water matric potential. Semi‐infinite domains with either freely draining or hydrostatic bottom boundary conditions and finite domains with no‐flow bottom boundary conditions are considered. Cases with gravity are directly compared to those without. The simplified solutions are verified by comparison to numerical solutions with fully realistic soil hydraulic functions for two soils at the extreme ends of the range of possible soil textures. Cumulative evaporation versus time and soil volumetric water content versus depth at selected times are determined for each case from the simplified solutions. These results are reported in terms of non‐dimensional variables that are universal, spanning all soil textures and other conditions. For the semi‐infinite domain cases cumulative evaporation with gravity is reduced by several orders of magnitude for very coarse soils at times of practical interest while gravity has a negligible effect for the finest textures at those times. For the finite domain cases gravity is less important because cumulative evaporation is ultimately limited by the fixed amount of water in the profile.

Data‐Driven Discovery of Soil Moisture Flow Governing Equation: A Sparse Regression Framework

AbstractConventionally, soil moisture dynamics are mathematically modeled by the Richardson‐Richards equation, whose derivation is based on the conservation of mass and the Buckingham‐Darcy law. However, it is complicated and even impossible to finish such rigorous derivations based on physical principles due to the complexity and uncertainties in the vadose zone. In this work, we propose a data‐driven sparse regression framework. For the first time, we discover the time‐dependent nonlinear soil moisture flow equation from only volumetric water content observations. The framework leverages linear approximations and group sparsity techniques. Except for a few assumptions, it requires no prior information, including a specific constitutive relationship model, boundary conditions, and initial conditions. Several numerical experiments are tested to demonstrate that the framework successfully discovers the underlying soil moisture flow equation from data and tends to discover the parsimonious equation governed by dominant physical processes. Besides, the identified nonlinear coefficients, which represent soil hydraulic properties, fit well with the actual coefficients, although they deviate slightly at near‐saturated ends. The results demonstrate the satisfactory performance of the proposed framework under various scenarios. Despite being based on a homogeneous soil assumption, this study provides a new perspective for deriving soil moisture flow governing equations.

Shooting the Numerical Solution of Moisture Flow Equation with Root Water Uptake Models: A Python Tool

Shooting the Numerical Solution of Moisture Flow Equation with Root Water Uptake Models: A Python Tool

Design approach for drainage layer in pavement subsurface drainage system considering unsaturated characteristics

Abstract Providing adequate subsurface drainage feature in a pavement system to remove the infiltrated moisture in a minimum time is an important design consideration, which prevents the premature failure of the pavement system, and hence helps in achieving a significantly lower life-cycle cost. Various surface drainage measures are taken to minimize the ingress of moisture into the pavement gradually lose their efficiency with the aging of the pavement. The use of an appropriate open-graded aggregate course as a drainage layer in the pavement is the best way to minimize the time for which the pavement materials are exposed to saturated conditions. The current drainage guidelines have been developed on the basis of moisture flow under saturated condition. A better understanding and estimation of moisture movement in a drainage layer can only be achieved by using seepage analysis that adopts the principles of saturated as well as unsaturated flow conditions. State-of-art of mathematical tools such as finite difference and FEA methods permits a rigorous solution of Richard’s equation for saturated and unsaturated moisture flow in a porous medium, the only major drawback is the need for rigorous modeling and computational tool for the simulations and the design of the drainage layer. This paper focuses on the development of an analytical model for estimating the time to drain considering the unsaturated characteristics of pavement base material and calibration of the developed model based on a mechanistic approach which is relatively inexpensive. The applicability of the approach is explained by using the four-standard aggregate gradations recommended by AASHTO for the drainage layer, as well as a dense graded aggregate layer, and the results are compared with those from the FHWA approach and finite element analysis. The study shows that the developed model performs as good as the finite element analysis, which requires rigorous numerical modeling, predicts drainage times that are significantly different from those obtained from the FHWA analysis, and that it is sensitive to key significant design parameters. Hence, the proposed model is recommended for regular use for the design of the drainage layer and for a parametric study of the complete drainage process.

