The soil moisture velocity equation

Ogden, Fred L.; Allen, Myron B.; Lai, Wencong; Zhu, Jianting; Seo, Mookwon; Douglas, Craig C.; Talbot, Cary A.

doi:10.1002/2017ms000931

Cited by 22 publications

(24 citation statements)

References 51 publications

(92 reference statements)

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“…Fluxes calculated using the SMVE advection-like term agree very closely with the numerical solution of Richards' equation (Ogden et al, 2015a), data from column experiments (Ogden et al, 2015b) and exact analytical solutions (Ogden et al, 2017). Results in all cases show that the diffusion-like term in Eq.…”

Section: Discussion and Alternativessupporting

confidence: 64%

“…It is possible, for example, to convert Richards' equation into a formulation for the evolution of soil moisture front location with θ as the independent variable under suitable assumptions (Philip, 1957;Swartzendruber, 1969). Ogden et al (2017) converted the one-dimensional Richards' equation into a form that they call the Soil Moisture Velocity Equation (SMVE) that describes the speed of propagation of particular moisture contents within a homogeneous soil layer:…”

Section: Discussion and Alternativesmentioning

confidence: 99%

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Numerical Solution of Richards' Equation: A Review of Advances and Challenges

Farthing

Ogden

2017

Soil Science Soc of Amer J

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248

138

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The flow of water in partially saturated porous media is of importance in fields such as hydrology, agriculture, environment and waste management. It is also one of the most complex flows in nature. The Richards' equation describes the flow of water in an unsaturated porous medium due to the actions of gravity and capillarity neglecting the flow of the non-wetting phase, usually air. Analytical solutions of Richards' equation exist only for simplified cases, so most practical situations require a numerical solution in one-two-or threedimensions, depending on the problem and complexity of the flow situation. Despite the fact that the first reasonably complete conservative numerical solution method was published in the early 1990s, the numerical solution of the Richards' equation remains computationally expensive and in certain circumstances, unreliable. A universally robust and accurate solution methodology has not yet been identified that is applicable across the range of soils, initial and boundary conditions found in practice. Existing solution codes have been modified over years to attempt to increase robustness. Despite theoretical results on the existence of solutions given sufficiently regular data and constitutive relations, our numerical methods often fail to demonstrate reliable convergence behavior in practice, especially for higher-order methods. Because of robustness, the lack of higher-order accuracy and computational expense, alternative solution approaches or methods are needed. There is also a need for better documentation of improved solution methodologies and benchmark test problems to facilitate consistent advances and avoid re-inventing of the wheel.T his review paper is intended to serve as a touchstone on the state of the science of calculating the flow of water through unsaturated porous media. As active researchers we believe it is good to occasionally take stock in what has been accomplished up to date, where things may be headed, and what important issues remain. This review concentrates on computational modeling of flow through the unsaturated zone via Richards' equation.This effort can help provide some focus to the research community and serve to help propel new research forward, particularly by those just joining the field. There are many practical problems that require calculation of one-, two-, and threedimensional fluxes in the unsaturated zone. For a much broader review of modeling soil processes, we recommend the recent paper from Vereecken et al. (2016). A detailed review of mathematical models of infiltration can be found (Assouline, 2013), while Paniconi and Putti (2015) provide historical perspective and an overview of modeling Richards' equation in the context of catchment hydrology.The equation attributed to Richards (1931) that describes the flow of water through unsaturated porous media under the action of capillarity and gravity was first published by the English mathematician and physicist Lewis Fry Richardson in 1922(Richardson, 1922. Therefore, the equation would r...

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Section: Discussion and Alternativessupporting

confidence: 64%

Section: Discussion and Alternativesmentioning

confidence: 99%

Numerical Solution of Richards' Equation: A Review of Advances and Challenges

Farthing

Ogden

2017

Soil Science Soc of Amer J

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248

138

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“…The sublayer was further divided into two domains, a matrix infiltration domain and a vertical PFP domain. In the matrix infiltration domain, downward water movement was simulated using the Green‐Ampt infiltration with redistribution (GAR) model with features from the Talbot‐Ogden (T‐O) infiltration and redistribution method (Lai et al, ), which is a simplified version of the finite moisture content solution of the Soil Moisture Velocity Equation (Ogden et al, , ). Macropores in the vertical PFP domain were assumed to fully penetrate the preferential flow layer and were referred to as “effective percolating vertical PFPs.” Water movement through these effective percolating vertical macropores was explicitly simulated using a laminar pipe flow equation.…”

