Analytical Solutions for Water Infiltration into Unsaturated–Semi-Saturated Soils Under Different Water Content Distributions on the Top Boundary

Sanayei, Hamed Reza Zarif; Talebbeydokhti, Nasser; Rakhshandehroo, Gholamreza

doi:10.1007/s40996-019-00245-3

Cited by 8 publications

(2 citation statements)

References 35 publications

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“…Soil hydraulic conductivity is essential information for soil water flow and solute transport simulations to represent hydrological processes such as water storage, release, and transfer in the soil, and is therefore a prerequisite and key link to ensure model effectiveness. Saturated hydraulic conductivity is often spatially heterogeneous and scaledependent [1,2]. Uncertainty in ground permeability can result in considerable alterations to the response of the porous medium [3,4].…”

Section: Introductionmentioning

confidence: 99%

High-Resolution Estimation of Soil Saturated Hydraulic Conductivity via Upscaling and Karhunen–Loève Expansion within DREAM(ZS)

Xia,

2024

Applied Sciences

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Quantification of the soil hydraulic conductivity is key to the study of water flow and solute transport in unsaturated soils. Rapid advances in measurement technology have provided a large number of observations at different scales, offering unprecedented opportunities and challenges for the estimation of hydraulic parameters. This paper proposes an inverse estimation method for downscaling of observations on coarse scales to estimate hydraulic parameters on high-resolution scales. Due to the significant spatial heterogeneity, the inversion faces the problems of dynamics-based integration of data at different scales, model uncertainty due to hundreds and thousands of parameters, and computational consumption due to the large number of forward simulations. To overcome these problems, this paper uses an efficient Bayesian optimization DREAM(ZS) as an inverse framework, and incorporates an analytical upscaling method and Karhunen–Loève (KL) expansion to infer finer-scale saturated hydraulic conductivity distribution conditioned on coarse-scale measurements. The efficient upscaling method is used to link measurements and hydraulic parameters at different scales, and Karhunen–Loève (KL) expansion is incorporated to greatly reduce the dimension of the parameter to be estimated. To further improve the efficiency of the inversion, a locally one-dimensional (LOD) algorithm is used to solve the multidimensional water flow model at coarse scales. The proposed inverse model is applied in a series of numerical experiments to demonstrate its applicability and effectiveness under different flow boundary conditions, different levels of ratio between coarse- and fine-scale grids, different densities of observation points, and different degrees of statistic heterogeneity of soil mediums.

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Section: Introductionmentioning

confidence: 99%

High-Resolution Estimation of Soil Saturated Hydraulic Conductivity via Upscaling and Karhunen–Loève Expansion within DREAM(ZS)

Xia,

2024

Applied Sciences

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“…Analytical and semi-analytical solutions continue and give a proper understanding for problems, compared to numerical solutions. Analytical solutions can be used as reference solutions for verifying numerical solutions and numerical programming [17,18]. Patil et al [19] introduced an improved direct method for the Chow method in prismatic channels to solve the GVF equation.…”

Section: Introductionmentioning

confidence: 99%

Simple Semi-analytical Solutions Using the Perturbation Method for Gradually Varied Flow Profile in Triangular Channels

Sanayei¹,

Nasiri²

2020

MMEP

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In hydraulic engineering, the steady non-uniform flow in a channel with the gradual changes at the water surface level is introduced as the Gradually Varied Flow (GVF). For the design of open channels, it is necessary to calculate the GVF profile along the channel flow. The GVF profile is described by a nonlinear Ordinary Differential Equation (ODE). Because this equation is strongly nonlinear, providing new analytical and/or semi-analytical solutions for this equation without any simplifications and/or linearizations would be necessary and helpful. In this research, the Perturbation Method (PM) is proposed to present a semi-analytical solution for solving the GVF equation in the prismatic triangular channel. A total of two cases are studied in this paper. In case 1, the Manning equation and in case 2, the Chezy equation are applied as the resistance equations. The GVF profiles in the two cases are compared with the Finite Difference Method (FDM) profiles. Also, the effect of the summation truncation in the PM is studied for these cases. The results show that by increasing the terms approximation in the PM, the GVF profile converges to the FDM profile. A reference solution for efficiency assessment of numerical techniques can be provided by presented semi-analytical solutions in this paper. Furthermore, the proposed method in this paper can be used as a new idea in providing semi-analytical solutions to other open channel works.

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Approximate analytical solution of a soil water movement equation under different ponding radii on the basis of numerical simulation

Luo,

Su,

Tao

et al. 2024

Soil Science Soc of Amer J

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This study addresses the problem of 2D soil water movement under ponding radii of 1, 2, and 3 cm. The soil water movement characteristics (shape parameters of the water content profile, ratio of horizontal wetting front to vertical wetting front, relationship between infiltration time and horizontal wetting front, and relationship between infiltration time and cumulative infiltration) under the above three kinds of water ponding radius were analyzed. On the basis of the assumption that the soil wetting body is a semi‐ellipse and the analytical solution of the 1D soil water movement equation at any angle, the approximate analytical solution of the 2D soil water movement equation under ponding conditions is optimized. The function relationships between infiltration time, wetting front, and cumulative infiltration are established. We applied the numerical data simulated by HYDRUS‐3D to validate the parameters in proposed analytical solutions and evaluated the relationships between the wetting front and hydraulic parameters. The results indicate that as the water ponding radius increases, the wetting body and 2D water content distribution becomes larger. When the water ponding radius was 2 cm, the numerical and analytical solution of 1D soil water distribution showed the best comparison results, and the model error was the smallest. The ratio of wetting fronts was linearly increased with the increase of air‐entry suction with R2 = 0.9969.

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Analytical Solutions for Water Infiltration into Unsaturated–Semi-Saturated Soils Under Different Water Content Distributions on the Top Boundary

Cited by 8 publications

References 35 publications

High-Resolution Estimation of Soil Saturated Hydraulic Conductivity via Upscaling and Karhunen–Loève Expansion within DREAM(ZS)

High-Resolution Estimation of Soil Saturated Hydraulic Conductivity via Upscaling and Karhunen–Loève Expansion within DREAM(ZS)

Simple Semi-analytical Solutions Using the Perturbation Method for Gradually Varied Flow Profile in Triangular Channels

Approximate analytical solution of a soil water movement equation under different ponding radii on the basis of numerical simulation

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