LINEAR ROOT WATER UPTAKE BY VEGETATION

The performance of a simple model with a linear root water extraction term that varies with time is presented in this paper. The research is based on the use of a one-dimensional form of Richard’s Equation for unsaturated moisture flow including a sink term. A numerical solution has been achieved via the finite element method for spatial discretisation along with a finite difference time-marching scheme. The model is assessed via a series of simulations of water uptake beneath uniform crop cover. A good correlation between the field data and simulated results has been achieved. This relatively straight forward approach is seemed more suitable for development and application to a range of geoengineering problems such as slope stability, shrinkage and heave prediction.

Estimation of non-linear root water uptake parameter using genetic algorithms

The present study is concerned with the estimation of non-linear root water uptake parameter using Genetic Algorithm (GA) technique. Various models have been proposed to predict root water uptake. However, from the studies and observations it has been found that the nature of root water uptake is non-linear. The non-linear root water uptake model termed as O–R model coupled with soil moisture flow equation is developed to predict the root water uptake pattern. The O–R model incorporates a parameter ‘β’ to account for the non-linearity in root water uptake. In the present study, parameter β is estimated through inverse modelling using GA optimization technique. The parameter is optimized by minimizing the difference between model predicted and experimentally observed percentage soil moisture depletion in the root zone. To check the efficacy of the developed model, the optimization procedure is validated from hypothetically generated percentage soil moisture depletion corresponding to an assumed β value. The model is applied to wheat crop (Triticum) for estimation of non-linear root water uptake parameter. The results show that linked simulation optimization model based on GA method accurately determines the non-linear root water uptake parameter for a given crop.

Soil Moisture Flow Modeling with Water Uptake by Plants (Wheat) under Varying Soil and Moisture Conditions

A variably saturated soil moisture flow model is developed for planted soils with depth varying properties by incorporating a nonuniform macroscopic root water uptake function. The model includes spatial and temporal variation of the root density with dynamic root growth for simulating water uptake by plants along with the impact of soil moisture availability. The governing partial differential moisture flow equation integrated over the depth with a plant water uptake term is solved numerically by the implicit finite difference method using an iterative scheme. The model is first tested for barren soils for two profiles considering constant and depth varying soil characteristics under constant inflow condition. The results obtained are later tested with experimental data available in the literature. A nonuniform plant water uptake term is subsequently incorporated in the model and water uptake by wheat plants under different soil moisture availability conditions is studied. Finally, the moisture flow model is validated with field data of rain fed wheat Triticum aestivum using a dynamic root growth model for a layered root zone soil profile. The simulated soil moisture regime of the layered root zone shows a reasonably good agreement with the observed data.

Soil Moisture Dynamics Modeling Considering the Root Compensation Mechanism for Water Uptake by Plants

A numerical model is developed in this study for simulating soil moisture flow in layered soil profile with plant growth. A dynamic root compensation mechanism (RCM) is used for a nonuniform root distribution pattern to compute water uptake by plants in a moisture scarce environment. The governing soil moisture flow equation integrated with the roots water uptake function is solved numerically by the implicit finite difference method coupled with the Picard iteration technique. The model is first tested for a barren layered soil profile using numerical simulation data available in the literature. A nonlinear function for water uptake by roots is then incorporated in the flow equation and the rate of water removal is simulated with and without considering the RCM for a characteristic example under optimal and water scare conditions. The model is finally applied to a rain-fed wheat (Triticum aestivum) field using a dynamic root growth model. The simulation considering the RCM shows better agreement with the observed data compared to the model results obtained without considering the RCM. Results show that under favorable soil moisture conditions, plants extract water at the maximum rate according to the root distribution pattern and when the moisture stress is developed in the upper soil profile, the diminished water uptake rate in the water scarce region is compensated for by an enhanced water uptake from the lower wetter layers. The model can be used for sound irrigation management practices especially in the water scarce arid and semiarid regions and can also be integrated with a transport equation to predict the solute uptake by plant root biomass.

