Approximate solution of a one-dimensional soil water infiltration equation based on the Brooks-Corey model

Su, Lijun; Wang, Jiao; Qin, Xinqiang; Wang, Quanjiu

doi:10.1016/j.geoderma.2017.02.026

Cited by 32 publications

(15 citation statements)

References 28 publications

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“…We used the Brooks–Corey model to determine the soil water diffusivity D ( θ ) and the unsaturated hydraulic conductivity k ( θ ) (Brooks & Corey, ; Dong & Wang, ; Su, Wang, Qin, & Wang, ):

k ((), Θ) = k_{s} Θ^{M},

D ((), Θ) = \frac{K_{S} h_{d} Θ^{l + 1 / N}}{N ((), θ_{s} - θ_{r})},

normalΘ = \frac{θ - θ_{r}}{θ_{s} - θ_{r}},

where N and M represent shape parameters ( M = 2 + 3 N ), h d is the air entry suction, l is the pore tortuosity (2 in the Brooks–Corey model), θ s is the saturated water content (%), θ r is the retention water content (%). θ s and θ are measured directly.…”

Section: Methodsmentioning

confidence: 99%

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Modelling soil solute release and transport in run‐off on a loessial slope with and without surface stones

Dong

Cui

et al. 2018

Hydrological Processes

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Stone covers on loessial slopes can increase the time of infiltration by slowing the velocity of the overland flow, which reduces the transport of solutes, but few mechanistic models have been tested under water‐scouring conditions. We carried out field experiments to test a previously proposed, physically based model of water and solute transport. The area of soil infiltration was calculated from the uncovered surface area, and Richards' equation and the kinematic wave equation were used to describe water infiltration and flow along slopes with stone covers. The transport of chemicals into the run‐off from the surface soil, presumably by diffusion, and their movement in the soil profile could be described by the convection–diffusion equations of the model. The simulated and measured data correlated well. The stones on the soil surface reduced the area available for infiltration but increased the Manning coefficient, eventually leading to increased water infiltration and decreased solute loss with run‐off. Our results indicated that the traditional model of water movement and solute migration could be used to simulate water transport and solute migration for stone‐covered soil on loessial slopes.

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“…We used the Brooks–Corey model to determine the soil water diffusivity D ( θ ) and the unsaturated hydraulic conductivity k ( θ ) (Brooks & Corey, ; Dong & Wang, ; Su, Wang, Qin, & Wang, ):

k ((), Θ) = k_{s} Θ^{M},

D ((), Θ) = \frac{K_{S} h_{d} Θ^{l + 1 / N}}{N ((), θ_{s} - θ_{r})},

normalΘ = \frac{θ - θ_{r}}{θ_{s} - θ_{r}},

Section: Methodsmentioning

confidence: 99%

“…We used the Brooks-Corey model to determine the soil water diffusivity D(θ) and the unsaturated hydraulic conductivity k(θ) (Brooks & Corey, 1964;Su, Wang, Qin, & Wang, 2017):…”

Section: Soil Hydraulic Parametersmentioning

confidence: 99%

Modelling soil solute release and transport in run‐off on a loessial slope with and without surface stones

Dong

Cui

et al. 2018

Hydrological Processes

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“…In these studies, undisturbed 20 cm depth soil samples were obtained for the hydraulic parameters that were estimated through the vertical infiltration method, which would save more time than the direct SWRC measurements. Su et al [22] used second-, third-, and fourth-order Taylor series expansions to obtain an approximate analytical solution for a one-dimensional, constant water head, vertical infiltration. This study, however, used first-order Taylor series expansion for parameter estimation with satisfying accuracy, which simplified the calculation.…”

Section: Discussionmentioning

confidence: 99%

Brooks–Corey Modeling by One-Dimensional Vertical Infiltration Method

Xing

Wang

2018

Water

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The laboratory methods used for the soil water retention curve (SWRC) construction and parameter estimation is time-consuming. A vertical infiltration method was proposed to estimate parameters α and n and to further construct the SWRC. In the present study, the relationships describing the cumulative infiltration and infiltration rate with the depth of the wetting front were established, and simplified expressions for estimating α and n parameters were proposed. The one-dimensional vertical infiltration experiments of four soils were conducted to verify if the proposed method would accurately estimate α and n. The fitted values of α and n, obtained from the RETC software, were consistent with the calculated values obtained from the infiltration method. The comparison between the measured SWRCs obtained from the centrifuge method and the calculated SWRCs that were based on the infiltration method displayed small values of root mean square error (RMSE), mean absolute percentage error (MAPE), and mean absolute error. SWMS_2D-based simulations of cumulative infiltration, based on the calculated α and n, remained consistent with the measured values due to small RMSE and MAPE values. The experiments verified the proposed one-dimensional vertical infiltration method, which has applications in field hydraulic parameter estimation.

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“…Approximate solutions are also derived using the form of Brooks and Corey of hydraulic conductivity and the moisture content vs. the pressure head and considering a rectangular profile of moisture content [16] [17] [18]. Su et al [19], solved the equation of Richards, using a new method based on the Principle of Least Action and the Variational Principle.…”

Section: Introductionmentioning

confidence: 99%

Fuzzy Analytical Solution to Vertical Infiltration

Tzimopoulos¹,

Papaevangelou²,

Papadopoulos³

et al. 2020

JSEA

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In this article, we examine the solution of the fuzzy linear vertical infiltration equation, which represents the water movement in porous media in that part which is called the vadose zone. This zone is very important for semi-arid areas, due to complex phenomena related to the moisture content in it. These phenomena concern the interchange of moisture content between the vadose zone and the atmosphere, groundwater and vegetation, transfer of moisture and vapor and retention of moisture. The equation describing the problem is a partial differential parabolic equation of second order. The calculation of water flow in the unsaturated zone requires the knowledge of the initial and boundary conditions as well as the various soil parameters. But these parameters are subject to different kinds of uncertainty due to human and machine imprecision. For that reason, fuzzy set theory was used here for facing imprecision or vagueness. As the problem concerns fuzzy differential equations, the generalized Hukuhara (gH) derivative was used for total derivatives, as well as the extension of this theory for partial derivatives. The results are the fuzzy moisture content, the fuzzy cumulative infiltration and the fuzzy infiltration rate versus time. These results allow researchers and engineers involved in Irrigation and Drainage Engineering to take into account the uncertainties involved in infiltration.

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Approximate solution of a one-dimensional soil water infiltration equation based on the Brooks-Corey model

Cited by 32 publications

References 28 publications

Modelling soil solute release and transport in run‐off on a loessial slope with and without surface stones

Modelling soil solute release and transport in run‐off on a loessial slope with and without surface stones

Brooks–Corey Modeling by One-Dimensional Vertical Infiltration Method

Fuzzy Analytical Solution to Vertical Infiltration

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