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.

Estimation of Soil Water Balance Components Based on Continuous Soil Moisture Measurement and Inversed Richards Method in an Irrigated Agricultural Field of a Desert Oasis

2020 ◽  
Author(s):  
Hu Liu ◽  
Yang Yu ◽  
Zhongkai Li ◽  
Wenzhi Zhao ◽  
Qiyue Yang ◽  
...  
Keyword(s):  
Soil Moisture ◽  
Water Balance ◽  
Soil Water ◽  
Estimation Method ◽  
Growing Season ◽  
Soil Water Balance ◽  
Richards Equation ◽  
Water Balance Components ◽  
Sustainable Water Resources Management ◽  
Irrigation Drainage

<p>An accurate assessment of soil water balance components (<em>SWBCs</em>) is necessary for improving irrigation strategies in any water-limited environment. However, quantitative information of <em>SWBCs</em> is usually challenging to obtain, because none of the components (i.e., irrigation, drainage, and evapotranspiration) can be easily measured under actual conditions. Soil moisture is a variable that integrates the water balance components of land surface hydrology, and the evolution of soil moisture is assumed to contain the memory of antecedent hydrologic fluxes, and thus can be used to determine <em>SWBCs</em> from a hydrologic balance. A database of soil moisture measurements from six experimental plots with different treatments in the middle Heihe River Basin of China was used to test the potential of a soil moisture database in estimating the <em>SWBCs</em>. We first compared the hydrophysical properties of the soils in these plots, such as vertical saturated hydraulic conductivity (<em>K</em><sub>s</sub>) and soil water retention features, for supporting the <em>SWBC</em> estimations. Then we determined evapotranspiration and other SWBCs through a method that combined the soil water balance method and the inverse Richards equation (a model of unsaturated soil water flow based on the Richards equation). To test the accuracy of our estimation, we used both indirect methods (such as power consumption of the pumping irrigation well, and published SWBCs values at nearby sites), and the water balance equation technique to verify the estimated <em>SWBCs</em> values, all of which showed a good reliability of our estimation method. Finally, the uncertainties of the proposed methods were analyzed to evaluate the systematic error of the <em>SWBC</em> estimation and any restrictions on its application. The results showed significant variances among the film-mulched plots in both the cumulative irrigation volumes (652.1~ 867.3 mm) and deep drainages (170.7~364.7 mm). Moreover, the unmulched plot had remarkably higher values in both cumulative irrigation volumes (1186.5 mm) and deep drainages (651.8 mm) compared with the mulched plots. Obvious correlation existed between the volume of irrigation and that of drained water. However, the ET demands for all the plots behaved pretty much the same, with the cumulative ET values ranging between 489.1 and 561.9 mm for the different treatments in 2016, suggesting that the superfluous irrigation amounts had limited influence on the accumulated ET throughout the growing season because of the poor water-holding capacity of the sandy soil. This work confirmed that relatively reasonable estimations of the <em>SWBCs</em> in coarse-textured sandy soils can be derived by using soil moisture measurements; the proposed methods provided a reliable solution over the entire growing season and showed a great potential for identifying appropriate irrigation amounts and frequencies, and thus a move toward sustainable water resources management, even under traditional surface irrigation conditions.</p>

Characterization of Soil Moisture Distribution and Movement Under the Influence of Watering-dewatering Using AHFO and BOTDA Technologies

2019 ◽  
Vol 25 (3) ◽  
pp. 189-202 ◽  
Author(s):  
Ding-Feng Cao ◽  
Bin Shi ◽  
Hong-Hu Zhu ◽  
Chao-Sheng Tang ◽  
Zhan-Pu Song ◽  
...  
Keyword(s):  
Soil Moisture ◽  
Hydraulic Conductivity ◽  
Fine Particles ◽  
Water Movement ◽  
Particle Migration ◽  
Moisture Distribution ◽  
Water Infiltration ◽  
Richards Equation ◽  
Laboratory Model ◽  
Soil Moisture Distribution