Biexponential model for water retention characteristics

Water retention characteristic (WRC) is an important soil property used in many hydrologic applications. Although there are numerous models in the literature for its prediction, the models are largely empirical with fundamental derivations based on soil textural pore-spaces. This paper presents a biexponential model for WRC that has its basis on textural and structural soil pore-spaces. The model contains physical parameters related to soil textural and structural pore characteristics and can also navigate through all inflections present in measured WRC. Thus, it adequately represents possible classes of soil pores in WRC. The performance of this model on different soil types from various parts of the world was compared to some of the popular WRC models in the literature. The models tested were those proposed by van Genuchten [van Genuchten, M.T., 1980. A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Science Society of America Journal, 44, 892–898], Campbell [Campbell, G.S., 1974. A simple method for determining unsaturated conductivity from moisture retention data. Soil Science, 117, 311–314], Brooks and Corey [Brooks, R.H., Corey, A.T., 1964. Hydraulic Properties of Porous Medium. Hydrology Paper Number 3. Colorado State University, USA.], Gardner [Gardner, W.R., 1958. Some steady state solutions of the unsaturated moisture flow equation with application to evaporation from a water table. Soil Science, 85, 228–232], Groenevelt and Grant [Groenevelt, P.H., Grant, C.D., 2004. A new model for the soil-water retention curve hat solves the problem of residual water contents. European Journal of Soil Science, 55, 479–485]. These models were found inadequate in fitting the whole range of measured WRC, are limited to certain geographic regions of the world, and contain parameters not directly linked to soil physical properties. The biexponential model does not only overcome these limitations but also gives the best fit of WRC. Its model parameters have physical significance and have been shown in this paper to be useful in fitting different soil physical conditions. The model is continuous and continuously differentiable throughout the whole range of WRC and is envisaged to perform equally well in fitting unsaturated hydraulic conductivity.

Modeling Soil Water Uptake by Plants Using Nonlinear Dynamic Root Density Distribution Function

Water uptake by plants is one of the major components of water balance of the vadose zone that greatly influences the contaminant and moisture movement in variably saturated soils. In this study, a nonlinear macroscopic root water uptake model that includes the impact of soil moisture stress is developed. The model incorporates the spatial and temporal variation of root density in addition to the dynamic root depth considerations. The governing moisture flow equation coupled with the water extraction by plants term is solved numerically by an implicit finite-difference method. The simulation is performed for various physical scenarios subjected to different boundary conditions. The model is tested first without considering the water uptake and results are compared with observed data available in the literature for two cases. A nonlinear water uptake term is subsequently incorporated in the model which is then simulated for corn crop for constant root depth under various characteristic moisture availability environments. Results show that the water extraction rate is closely related to the soil moisture availability in addition to the root density. The plants are observed to extract moisture mainly from the upper root dense soil profile when water content is in an optimal range, otherwise, the peak of the uptake moves to other soil layers where the moisture is easily available. Finally, the model is applied to a corn field and simulated results are validated with field data. The simulated moisture content for 2 months of crop growing season shows a reasonably good agreement with the observed data.

Seasonal water uptake near trees: a numerical and experimental study

Issues related to the numerical simulation of moisture migration patterns in the unsaturated zone and in the vicinity of mature trees are explored in this paper. The research is based on the use of Richard's equation for unsaturated moisture flow incorporating a sink term. A numerical solution has been achieved via the finite-element method for spatial discretization along with a finite-difference time-marching scheme. An axisymmetric solution is developed to represent water uptake near an established tree. The approach adopted utilizes radial symmetry and assumes a linear distribution of water extraction rates with both depth and radius. The model has been validated by direct comparison with field measurements recorded (by others) for a mature lime tree located on a boulder clay subsoil. Non-linear hydraulic properties have been obtained from independent published data. A good correlation between field data and simulated results has been achieved. The simulation covers a full annual cycle starting from field capacity in winter, extending through a full spring–summer drying period and subsequent autumn recharge. It is believed that this is the first attempt to simulate the behaviour of an established tree over such a time-scale. This relatively straightforward approach is thought to be suitable for development and application to a range of geo-engineering problems (e.g. slope stability, shrinkage/heave prediction, etc).

