A Transformed Pressure Head-Based Approach to Solve Richards' Equation for Variably Saturated Soils

1995 ◽  
Vol 31 (4) ◽  
pp. 925-931 ◽  
Author(s):  
Lehua Pan ◽  
Peter J. Wierenga
Keyword(s):  
Pressure Head ◽  
Richards Equation ◽  
Saturated Soils

scholarly journals Multi-source data assimilation for physically-based hydrological modeling of an experimental hillslope

2018 ◽  
Author(s):  
Anna Botto ◽  
Enrica Belluco ◽  
Matteo Camporese
Keyword(s):  
Soil Moisture ◽  
Data Assimilation ◽  
Hydrological Modeling ◽  
Nonlinear Models ◽  
Pressure Head ◽  
Richards Equation ◽  
Hydrological Models ◽  
Filter Performance ◽  
Trade Offs ◽  
Source Data

Abstract. Data assimilation has been recently the focus of much attention for integrated surface-subsurface hydrological models, whereby joint assimilation of water table, soil moisture, and river discharge measurements with the ensemble Kalman filter (EnKF) have been extensively applied. Although the EnKF has been specifically developed to deal with nonlinear models, integrated hydrological models based on the Richards equation still represent a challenge, due to strong nonlinearities that may significantly affect the filter performance. Thus, more studies are needed to investigate the capabilities of the EnKF to correct the system state and identify parameters in cases where the unsaturated zone dynamics are dominant, as well as to quantify possible tradeoffs associated with assimilation of multi-source data. Here, the model CATHY (CATchment HYdrology) is applied to reproduce the hydrological dynamics observed in an experimental two-layered hillslope, equipped with tensiometers, water content reflectometer probes, and tipping bucket flow gages to monitor the hillslope response to a series of artificial rainfall events. Pressure head, soil moisture, and subsurface outflow are assimilated with the EnKF in a number of scenarios and the challenges and issues arising from the assimilation of multi-source data in this real-world test case are discussed. Our results demonstrate that the EnKF is able to effectively correct states and parameters even in a real application characterized by strong nonlinearities. However, multi-source data assimilation may lead to significant trade-offs: the assimilation of additional variables can lead to degradation of model predictions for other variables that were otherwise well reproduced. Furthermore, we show that integrated observations such as outflow discharge cannot compensate for the lack of well-distributed data in heterogeneous hillslopes.

scholarly journals Hydraulic and transport parameter assessment using column infiltration experiments

2016 ◽  
Author(s):  
A. Younes ◽  
T. A. Mara ◽  
M. Fahs ◽  
O. Grunenberger ◽  
Ph. Ackerer
Keyword(s):  
Pressure Head ◽  
Solute Concentration ◽  
Richards Equation ◽  
Transport Parameter ◽  
State Variables ◽  
Transport Parameters ◽  
Uncertainty Range ◽  
Infiltration Experiment ◽  
Statistical Calibration

Abstract. In the present work, we study the quality of the statistical calibration of hydraulic and transport soil properties using an infiltration experiment in which, over a given period, tracer-contaminated water is injected into a laboratory column filled with a homogeneous soil. The numerical model is based on the Richards' equation for solving water flow and the advection-dispersion equation for solving solute transport. Several state variables (e.g., water content, solute concentration, pressure head) are measured during the experiment. Statistical calibration of the computer model is then carried out for different data sets and injection scenarios with the DREAM(ZS) Markov Chain Monte Carlo sampler. The results show that the injection period has a significant effect on the quality of the estimation, in particular, the posterior uncertainty range. The hydraulic and transport parameters of the investigated soil can be estimated from the infiltration experiment using the concentration and cumulative outflow, which are measured non-intrusively. A significant improvement of the identifiability of the parameters is observed when the pressure data from measurements taken inside the column are also considered in the inversion.

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

Water ◽  
2019 ◽  
Vol 11 (11) ◽  
pp. 2232 ◽  
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.

scholarly journals Multi-source data assimilation for physically based hydrological modeling of an experimental hillslope

2018 ◽  
Vol 22 (8) ◽  
pp. 4251-4266 ◽  
Author(s):  
Anna Botto ◽  
Enrica Belluco ◽  
Matteo Camporese
Keyword(s):  
Soil Moisture ◽  
Data Assimilation ◽  
Hydrological Modeling ◽  
Nonlinear Models ◽  
Pressure Head ◽  
Richards Equation ◽  
Test Case ◽  
Hydrological Models ◽  
Filter Performance ◽  
Source Data