ABSTRACT The infiltration and distribution of water through unsaturated soil determine its mechanical and hydrological properties. However, there are few methods that can accurately capture the spatial distribution of moisture inside soil. This study aims to demonstrate the use of actively heated fiber optic (AHFO) and Brillouin optical time domain analysis (BOTDA) technologies for monitoring soil moisture distribution as well as strain distribution. In addition to a laboratory model test, finite element analyses were conducted to interpret the measurements. During the experiment, the fine particle migration was also measured to understand its influence on soil hydraulic conductivity. The results of the experiment indicate that (i) for a soil that has never experienced a watering-dewatering cycle, water infiltration can be accurately calculated using the Richards’ equation; (ii) migration of fine soil particles caused by the watering-dewatering cycle significantly increases the hydraulic conductivity; and (iii) two critical zones (drainage and erosion) play significant roles in determining the overall hydraulic conductivity of the entire soil. This study provides a new method for monitoring the changes in soil moisture, soil strain, and hydraulic conductivity. The observations suggest that the effect of fine particles migration should be considered while evaluating soil moisture distribution and water movement.

scholarly journals Quantification of soil water balance components based on continuous soil moisture measurement and the Richards equation in an irrigated agricultural field of a desert oasis

2019 ◽  
Vol 23 (11) ◽  
pp. 4685-4706 ◽  
Author(s):  
Zhongkai Li ◽  
Hu Liu ◽  
Wenzhi Zhao ◽  
Qiyue Yang ◽  
Rong Yang ◽  
...  
Keyword(s):  
Soil Moisture ◽  
Water Balance ◽  
Soil Water ◽  
Estimation Method ◽  
Growing Season ◽  
Soil Water Balance ◽  
Richards Equation ◽  
Water Balance Components ◽  
Sustainable Water Resources Management ◽  
Irrigation Drainage

Abstract. An accurate assessment of soil water balance components (SWBCs) is necessary for improving irrigation strategies in any water-limited environment. However, quantitative information on SWBCs is usually challenging to obtain, because none of the components (i.e., irrigation, drainage, and evapotranspiration) can be easily measured under actual conditions. Soil moisture is a variable that integrates the water balance components of land surface hydrology, and the evolution of soil moisture is assumed to contain the memory of antecedent hydrologic fluxes, and can thus be used to determine SWBCs from a hydrologic balance. A database of soil moisture measurements from six experimental plots with different treatments in the middle Heihe River basin of China was used to test the potential of a such a database for estimating SWBCs. We first compared the hydrophysical properties of the soils in these plots, such as vertical saturated hydraulic conductivity (Ks) and soil water retention features, for supporting SWBC estimations. We then determined evapotranspiration and other SWBCs using a method that combined the soil water balance method and the inverse Richards equation (a model of unsaturated soil water flow based on the Richards equation). To test the accuracy of our estimation, we used both indirect methods (such as power consumption of the pumping irrigation well and published SWBCs values at nearby sites) and the water balance equation technique to verify the estimated SWBCs values, all of which showed good reliability with respect to our estimation method. Finally, the uncertainties of the proposed methods were analyzed to evaluate the systematic error of the SWBC estimation and any restrictions regarding its application. The results showed significant variances among the film-mulched plots in both the cumulative irrigation volumes (652.1–867.3 mm) and deep drainages (170.7–364.7 mm). Moreover, the un-mulched plot had remarkably higher values in both cumulative irrigation volumes (1186.5 mm) and deep drainages (651.8 mm) compared with the mulched plots. Obvious correlation existed between the volume of irrigation and that of drained water. However, the ET demands for all of the plots behaved pretty much the same, with the cumulative ET values ranging between 489.1 and 561.9 mm for the different treatments in 2016, suggesting that the superfluous irrigation amounts had limited influence on the accumulated ET throughout the growing season due to the poor water-holding capacity of the sandy soil. This work confirmed that relatively reasonable estimations of the SWBCs in coarse-textured sandy soils can be derived by using soil moisture measurements; the proposed methods provided a reliable solution over the entire growing season and showed a great potential for identifying appropriate irrigation amounts and frequencies, and thus a move toward sustainable water resources management, even under traditional surface irrigation conditions.