Sensitivity of playa windblown-dust emissions to climatic and anthropogenic change

Windblown dust is a significant component of atmospheric PM (particulate matter) in arid regions worldwide, with adverse effects on human health and visibility. In the future, windblown-dust emissions are likely to increase if water tables drop as a result of climatic or anthropogenic changes. To manage this hazard, air-quality managers need quantitative models that predict the impact of climatic and anthropogenic change on dust emissions. To meet this need, we constructed a process-based numerical model that includes Richards’ equation for vertical moisture flow in the unsaturated zone, Chepil's model for the effect of surface soil moisture on threshold wind speed, and the saltation equation, which also predicts the rate of dust emission from the surface to within a multiplicative factor. This model is solved analytically for a Weibull distribution of wind speeds under steady-state moisture conditions, providing a single predictive equation for the long-term average saltation flux based on local meteorological and hydrological parameters. The model equations are used to predict the increase in saltation flux and dust emissions resulting from the dessication of a wet playa by climatic change, stream diversion, or groundwater withdrawal. The model is calibrated using CLIM-MET station data collected near Soda (dry) Lake, California. The model results identify a critical range of water-table depths between 3 and 10 m (depending on hydrological parameters) in which small increases in water-table depth cause large, nonlinear increases in windblown-dust emissions. For water tables deeper than 10 m, dust emissions are close to their maximum value and are largely independent of water-table depth. This analysis highlights the importance of preserving the hydrological balance of wet playas in order to minimize windblown-dust emissions. Future climatic changes may also influence dust emissions through changes in the mean or variability of wind speeds. For representative model parameters, 10% increases in the mean and variability of wind speeds, for example, are predicted to increase dust emissions by 80% and 20% within this model framework.

Non-classical and potential symmetry analysis of Richard's equation for moisture flow in soil

This paper focuses upon the derivation of the non-classical symmetries of Bluman and Cole as they apply to Richard's equation for water flow in an unsaturated uniform soil. It is shown that the determining equations for the non-classical case lead to four highly non-linear equations which have been solved in five particular cases. In each case the corresponding similarity ansatz has been derived and Richard's equation is reduced to an ordinary differential equation. Explicit solutions are produced when possible. Richard's equation is also expressed as a potential system and in reviewing the classical Lie solutions a new symmetry is derived together with its similarity ansatz. Determining equations are then produced for the potential system using the non-classical algorithm. This results in an under-determined set of equations and an example symmetry that reveals a missing classical case is presented. An example of a classical and a non-classical symmetry reduction applied to the infiltration of moisture in soil is presented. The condition for surface invariance is used to demonstrate the equivalence of a classical Lie and a potential symmetry.

Comment on “One‐dimensional nonlinear steady infiltration” by H. A. Basha

Water Resources ResearchVolume 36, Issue 10 p. 3111-3113 CommentariesFree Access Comment on “One-dimensional nonlinear steady infiltration” by H. A. Basha R. D. Braddock, R. D. BraddockSearch for more papers by this authorJ.-Y. Parlange, J.-Y. ParlangeSearch for more papers by this author R. D. Braddock, R. D. BraddockSearch for more papers by this authorJ.-Y. Parlange, J.-Y. ParlangeSearch for more papers by this author First published: 01 October 2000 https://doi.org/10.1029/2000WR900156Citations: 3AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL No abstract is available for this article. References Basha, H. A., One-dimensional nonlinear steady infiltration, Water Resour. Res., 35, 1697– 1704, 1999. Gardner, W. R., Some steady-state solutions to the unsaturated moisture flow equations with application to evaporation from a water table, Soil Sci., 85, 228– 232, 1958. Parlange, J.-Y., Simple method for predicting drainage from field plot—Comment, Soil Sci. Soc. Am. J., 46, 887– 888, 1982. Warrick, A. W., Solution to the one-dimensional linear moisture flow equation with water extraction, Soil Sci. Soc. Am. J., 38, 573– 576, 1974. Citing Literature Volume36, Issue10October 2000Pages 3111-3113 ReferencesRelatedInformation

Commentary on Russo [1991], Serrano [1990, 1998], and other applications of the water‐content‐based form of Richards' Equation to heterogeneous soils

Commentary on <i>Russo</i> [1991], <i>Serrano</i> [1990, 1998], and other applications of the water‐content‐based form of Richards' Equation to heterogeneous soils