Abstract. Data assimilation has recently been the focus of much attention for integrated surface–subsurface hydrological models, whereby joint assimilation of water table, soil moisture, and river discharge measurements with the ensemble Kalman filter (EnKF) has been extensively applied. Although the EnKF has been specifically developed to deal with nonlinear models, integrated hydrological models based on the Richards equation still represent a challenge, due to strong nonlinearities that may significantly affect the filter performance. Thus, more studies are needed to investigate the capabilities of the EnKF to correct the system state and identify parameters in cases where the unsaturated zone dynamics are dominant, as well as to quantify possible tradeoffs associated with assimilation of multi-source data. Here, the CATHY (CATchment HYdrology) model is applied to reproduce the hydrological dynamics observed in an experimental two-layered hillslope, equipped with tensiometers, water content reflectometer probes, and tipping bucket flow gages to monitor the hillslope response to a series of artificial rainfall events. Pressure head, soil moisture, and subsurface outflow are assimilated with the EnKF in a number of scenarios and the challenges and issues arising from the assimilation of multi-source data in this real-world test case are discussed. Our results demonstrate that the EnKF is able to effectively correct states and parameters even in a real application characterized by strong nonlinearities. However, multi-source data assimilation may lead to significant tradeoffs: the assimilation of additional variables can lead to degradation of model predictions for other variables that are otherwise well reproduced. Furthermore, we show that integrated observations such as outflow discharge cannot compensate for the lack of well-distributed data in heterogeneous hillslopes.

scholarly journals Investigation of the Influence of Rainfall Runoff on Shallow Landslides in Unsaturated Soil Using a Mathematical Model

Water ◽  
2019 ◽  
Vol 11 (6) ◽  
pp. 1178 ◽  
Author(s):  
Yen-Yu Chiu ◽  
Hung-En Chen ◽  
Keh-Chia Yeh
Keyword(s):  
Surface Water ◽  
Slope Failure ◽  
Shallow Water Equation ◽  
Pressure Head ◽  
Shallow Landslide ◽  
Shallow Landslides ◽  
Richards Equation ◽  
Rainfall Runoff ◽  
Infinite Slope ◽  
Small Catchment

Infiltration and groundwater have been widely considered as the main factors that cause shallow landslides; however, the effect of runoff has received less attention. In this study, an in-house physical-process-based shallow landslide model is developed to demonstrate the influence of runoff. The model is controlled by coupling the shallow water equation (dynamic) and Richards’ equation. An infinite slope stability analysis is applied to evaluate the possibility of regional landslides. A real, small catchment topography is adopted as a demonstration example. The simulation illustrates the variations of runoff and the factor of safety (FS) during a storm. The results indicate that, after the surface becomes saturated, the FS may keep varying due to the increasing pressure head, which is caused by increasing surface water depth. This phenomenon most likely occurs downstream where the slopes easily accumulate water. The depth of the surface water may also be a factor of slope failure. Therefore, it is essential to increase the accuracy of calculating the runoff depth when assessing regional shallow landslides.

scholarly journals Examples of numerical simulations of two-dimensional unsaturated flow with VS2DI code using different interblock conductivity averaging schemes

Geologos ◽  
2015 ◽  
Vol 21 (3) ◽  
pp. 161-167 ◽  
Author(s):  
Adam Szymkiewicz ◽  
Witold Tisler ◽  
Kazimierz Burzyński
Keyword(s):  
Hydraulic Conductivity ◽  
Unsaturated Flow ◽  
Water Pressure ◽  
Geometric Mean ◽  
Pressure Head ◽  
Richards Equation ◽  
Test Problems ◽  
Simulation Code ◽  
Arithmetic Average ◽  
The Difference

AbstractFlow in unsaturated porous media is commonly described by the Richards equation. This equation is strongly nonlinear due to interrelationships between water pressure head (negative in unsaturated conditions), water content and hydraulic conductivity. The accuracy of numerical solution of the Richards equation often depends on the method used to estimate average hydraulic conductivity between neighbouring nodes or cells of the numerical grid. The present paper discusses application of the computer simulation code VS2DI to three test problems concerning infiltration into an initially dry medium, using various methods for inter-cell conductivity calculation (arithmetic mean, geometric mean and upstream weighting). It is shown that the influence of the averaging method can be very large for coarse grid, but that it diminishes as cell size decreases. Overall, the arithmetic average produced the most reliable results for coarse grids. Moreover, the difference between results obtained with various methods is a convenient indicator of the adequacy of grid refinement.

scholarly journals Identification of Parameters of Richards Equation Using Modified Hybrid Grey Wolf Optimizer-Genetic Algorithm (HmGWOGA)

