Reply [to “Comment onRusso[1991],Serrano[1990, 1998], and other applications of the water-content-based form of Richards' Equation to heterogeneous soils”]

A local fractional Richards equation is derived by considering the soil as fractal porous media, and an exact solution is obtained by a generalized Boltzmann transform and the fractional complex transform. The new theory predicts that the volumetric water content depends on the ratio (distance)2a /(time), where a is the value of fractal dimensions of the porous soil, and its value is recommended for various soils.

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Numerical homogenization of the Richards equation for unsaturated water flow through heterogeneous soils

Water Resources Research ◽

10.1002/2015wr018508 ◽

2016 ◽

Vol 52 (11) ◽

pp. 8500-8525 ◽

Cited By ~ 3

Author(s):

Na Li ◽

Xingye Yue ◽

Li Ren

Keyword(s):

Water Flow ◽

Richards Equation ◽

Numerical Homogenization ◽

Heterogeneous Soils ◽

Flow Through ◽

Unsaturated Water Flow

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Laboratory Experiments of Drainage, Imbibition and Infiltration under Artificial Rainfall Characterized by Image Analysis Method and Numerical Simulations

Water ◽

10.3390/w11112232 ◽

2019 ◽

Vol 11 (11) ◽

pp. 2232 ◽

Cited By ~ 2

Author(s):

Belfort ◽

Weill ◽

Fahs ◽

Lehmann

Keyword(s):

Image Analysis ◽

Numerical Simulations ◽

Water Content ◽

Laboratory Experiments ◽

Pressure Head ◽

Richards Equation ◽

Analysis Method ◽

Image Analysis Method ◽

Artificial Rainfall ◽

Classical Image

Two laboratory experiments consisting of drainage/imbibition and rainfall were carried out to study flow in variably saturated porous media and to test the ability of a new measurement method. 2D maps of water content are obtained through a non-invasive image analysis method based on photographs. This method requires classical image analysis steps, i.e., normalization, filtering, background subtraction, scaling and calibration. The procedure was applied and validated for a large experimental tank of internal dimensions 180 cm long, 120 cm wide and 4 cm deep that had been homogenously packed with monodisperse quartz sand. The calibration curve relating water content and reflected light intensities was established during the main monitoring phase of each experiment, making this procedure very advantageous. Direct measurements carried out during the water flow experiments correspond to water content, pressure head, temperature, and cumulative outflow. Additionally, a great advantage of the proposed method is that it does not require any tracer or dye to be injected into the flow tank. The accuracy and other benefits of our approach were also assessed using numerical simulations with state-of-the-art computational code that solves Richards’ equation.

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Handling the water content discontinuity at the interface between layered soils within a numerical scheme

Soil Research ◽

10.1071/sr05069 ◽

2005 ◽

Vol 43 (8) ◽

pp. 945 ◽

Cited By ~ 8

Author(s):

C. J. Matthews ◽

F. J. Cook ◽

J. H. Knight ◽

R. D. Braddock

Keyword(s):

Numerical Solution ◽

Water Content ◽

Numerical Scheme ◽

Iterative Scheme ◽

Method Of Lines ◽

Soil Layer ◽

Iterative Solution ◽

Richards Equation ◽

Layered Soils ◽

Fine Soil

In general, the water content (θ) form of Richards’ equation is not used when modeling water flow through layered soil since θ is discontinuous across soil layers. Within the literature, there have been some examples of models developed for layered soils using the θ-form of Richards’ equation. However, these models usually rely on an approximation of the discontinuity at the soil layer interface. For the first time, we will develop an iterative scheme based on Newton’s method, to explicitly solve for θ at the interface between 2 soils within a numerical scheme. The numerical scheme used here is the Method of Lines (MoL); however, the principles of the iterative solution could be used in other numerical techniques. It will be shown that the iterative scheme is highly effective, converging within 1 to 2 iterations. To ensure the convergence behaviour holds, the numerical scheme will be tested on a fine-over-coarse and a coarse-over-fine soil with highly contrasting soil properties. For each case, the contrast between the soil types will be controlled artificially to extend and decrease the extent of the θ discontinuity. In addition, the numerical solution will be compared against a steady-state analytical solution and a numerical solution from the literature.

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Kalman filters for assimilating near-surface observations into the Richards equation – Part 3: Retrieving states and parameters from laboratory evaporation experiments

Hydrology and Earth System Sciences ◽

10.5194/hess-18-2543-2014 ◽

2014 ◽

Vol 18 (7) ◽

pp. 2543-2557 ◽

Cited By ~ 10

Author(s):

H. Medina ◽

N. Romano ◽

G. B. Chirico

Keyword(s):

Kalman Filter ◽

Water Content ◽

Soil Water ◽

Soil Water Content ◽

Initial Conditions ◽

Estimation Method ◽

Richards Equation ◽

Porous System ◽

Data Set ◽

Near Surface

Abstract. The purpose of this work is to evaluate the performance of a dual Kalman filter procedure in retrieving states and parameters of a one-dimensional soil water budget model based on the Richards equation, by assimilating near-surface soil water content values during evaporation experiments carried out under laboratory conditions. The experimental data set consists of simultaneously measured evaporation rates, soil water content and matric potential profiles. The parameters identified by assimilating the data measured at 1 and 2 cm soil depths are in very good agreement with those obtained by exploiting the observations carried out in the entire soil profiles. A reasonably good correspondence has been found between the parameter values obtained from the proposed assimilation technique and those identified by applying a non-sequential parameter estimation method. The dual Kalman filter also performs well in retrieving the water state in the porous system. Bias and accuracy of the predicted state profiles are affected by observation depth changes, particularly for the experiments involving low state vertical gradients. The assimilation procedure proved flexible and very stable in both experimental cases, independently from the selected initial conditions and the involved uncertainty.

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

Revista Brasileira de Ciência do Solo ◽

10.1590/s0100-06832014000200010 ◽

2014 ◽

Vol 38 (2) ◽

pp. 454-463 ◽

Cited By ~ 1

Author(s):

Antônio Cláudio Marques Afonso ◽

André Maciel Netto ◽

Wagner Estáquio de Vasconcelos

Keyword(s):

Fuzzy Logic ◽

Water Content ◽

Numerical Models ◽

Nonlinear Partial Differential Equation ◽

Fuzzy Model ◽

Water Dynamics ◽

Northeastern Brazil ◽

Richards Equation ◽

Physical Parameters ◽

Moisture Profiles

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.

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