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Finite Water-content Vadose Zone Flow Method
The finite water-content vadose zone flux methodTalbot, C.A., and F. L. Ogden (2008), A method for computing infiltration and redistribution in a discretized moisture content domain, ''Water Resour. Res.'', 44(8), doi: 10.1029/2008WR006815.Ogden, F. L., W. Lai, R. C. Steinke, J. Zhu, C. A. Talbot, and J. L. Wilson (2015), A new general 1-D vadose zone solution method, ''Water Resour.Res.'', 51, doi:10.1002/2015WR017126. represents a one-dimensional alternative to the numerical solution of Richards' equation for simulating the movement of water in unsaturated soils. The finite water-content method solves the advection-like term of the Soil Moisture Velocity Equation, which is an ordinary differential equation alternative to the Richards partial differential equation. The Richards equation is difficult to approximate in general because it does not have a closed-form analytical solution except in a few cases.Ross, P.J., and J.-Y. Parlange (1994). Comparing exact and numerical solu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Richards' Equation
The Richards equation represents the movement of water in unsaturated soils, and is attributed to Lorenzo A. Richards who published the equation in 1931. It is a quasilinear partial differential equation; its analytical solution is often limited to specific initial and boundary conditions. Proof of the existence and uniqueness of solution was given only in 1983 by Alt and Luckhaus. The equation is based on Darcy-Buckingham law representing flow in porous media under variably saturated conditions, which is stated as :\vec=-\mathbf(\theta) (\nabla h + \nabla z), where :\vec is the volumetric flux; :\theta is the volumetric water content; :h is the liquid pressure head, which is negative for unsaturated porous media; :\mathbf(h) is the unsaturated hydraulic conductivity; :\nabla z is the geodetic head gradient, which is assumed as \nabla z = \left(\begin 0 \\ 0 \\ 1 \end \right) for three-dimensional problems. Considering the law of mass conservation for an incompressible ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ordinary Differential Equations
In mathematics, an ordinary differential equation (ODE) is a differential equation whose unknown(s) consists of one (or more) function(s) of one variable and involves the derivatives of those functions. The term ''ordinary'' is used in contrast with the term partial differential equation which may be with respect to ''more than'' one independent variable. Differential equations A linear differential equation is a differential equation that is defined by a linear polynomial in the unknown function and its derivatives, that is an equation of the form :a_0(x)y +a_1(x)y' + a_2(x)y'' +\cdots +a_n(x)y^+b(x)=0, where , ..., and are arbitrary differentiable functions that do not need to be linear, and are the successive derivatives of the unknown function of the variable . Among ordinary differential equations, linear differential equations play a prominent role for several reasons. Most elementary and special functions that are encountered in physics and applied mathematics ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hydrology
Hydrology () is the scientific study of the movement, distribution, and management of water on Earth and other planets, including the water cycle, water resources, and environmental watershed sustainability. A practitioner of hydrology is called a hydrologist. Hydrologists are scientists studying earth or environmental science, civil or environmental engineering, and physical geography. Using various analytical methods and scientific techniques, they collect and analyze data to help solve water related problems such as environmental preservation, natural disasters, and water management. Hydrology subdivides into surface water hydrology, groundwater hydrology (hydrogeology), and marine hydrology. Domains of hydrology include hydrometeorology, surface hydrology, hydrogeology, drainage-basin management, and water quality, where water plays the central role. Oceanography and meteorology are not included because water is only one of many important aspects within those fiel ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Soil Physics
Soil physics is the study of soil's physical properties and processes. It is applied to management and prediction under natural and managed ecosystems. Soil physics deals with the dynamics of physical soil components and their phases as solids, liquids, and gases. It draws on the principles of physics, physical chemistry, engineering, and meteorology. Soil physics applies these principles to address practical problems of agriculture, ecology, and engineering. Prominent soil physicists * Edgar Buckingham (1867–1940) :The theory of gas diffusion in soil and vadose zone water flow in soil. *Willard Gardner (1883-1964) :First to use porous cups and manometers for capillary potential measurements and accurately predicted the moisture distribution above a water table.Sterling A. Taylor: Willard Gardner, 1883-1964. Soil Science 100(2), 1965. * Lorenzo A. Richards (1904–1993) :General transport of water in unsaturated soil, measurement of soil water potential using tensiom ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Infiltration (hydrology)
Infiltration is the process by which water on the ground surface enters the soil. It is commonly used in both hydrology and soil sciences. The infiltration capacity is defined as the maximum rate of infiltration. It is most often measured in meters per day but can also be measured in other units of distance over time if necessary. The infiltration capacity decreases as the soil moisture content of soils surface layers increases. If the precipitation rate exceeds the infiltration rate, runoff will usually occur unless there is some physical barrier. Infiltrometers, permeameters and rainfall simulators are all devices that can be used to measure infiltration rates. Infiltration is caused by multiple factors including; gravity, capillary forces, adsorption and osmosis. Many soil characteristics can also play a role in determining the rate at which infiltration occurs. Factors that affect infiltration Precipitation Precipitation can impact infiltration in many ways. T ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Water Retention Curve
