scholarly journals Effective saturation-based weighting for interblock hydraulic conductivity in unsaturated zone soil water flow modelling using one-dimensional vertical finite-difference model

2019 ◽  
Vol 22 (2) ◽  
pp. 423-439
Author(s):  
Mohanasundaram Shanmugam ◽  
G. Suresh Kumar ◽  
Balaji Narasimhan ◽  
Sangam Shrestha
Keyword(s):  
Hydraulic Conductivity ◽  
Finite Difference ◽  
Soil Water ◽  
Unsaturated Zone ◽  
Estimation Methods ◽  
Richards Equation ◽  
Difference Model ◽  
One Dimensional ◽  
Soil Water Flow ◽  
Effective Saturation

Abstract Richards equation is solved for soil water flow modeling in the unsaturated zone continuum. Interblock hydraulic conductivities, while solving for Richards equation, are estimated by some sort of averaging process based on upstream and downstream nodes hydraulic conductivity values. The accuracy of the interblock hydraulic conductivity estimation methods mainly depends on the distance between two adjacent discretized nodes. In general, the accuracy of the numerical solution of the Richards equation decreases as nodal grid discretization increases. Conventional interblock hydraulic conductivity estimation methods are mostly mere approximation approaches while the Darcian-based interblock hydraulic conductivities involve complex calculations and require intensive computation under different flow regimes. Therefore, in this study, we proposed an effective saturation-based weighting approach in the soil hydraulic curve functions for estimating interblock hydraulic conductivity using a one-dimensional vertical finite-difference model which provides a parametric basis for interblock hydraulic conductivity estimation while reducing complexity in the calculation and computational processes. Furthermore, we compared four test case simulation results from different interblock hydraulic conductivity methods with the reference solutions. The comparison results show that the proposed method performance in terms of percentage reduction in root mean square and mean absolute error over other methods compared in this study were 59.5 and 60%, respectively.

Soil Water Flow

2003 ◽  
Author(s):  
Arthur W. Warrick
Keyword(s):  
Soil Water ◽  
Water Flow ◽  
Darcy’S Law ◽  
Soil Water Potential ◽  
Hydraulic Head ◽  
Flow Equation ◽  
Darcy's Law ◽  
Richards Equation ◽  
Flow Equations ◽  
Soil Water Flow

The definitions of hydraulic head and soil water potential in chapter 1 assumed equilibrium. However, the primary motivation was to develop a background useful to describe dynamic systems. If a system is in equilibrium, no flow will occur; otherwise, flow will occur from regions of high to low hydraulic head. The primary flow equation will be Darcy’s law. When Darcy’s law is combined with conservation of mass, the result is a continuity equation that can have several different forms. We will refer to all of those forms generically as soil water flow equations. Generally, for unsaturated conditions, the soil water flow equation is called the Richards equation. A starting point is to examine two classical relationships from fluid dynamics, the Bernoulli and the Poiseuille laws. Bernoulli’s law relates the total potential for ideal fluids and is commonly derived in introductory physics and fluid mechanics texts (see Serway, 1990). Assumptions include an ideal fluid (non-viscous), which is one that is incompressible and which exhibits steady and irrotational flow. For these conditions, the sum of gravitational, pressure, and inertial energy at positions S1and S2 are the same along any streamline For a real fluid, viscosity causes a loss of energy as friction that must be overcome. Additionally, for most problems of interest in soils, the velocity head will be negligible compared with the pressure and gravitational terms.

Functional-structural modelling of root water uptake based on measured MRI images of root systems

2020 ◽  
Author(s):  
Tobias Selzner ◽  
Magdalena Landl ◽  
Andreas Pohlmeier ◽  
Daniel Leitner ◽  
Jan Vanderborght ◽  
...  
Keyword(s):  
Hydraulic Conductivity ◽  
Drought Tolerance ◽  
Soil Water ◽  
Water Uptake ◽  
Root Architecture ◽  
Soil Water Potential ◽  
Computational Cost ◽  
Root Water Uptake ◽  
Extreme Weather Events ◽  
Richards Equation

<p>In the course of climate change, the occurrence of extreme weather events is expected to increase. Drought tolerance of crops and careful irrigation management are becoming key factors for global food security and the sustainable resource use of water in agriculture. Root water uptake plays a vital role in drought tolerance. It is influenced by root architecture, plant and soil water status and their respective hydraulic properties. Models of said factors aid in organizing the current state of knowledge and enable a deeper understanding of their respective influence on crop performance. Water uptake by roots leads to a decrease in soil moisture and may cause the formation of soil water potential gradients between the bulk soil and the soil-root interface. Although the Richards equation in theory takes these gradients into account, a very fine discretization of the soil domain is necessary to capture these gradients in simulations. However, especially during drought stress, the drop in hydraulic conductivity in the rhizosphere could have a major impact on the overall water uptake of the root system. In order to investigate computationally feasible alternative approaches for simulations with source terms that take these hydraulic conductivity drops into account, we conducted experiments with lupine plants. The root architecture of the growing plants was measured several times using an MRI. Subsequently, these MRI images were used in a holobench for manual tracing of the roots. We were able to mimic the root growth between the measurement dates using linear interpolation. In addition to root architecture, soil water contents and transpiration rates were monitored. We then used this data to systematically compare the computational effort of different approaches to consider the hydraulic conductivity drop near roots in terms of accuracy and computational cost. Eventually we aim at using these results to improve existing root water uptake models for the presence of hydraulic conductivity drops in the rhizosphere in an efficient and accurate way.</p>

scholarly journals Modeling Soil Water Redistribution under Gravity Irrigation with the Richards Equation