Modelling water uptake by a mature apple tree

Soil Research ◽  
2003 ◽  
Vol 41 (3) ◽  
pp. 365 ◽  
Author(s):  
S. R. Green ◽  
I. Vogeler ◽  
B. E. Clothier ◽  
T. M. Mills ◽  
C. van den Dijssel
Keyword(s):  
Experimental Data ◽  
Water Content ◽  
Soil Water ◽  
Water Uptake ◽  
Apple Tree ◽  
Water Movement ◽  
Root Zone ◽  
Time Domain Reflectometry ◽  
Richards Equation ◽  
Mature Apple

We report the results from a field experiment in which we examined the spatial and temporal patterns of water uptake by a mature apple tree (Malus domestica Borkh., 'Splendour') in an orchard. Time domain reflectometry was used to measure changes in the soil's volumetric water content, and heat-pulse was used to monitor locally the rates of sap flow in the trunk and roots of the tree. The tree's distribution of root-length density and supporting data to characterise the soil's hydraulic properties were determined for the purpose of modelling soil water movement in the root-zone under an apple tree. Experimental data are compared against the output from a numerical model of the soil water balance that uses Richards' equation for water flow, and uses a distributed macroscopic sink term for root uptake. In general, there was a very good agreement between the measured and modelled results. The apple trees consumed some 70 L of water per day during the middle of summer. The daily water use declined to about 20 L per day with the onset of autumn, coinciding with a reduced evaporative demand and an increasing number of rain days. Water movement in the root-zone soil was dominated by the water uptake via surface roots. Large changes in soil water content were also associated with each irrigation event. Our experimental data support the contention that more frequent irrigation in smaller doses will result in less water percolating through the root-zone. Such an irrigation strategy should make more efficient use of water by minimising the leaching losses. It will also be helpful for environmental protection by reducing the percolation losses of water and solute beyond the grasp of the roots.

scholarly journals Soil hydraulic material properties and layered architecture from time-lapse GPR

2018 ◽  
Vol 22 (4) ◽  
pp. 2551-2573 ◽  
Author(s):  
Stefan Jaumann ◽  
Kurt Roth
Keyword(s):  
Soil Water ◽  
Material Properties ◽  
Simulated Annealing Algorithm ◽  
Water Movement ◽  
Time Domain Reflectometry ◽  
Groundwater Table ◽  
Richards Equation ◽  
Ground Truth Data ◽  
Marquardt Algorithm ◽  
Soil Hydraulic

Abstract. Quantitative knowledge of the subsurface material distribution and its effective soil hydraulic material properties is essential to predict soil water movement. Ground-penetrating radar (GPR) is a noninvasive and nondestructive geophysical measurement method that is suitable to monitor hydraulic processes. Previous studies showed that the GPR signal from a fluctuating groundwater table is sensitive to the soil water characteristic and the hydraulic conductivity function. In this work, we show that the GPR signal originating from both the subsurface architecture and the fluctuating groundwater table is suitable to estimate the position of layers within the subsurface architecture together with the associated effective soil hydraulic material properties with inversion methods. To that end, we parameterize the subsurface architecture, solve the Richards equation, convert the resulting water content to relative permittivity with the complex refractive index model (CRIM), and solve Maxwell's equations numerically. In order to analyze the GPR signal, we implemented a new heuristic algorithm that detects relevant signals in the radargram (events) and extracts the corresponding signal travel time and amplitude. This algorithm is applied to simulated as well as measured radargrams and the detected events are associated automatically. Using events instead of the full wave regularizes the inversion focussing on the relevant measurement signal. For optimization, we use a global–local approach with preconditioning. Starting from an ensemble of initial parameter sets drawn with a Latin hypercube algorithm, we sequentially couple a simulated annealing algorithm with a Levenberg–Marquardt algorithm. The method is applied to synthetic as well as measured data from the ASSESS test site. We show that the method yields reasonable estimates for the position of the layers as well as for the soil hydraulic material properties by comparing the results to references derived from ground truth data as well as from time domain reflectometry (TDR).