Section: Methodsmentioning

confidence: 99%

Land Use‐Dependent Preferential Flow Paths Affect Hydrological Response of Steep Tropical Lowland Catchments With Saprolitic Soils

Cheng

Ogden

Zhu

et al. 2018

Water Resources Research

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Forested catchments in Central Panama can produce more base flow during the dry season compared to pasture catchments—the so‐called “forest sponge effect.” During rainfall events, peak storm runoff rates and storm runoff coefficients can be lower for forested catchments than pasture catchments, even when they have similar topographic characteristics, underlying geology, and soil texture. The internal mechanism of these differences in hydrological response due to land use is yet to be fully understood. A distributed model explicitly simulating preferential flow paths (PFPs), which is referred to as “PFPMod,” is used to explain the hydrological response caused by land use using data from three catchments with distinct land covers in Central Panama. Input parameters of forest and pasture land covers were identified using field observations and literature values. Multiple satisfactory objective criteria demonstrate that the two end‐member land cover parameter sets are adequate to explain the observed difference in dry‐season base flow and storm runoff coefficients. Field measurements of matrix infiltrability using soil cores and plot‐scale infiltration capacity enabled estimating the number of vertical macropores that fully penetrate the root zone. Model simulation results demonstrate that fast drainage through lateral PFPs in the early wet season and high flow in vertical PFPs to recharge deep groundwater in the late wet season contribute to the observed differences in peak storm runoff and the “forest sponge effect” during the dry season. This study provided insights to the mechanism by which reforestation may help to restore ecosystem services and water security in tropical settings.

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“…However, neglecting capillary pressure gradient is an obvious oversimplification if the groundwater table is shallow or the soil moisture profile is nonuniform. Recently, starting from RRE, Ogden et al () have derived a new equation—Soil Moisture Velocity Equation (SMVE), which allows calculation of the speed of travel of specific moisture contents in the soils:

{(\frac{\partial z}{\partial t})}_{θ} = - \frac{\partial K}{\partial θ} ((), \frac{\partial h}{\partial z} - 1) - D \frac{\partial^{2} h}{\partial z^{2}} / \frac{\partial h}{\partial z}

where the first and second terms are the advection‐like and the diffusion‐like terms. It should be noted that the derivation of SMVE does not introduce any approximation to RRE from a mathematical point of view.…”

Section: Limitations Challenges and Opportunitiesmentioning

confidence: 99%

Review of numerical solution of Richardson–Richards equation for variably saturated flow in soils

et al. 2019

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Modeling variably saturated flow in the vadose zone is of vital importance to many scientific fields and engineering applications. Richardson-Richards equation (RRE, which is conventionally known as Richards' equation) is often chosen to physically represent the fluxes in the vadose zone when the accurate characterization of the soil water dynamics is required. Being a highly nonlinear partial differential equation, RRE is often solved numerically. Although there are mature software and codes available for simulating variably saturated flow by solving RRE, the numerical solution of RRE is nevertheless computationally expensive.Moreover, sometimes the robustness and the efficiency of RRE-based models can deteriorate rapidly when certain unfavorable conditions are met. These demerits of RRE hinder its application on large-scale vadose zone hydrology problems and uncertainty quantification, both of which requires many runs of the prediction model. To address these challenges, the accuracy, convergence, and efficiency of the numerical schemes of RRE should be further improved by testing a wide variety of cases covering different initial conditions, boundary conditions, and soil types. We reviewed and highlighted several critical issues related to the numerical modeling of RRE, including spatial and temporal discretization, the different forms of RREs, iterative and noniterative schemes, benchmark solutions, and available software and codes. Based on the review, we summarize the challenges and future work for solving RRE numerically.

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The soil moisture velocity equation

Cited by 22 publications

References 51 publications

Numerical Solution of Richards' Equation: A Review of Advances and Challenges

Numerical Solution of Richards' Equation: A Review of Advances and Challenges

Land Use‐Dependent Preferential Flow Paths Affect Hydrological Response of Steep Tropical Lowland Catchments With Saprolitic Soils

Review of numerical solution of Richardson–Richards equation for variably saturated flow in soils

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