Water retention curve is the relationship between the water content, θ, and the soil water potential, ψ. This curve is characteristic for different types of soil, and is also called the soil moisture characteristic. It is used to predict the soil water storage, water supply to the plants ( field capacity) and soil aggregate stability. Due to the hysteretic effect of water filling and draining the pores, different wetting and drying curves may be distinguished. The general features of a water retention curve can be seen in the figure, in which the volume water content, θ, is plotted against the matric potential, \Psi_m. At potentials close to zero, a soil is close to saturation, and water is held in the soil primarily by capillary forces. As θ decreases, binding of the water becomes stronger, and at small potentials (more negative, approaching wilting point) water is strongly bound in the smallest of pores, at contact points between grains and as films bound by adsorptive ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Groundwater Fronts
Groundwater is the water present beneath Earth's surface in rock and soil pore spaces and in the fractures of rock formations. About 30 percent of all readily available freshwater in the world is groundwater. A unit of rock or an unconsolidated deposit is called an aquifer when it can yield a usable quantity of water. The depth at which soil pore spaces or fractures and voids in rock become completely saturated with water is called the water table. Groundwater is recharged from the surface; it may discharge from the surface naturally at springs and seeps, and can form oases or wetlands. Groundwater is also often withdrawn for agricultural, municipal, and industrial use by constructing and operating extraction wells. The study of the distribution and movement of groundwater is hydrogeology, also called groundwater hydrology. Typically, groundwater is thought of as water flowing through shallow aquifers, but, in the technical sense, it can also contain soil moisture, permafr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Falling Slugs
Falling or fallin' may refer to: * Falling (physics), movement due to gravity * Falling (accident) * Falling (execution) * Falling (sensation) People *Christine Falling (born 1963), American serial killer who murdered six children Books * ''Falling'' (Provoost novel), a 1994 novel by Anne Provoost * ''Falling'' (Howard novel), a 1999 novel by Elizabeth Jane Howard *"Falling", a 1967 poem by James Dickey Film and television * ''Falling'' (2008 film), a film by Richard Dutcher * ''Falling'' (2015 film), starring Adesua Etomi and Blossom Chukwujekwu * ''Falling'' (2020 film), an American-British-Canadian drama film * ''The Falling'' (1987 film), an American film by Deran Sarafian * ''The Falling'' (2014 film), a British film by Carol Morley *''Falling'' (Dutch: ''Vallen''), a 2001 film by Hans Herbots based on the novel by Anne Provoost *''Falling'', a 2005 ITV adaptation of the novel by Elizabeth Jane Howard *"Falling", an episode of the Adult Swim television series ''Off the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Method Of Lines
The method of lines (MOL, NMOL, NUMOL) is a technique for solving partial differential equations (PDEs) in which all but one dimension is discretized. By reducing a PDE to a single continuous dimension, the method of lines allows solutions to be computed via methods and software developed for the numerical integration of ordinary differential equations (ODEs) and differential-algebraic systems of equations (DAEs). Many integration routines have been developed over the years in many different programming languages, and some have been published as open source resources. The method of lines most often refers to the construction or analysis of numerical methods for partial differential equations that proceeds by first discretizing the spatial derivatives only and leaving the time variable continuous. This leads to a system of ordinary differential equations to which a numerical method for initial value ordinary equations can be applied. The method of lines in this context dates bac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Inf Fronts
Inf or INF may refer to: Politics * Intermediate-Range Nuclear Forces Treaty, a 1987 arms control treaty between the United States and the Soviet Union * International Naturist Federation, the global umbrella organisation representing official national naturist societies * International Netball Federation, the international governing body for the sport of netball * Irish National Federation, a nationalist political party in Ireland 1891–1900 Computing * INF file, a file extension (information file) used by software and hardware driver installation routines * INF help file, a binary help file created after compiling IPF help source with IBM or Open Watcom's help compiler. * Informatics (academic field), the science of information and the practice of information processing Mathematics * Infinity, referring to something without any limit * Infimum, the greatest lower bound of a subset of a partially ordered set Places * In Guezzam Airport, Algeria * INF Clairefontaine ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Partial Differential Equation
In mathematics, a partial differential equation (PDE) is an equation which imposes relations between the various partial derivatives of a multivariable function. The function is often thought of as an "unknown" to be solved for, similarly to how is thought of as an unknown number to be solved for in an algebraic equation like . However, it is usually impossible to write down explicit formulas for solutions of partial differential equations. There is, correspondingly, a vast amount of modern mathematical and scientific research on methods to numerically approximate solutions of certain partial differential equations using computers. Partial differential equations also occupy a large sector of pure mathematical research, in which the usual questions are, broadly speaking, on the identification of general qualitative features of solutions of various partial differential equations, such as existence, uniqueness, regularity, and stability. Among the many open questions are the ex ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Finite Difference
A finite difference is a mathematical expression of the form . If a finite difference is divided by , one gets a difference quotient. The approximation of derivatives by finite differences plays a central role in finite difference methods for the numerical solution of differential equations, especially boundary value problems. The difference operator, commonly denoted \Delta is the operator that maps a function to the function \Delta /math> defined by :\Delta x)= f(x+1)-f(x). A difference equation is a functional equation that involves the finite difference operator in the same way as a differential equation involves derivatives. There are many similarities between difference equations and differential equations, specially in the solving methods. Certain recurrence relations can be written as difference equations by replacing iteration notation with finite differences. In numerical analysis, finite differences are widely used for approximating derivatives, and the term " ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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