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1581 ◽  
Author(s):  
Sebastián Fuentes ◽  
Josué Trejo-Alonso ◽  
Antonio Quevedo ◽  
Carlos Fuentes ◽  
Carlos Chávez
Keyword(s):  
Finite Difference ◽  
Numerical Solution ◽  
Soil Water ◽  
Water Movement ◽  
Soil Mechanics ◽  
Water Infiltration ◽  
Richards Equation ◽  
Water Redistribution ◽  
Irrigation Drainage ◽  
Transfer Problems

Soil water movement is important in fields such as soil mechanics, irrigation, drainage, hydrology, and agriculture. The Richards equation describes the flow of water in an unsaturated porous medium, and analytical solutions exist only for simplified cases. However, numerous practical situations require a numerical solution (1D, 2D, or 3D) depending on the complexity of the studied problem. In this paper, numerical solution of the equation describing water infiltration into soil using the finite difference method is studied. The finite difference solution is made via iterative schemes of local balance, including explicit, implicit, and intermediate methods; as a special case, the Laasonen method is shown. The found solution is applied to water transfer problems during and after gravity irrigation to observe phenomena of infiltration, evaporation, transpiration, and percolation.

scholarly journals An Explicit Stabilized Runge–Kutta–Legendre Super Time-Stepping Scheme for the Richards Equation

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Ramesh Chandra Timsina ◽  
Harihar Khanal ◽  
Kedar Nath Uprety
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Richards Equation ◽  
One Dimensional ◽  
Time Stepping ◽  
Runge Kutta ◽  
Crank Nicolson

We solve one-dimensional Kirchhof transformed Richards equation numerically using finite difference method with various time-stepping schemes, forward in time central in space (FTCS), backward in time central in space (BTCS), Crank–Nicolson (CN), and a stabilized Runge–Kutta–Legendre super time-stepping (RKL), and compare their performances.

scholarly journals Kalman filters for assimilating near-surface observations in the Richards equation – Part 1: Retrieving state profiles with linear and nonlinear numerical schemes

2012 ◽  
Vol 9 (12) ◽  
pp. 13291-13327 ◽  
Author(s):  
G. B. Chirico ◽  
H. Medina ◽  
N. Romano
Keyword(s):  
Kalman Filter ◽  
Finite Difference ◽  
Difference Scheme ◽  
Soil Water ◽  
Finite Difference Scheme ◽  
Richards Equation ◽  
Near Surface ◽  
Backward Euler ◽  
Explicit Finite Difference ◽  
Surface Observations

Abstract. This paper examines the potential of different algorithms, based on the Kalman filtering approach, for assimilating near-surface observations in a one-dimensional Richards' equation. Our specific objectives are: (i) to compare the efficiency of different Kalman filter algorithms, implemented with different numerical schemes of the Richards equation, in retrieving soil water potential profiles; (ii) to evaluate the performance of these algorithms when nonlinearities arise from the nonlinearity of the observation equation, i.e. when surface soil water content observations are assimilated to retrieve pressure head values. The study is based on a synthetic simulation of an evaporation process from a homogeneous soil column. A standard Kalman Filter algorithm is implemented with both an explicit finite difference scheme and a Crank-Nicolson finite difference scheme of the Richards equation. Extended and Unscented Kalman Filters are instead both evaluated to deal with the nonlinearity of a backward Euler finite difference scheme. While an explicit finite difference scheme is computationally too inefficient to be implemented in an operational assimilation scheme, the retrieving algorithm implemented with a Crank-Nicolson scheme is found computationally more feasible and robust than those implemented with the backward Euler scheme. The Unscented Kalman Filter reveals as the most practical approach when one has to deal with further nonlinearities arising from the observation equation, as result of the nonlinearity of the soil water retention function.

Estimating finite difference block equivalent hydraulic conductivity for numerically solving the Richards' equation

2007 ◽  
Vol 21 (26) ◽  
pp. 3587-3600 ◽  
Author(s):  
Chih-Yung Feng ◽  
Tim Hau Lee ◽  
Wen Sen Lee ◽  
Chu-Hui Chen
Keyword(s):  
Hydraulic Conductivity ◽  
Finite Difference ◽  
Richards Equation

scholarly journals Numerical Evaluation of Fractional Vertical Soil Water Flow Equations

Water ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 511
Author(s):  
Ali Ercan ◽  
M. Levent Kavvas
Keyword(s):  
Porous Media ◽  
Soil Water ◽  
Water Flow ◽  
Water Movement ◽  
Least Square ◽  
Flow In Porous Media ◽  
Fickian Diffusion ◽  
Richards Equation ◽  
Governing Equations ◽  
Soil Water Flow

Significant deviations from standard Boltzmann scaling, which corresponds to normal or Fickian diffusion, have been observed in the literature for water movement in porous media. However, as demonstrated by various researchers, the widely used conventional Richards equation cannot mimic anomalous diffusion and ignores the features of natural soils which are heterogeneous. Within this framework, governing equations of transient water flow in porous media in fractional time and multi-dimensional fractional soil space in anisotropic media were recently introduced by the authors by coupling Brooks–Corey constitutive relationships with the fractional continuity and motion equations. In this study, instead of utilizing Brooks–Corey relationships, empirical expressions, obtained by least square fits through hydraulic measurements, were utilized to show the suitability of the proposed fractional approach with other constitutive hydraulic relations in the literature. Next, a finite difference numerical method was proposed to solve the fractional governing equations. The applicability of the proposed fractional governing equations was investigated numerically in comparison to their conventional counterparts. In practice, cumulative infiltration values are observed to deviate from conventional infiltration approximation, or the wetting front through time may not be consistent with the traditional estimates of Richards equation. In such cases, fractional governing equations may be a better alternative for mimicking the physical process as they can capture sub-, super-, and normal-diffusive soil water flow processes during infiltration.

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