2019 ◽  
Vol 12 (4) ◽  
pp. 1567-1583
Author(s):  
Wenddabo Olivier Sawadogo ◽  
Pengdwende Ousseni Fabrice Ouedraogo ◽  
Ousseni So ◽  
Genevieve Barro ◽  
Blaise Some
Keyword(s):  
Genetic Algorithm ◽  
Genetic Algorithms ◽  
Meshless Method ◽  
Direct Problem ◽  
Pressure Head ◽  
Optimization Method ◽  
Richards Equation ◽  
Grey Wolf Optimizer ◽  
Grey Wolf ◽  
Better Than

In this paper, it is a question of identification of the parameters in the equation ofRichards modelling the flow in unsaturated porous medium. The mixed formulation pressure head-moisture content has been used. The direct problem was solved using Multiquadratic Radial Basis Function ( RBF-MQ ) method which is a meshless method. The Newton-Raphson’s method was used to linearize the equation. The function cost used is built by using the infiltration. The optimization method used is a meta-heuristic called Modified hybrid Grey Wolf Optimizer -Genetic Algorithm (HmGWOGA). A test on experimental data has been carried. We compared the results with genetic algorithms. The results showed that this new method was better than genetic algorithms.

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

2014 ◽  
Vol 18 (7) ◽  
pp. 2503-2520 ◽  
Author(s):  
G. B. Chirico ◽  
H. Medina ◽  
N. Romano
Keyword(s):  
Kalman Filter ◽  
Finite Difference ◽  
Difference Scheme ◽  
Finite Difference Scheme ◽  
Pressure Head ◽  
Observation Equation ◽  
Richards Equation ◽  
Numerical Schemes ◽  
Near Surface ◽  
Backward Euler

Abstract. This paper examines the potential of different algorithms, based on the Kalman filtering approach, for assimilating near-surface observations into a one-dimensional Richards equation governing soil water flow in soil. Our specific objectives are: (i) to compare the efficiency of different Kalman filter algorithms in retrieving matric pressure head profiles when they are implemented with different numerical schemes of the Richards equation; (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 matric pressure head values. The study is based on a synthetic simulation of an evaporation process from a homogeneous soil column. Our first objective is achieved by implementing a Standard Kalman Filter (SKF) algorithm with both an explicit finite difference scheme (EX) and a Crank-Nicolson (CN) linear finite difference scheme of the Richards equation. The Unscented (UKF) and Ensemble Kalman Filters (EnKF) are applied to handle the nonlinearity of a backward Euler finite difference scheme. To accomplish the second objective, an analogous framework is applied, with the exception of replacing SKF with the Extended Kalman Filter (EKF) in combination with a CN numerical scheme, so as to handle the nonlinearity of the observation equation. While the EX scheme is computationally too inefficient to be implemented in an operational assimilation scheme, the retrieval algorithm implemented with a CN scheme is found to be computationally more feasible and accurate than those implemented with the backward Euler scheme, at least for the examined one-dimensional problem. The UKF appears to be as feasible as the EnKF when one has to handle nonlinear numerical schemes or additional nonlinearities arising from the observation equation, at least for systems of small dimensionality as the one examined in this study.

scholarly journals A Solution of Richards’ Equation by Generalized Finite Differences for Stationary Flow in a Dam

Mathematics ◽  
2021 ◽  
Vol 9 (14) ◽  
pp. 1604
Author(s):  
Carlos Chávez-Negrete ◽  
Daniel Santana-Quinteros ◽  
Francisco Domínguez-Mota
Keyword(s):  
Finite Differences ◽  
Test Problem ◽  
Soil Mechanics ◽  
Stationary Flow ◽  
Standard Test ◽  
Richards Equation ◽  
Saturated Soils ◽  
Transient Case ◽  
Comparative Results ◽  
Stationary Form

The accurate description of the flow of water in porous media is of the greatest importance due to its numerous applications in several areas (groundwater, soil mechanics, etc.). The nonlinear Richards equation is often used as the governing equation that describes this phenomenon and a large number of research studies aimed to solve it numerically. However, due to the nonlinearity of the constitutive expressions for permeability, it remains a challenging modeling problem. In this paper, the stationary form of Richards’ equation used in saturated soils is solved by two numerical methods: generalized finite differences, an emerging method that has been successfully applied to the transient case, and a finite element method, for benchmarking. The nonlinearity of the solution in both cases is handled using a Newtonian iteration. The comparative results show that a generalized finite difference iteration yields satisfactory results in a standard test problem with a singularity at the boundary.

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