scholarly journals Soil hydraulic material properties and subsurface architecture from time-lapse GPR

2017 ◽  
Author(s):  
Stefan Jaumann ◽  
Kurt Roth
Keyword(s):  
Soil Water ◽  
Material Properties ◽  
Simulated Annealing Algorithm ◽  
Water Movement ◽  
Ground Truth ◽  
Time Domain Reflectometry ◽  
Richards Equation ◽  
Ground Truth Data ◽  
Marquardt Algorithm ◽  
Soil Hydraulic

Abstract. Quantitative knowledge of effective soil hydraulic material properties is essential to predict soil water movement. Ground-penetrating radar (GPR) is a non-invasive and non-destructive geophysical measurement method to monitor the hydraulic processes precisely. Previous studies showed that the GPR signal from a fluctuating groundwater table is sensitive to the soil water characteristic and the hydraulic conductivity function. In this work, we show that this signal is suitable to accurately estimate the subsurface architecture and the associated effective soil hydraulic material properties with inversion methods. Therefore, we parameterize the subsurface architecture, solve the Richards equation, convert the resulting water content to relative permittivity with the complex reflective index model (CRIM), and solve Maxwell's equations numerically. In order to analyze the GPR signal, we implemented a new heuristic event detection and association algorithm. Using events instead of the full wave regularizes the inversion as it allows to focus on the relevant measurement signal. Starting from an ensemble of Latin hypercube drawn initial parameter sets, we sequentially couple the simulated annealing algorithm with the Levenberg–Marquardt algorithm. We apply the method to synthetic as well as measured data from the ASSESS test site and show that the method yields accurate estimates for the soil hydraulic material properties as well as for the subsurface architecture by comparing the results to references derived from time domain reflectometry (TDR) and subsurface architecture ground truth data.

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.

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.

scholarly journals Using Soil Water Stable Isotopes to Investigate Soil Water Movement in a Water Conservation Forest in Hani Terrace

Water ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 3520
Author(s):  
Huimei Pu ◽  
Weifeng Song ◽  
Jinkui Wu
Keyword(s):  
Stable Isotopes ◽  
Soil Water ◽  
Water Conservation ◽  
Rainy Season ◽  
Preferential Flow ◽  
Water Movement ◽  
Soil Depth ◽  
Dry Season ◽  
Water Infiltration ◽  
Soil Water Movement

Water conservation forests significantly contribute to the stability of mountain agricultural ecosystems in Hani Terrace. In this study, we analyzed the relationship between the stable isotopic composition of soil water and precipitation to determine the mechanisms of soil water movement in the small watershed of Quanfuzhuang. We observed significant seasonal variations in soil water sources: antecedent precipitation was the dominant supply during the dry season, and current precipitation dominated during the rainy season. The recharge ratio of precipitation to soil water in the grassland was significantly higher than that in the arbor land and shrubland. The influence of water infiltration, old and new soil water mixing, and soil evaporation on the soil water stable isotopes gradually decreased from the surface (0–20 cm) to the deep (60–80 cm) soil. We observed significant seasonal variability in average soil water δ18O in the upper 0–60 cm and lower variability at 60–100 cm. The average soil water δ18O was generally higher in the dry season than in the rainy season. The mixing of old and new water is a continuous and cumulative process that is impacted by soil structure, soil texture, and precipitation events. We therefore identified a significant time delay in soil water supply with increasing soil depth. Moreover, the piston flow of soil water co-occurred with preferential flow, and the latter was the dominant supply during the rainy season.

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