MEASURING AND MODELING ROOT WATER UPTAKE BASED ON 36CHLORIDE DISCRIMINATION IN A SILT LOAM SOIL AFFECTED BY GROUNDWATER

Water uptake by plant roots was successfully simulated by use of a volumetric sink term S(z) added to the continuity equation for soil moisture flow, which generally requires detailed information about the root system as functions of root density, root distribution, and root length. Unfortunately, these factors are difficult to evaluate. This paper describes a simple method for the estimation of soil water extraction by roots based on root discrimination of selected solute species such as chloride. A silt loam soil planted with carrots and affected by groundwater at different depths was used for the investigation. The soil was characterized by soil matric potentials close to hydrostatic equilibrium conditions. Aeration in the root zone was impeded by high moisture content. Because chloride was strongly discriminated by the roots, root water uptake was found to be related to the increase in soil 36chloride solution concentration. Consequently, the chloride in the soil water was found to be an ideal indicator of water uptake in plants. Based on this proposed approach, patterns of water extraction by carrot roots could be described using a quasi steady-state model. We also found that in the groundwater-affected silt loam soil with impeded aeration, about 80% of the water transpired was extracted from the top 5 cm of the root zone

Boundary integral solutions to the unsaturated moisture flow equation : Khanbilvardi, R M; Ahmed, S; Sadegh, A M Water Resour ResV29, N5, May 1993, P1425–1434

Boundary integral solutions to the unsaturated moisture flow equation : Khanbilvardi, R M; Ahmed, S; Sadegh, A M Water Resour ResV29, N5, May 1993, P1425–1434

Boundary integral solutions to the unsaturated moisture flow equation

The boundary integral equation method is formulated for problems concerning unsaturated moisture flow in porous media. The boundary integral formulation presented here is derived using the time‐dependent fundamental solution of the governing partial differential equation. Two boundary integral approaches are presented. The first approach solves the unsaturated moisture flow problem by directly applying the time‐dependent Green's function. The second method is based on the expansion of moisture content into a perturbation series. The governing equation is decomposed into a moisture flow equation without a known gravity term on the right‐hand side. The perturbation equations are then solved in succession by evaluating the gravity term of the unsaturated leachate flow equation from the preceding solution level. The two boundary integral approaches, the direct Green's function and the perturbation Green's function, are closely related because the same time‐dependent fundamental solution is used to formulate the boundary integral expressions. The direct Green's function formulation solves the boundary integral expression in one step. However, the perturbation Green's function approach requires solution of the integral expression for homogeneous boundary conditions. The solutions obtained by both methods are compared with the exact solution. A close agreement of the internal fluxes between boundary integral methods and the exact solution, for an unsaturated portion of a landfill, shows the stability of the boundary integral methods to compute accurate recharge from the unsaturated zone to the saturated leachate mound.

Soil Moisture Simulation under Cropped Condition Using a Moisture Dependent Root Sink Function

AbstractMoisture dependent root sink function developed by Feddes et al. (1976) which incorporates linearly varying moisture availability proposal between field capacity and wilting point was embedded in the continuity equation for transient moisture flow in conjunction with Darcy's law and moisture contents in a homogeneous soil profile under wheat cropped condition were simulated numerically using implicit finite difference scheme. Simulated moisture contents were observed to be reasonably in good agreement with the observed moisture contents as the variations between the simulated and observed values varied from 2.97 to 21.76 percent.

A Generalized Solution to Infiltration

AbstractA generalized solution to the moisture flow (Richards') equation is developed for infiltration. The equation is expressed in terms of dimensionless time, depth, and water content. The reduced form applies for the hydraulic functions of van Genuchten or of Brooks and Corey as well as to other scaled forms and the solution utilizes the procedure of Philip. Answers are presented in concise tables which, in principle, allow for finding moisture profiles, wetting front, intake rate and cumulative intake for a variety of soils and for varying initial water contents. For application, specifically measured hydraulic conductivities can be best‐fitted to the forms used here or generalized empirical values can be used from the literature. Thus, either specific or generic parameters may be used, depending on availability for a given problem.