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Richards Equation
The Richards equation represents the movement of water in Vadose zone, unsaturated soils, and is attributed to Lorenzo A. Richards who published the equation in 1931. It is a Differential equation, quasilinear partial differential equation; its analytical solution is often limited to specific initial and boundary conditions. Proof of the Existence theorem, existence and Uniqueness theorem, uniqueness of solution was given only in 1983 by Hans Wilhelm Alt, Alt and Stephan Luckhaus, 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 [L/T]; :\theta is the Water content, volumetric water content [~]; :h is the liquid pressure head, which is negative for unsaturated porous media [L]; :\mathbf(h) is the unsaturated hydraulic conductivity [L/T]; :\nabla z is the geodetic head gradient, which is assumed as \nabla ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vadose Zone
The vadose zone (from the Latin word for "shallow"), also termed the unsaturated zone, is the part of Earth between the land surface and the top of the phreatic zone, the position at which the groundwater (the water in the soil's pores) is at atmospheric pressure. Hence, the vadose zone extends from the top of the ground surface to the water table. Water in the vadose zone has a pressure head less than atmospheric pressure, and is retained by a combination of adhesion (''funiculary groundwater''), and capillary action (''capillary groundwater''). If the vadose zone envelops soil, the water contained therein is termed soil moisture. In fine grained soils, capillary action can cause the pores of the soil to be fully saturated above the water table at a pressure less than atmospheric. The vadose zone does not include the area that is still saturated above the water table, often referred to as the capillary fringe. Freeze, R.A. and Cherry, J.A., 1979. Groundwater. Englewood Clif ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chain Rule
In calculus, the chain rule is a formula that expresses the derivative of the Function composition, composition of two differentiable functions and in terms of the derivatives of and . More precisely, if h=f\circ g is the function such that h(x)=f(g(x)) for every , then the chain rule is, in Lagrange's notation, h'(x) = f'(g(x)) g'(x). or, equivalently, h'=(f\circ g)'=(f'\circ g)\cdot g'. The chain rule may also be expressed in Leibniz's notation. If a variable depends on the variable , which itself depends on the variable (that is, and are dependent variables), then depends on as well, via the intermediate variable . In this case, the chain rule is expressed as \frac = \frac \cdot \frac, and \left.\frac\_ = \left.\frac\_ \cdot \left. \frac\_ , for indicating at which points the derivatives have to be evaluated. In integral, integration, the counterpart to the chain rule is the substitution rule. Intuitive explanation Intuitively, the chain rule states that knowing t ... [...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 state of matter, phases as solid, solids, liquid, liquids, and gas, 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 soil gas, 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, measurem ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 Vadose zone, 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 expression, closed-form analytical solution except in a few cases.Ross, P.J., and J.-Y. Parlange (1994). ... [...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, Surface runoff, runoff will usually occur unless there is some physical barrier. Infiltrometers, parameters 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 ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Aspect Ratio
The aspect ratio of a geometry, geometric shape is the ratio of its sizes in different dimensions. For example, the aspect ratio of a rectangle is the ratio of its longer side to its shorter side—the ratio of width to height, when the rectangle is oriented as a "landscape format, landscape". The aspect ratio is most often expressed as two integer numbers separated by a colon (x:y), less commonly as a simple or decimal Fraction (mathematics), fraction. The values x and y do not represent actual widths and heights but, rather, the proportion between width and height. As an example, 8:5, 16:10, 1.6:1, and 1.6 are all ways of representing the same aspect ratio. In objects of more than two dimensions, such as hyperrectangles, the aspect ratio can still be defined as the ratio of the longest side to the shortest side. Applications and uses The term is most commonly used with reference to: * Graphic / image ** Aspect ratio (image), Image aspect ratio ** Display aspect ratio ** Pape ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Representative Elementary Volume
In the theory of composite materials, the representative elementary volume (REV) (also called the representative volume element (RVE) or the unit cell) is the smallest volume over which a measurement can be made that will yield a value representative of the whole. In the case of periodic materials, one simply chooses a periodic unit cell (which, however, may be non-unique), but in random media, the situation is much more complicated. For volumes smaller than the RVE, a representative property cannot be defined and the continuum (measurement), continuum description of the material involves Statistical Volume Element (SVE) and random fields. The property of interest can include mechanical properties such as elastic modulus, elastic moduli, hydrogeology, hydrogeological properties, electromagnetism, electromagnetic properties, heat transfer, thermal properties, and other averaged quantities that are used to describe physical systems. Definition Rodney Hill defined the RVE as a samp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tensor
In mathematics, a tensor is an algebraic object that describes a multilinear relationship between sets of algebraic objects associated with a vector space. Tensors may map between different objects such as vectors, scalars, and even other tensors. There are many types of tensors, including scalars and vectors (which are the simplest tensors), dual vectors, multilinear maps between vector spaces, and even some operations such as the dot product. Tensors are defined independent of any basis, although they are often referred to by their components in a basis related to a particular coordinate system; those components form an array, which can be thought of as a high-dimensional matrix. Tensors have become important in physics because they provide a concise mathematical framework for formulating and solving physics problems in areas such as mechanics ( stress, elasticity, quantum mechanics, fluid mechanics, moment of inertia, ...), electrodynamics ( electromagnetic ten ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Isotropy
In physics and geometry, isotropy () is uniformity in all orientations. Precise definitions depend on the subject area. Exceptions, or inequalities, are frequently indicated by the prefix ' or ', hence ''anisotropy''. ''Anisotropy'' is also used to describe situations where properties vary systematically, dependent on direction. Isotropic radiation has the same intensity regardless of the direction of measurement, and an isotropic field exerts the same action regardless of how the test particle is oriented. Mathematics Within mathematics, ''isotropy'' has a few different meanings: ; Isotropic manifolds: A manifold is isotropic if the geometry on the manifold is the same regardless of direction. A similar concept is homogeneity. ; Isotropic quadratic form: A quadratic form ''q'' is said to be isotropic if there is a non-zero vector ''v'' such that ; such a ''v'' is an isotropic vector or null vector. In complex geometry, a line through the origin in the direction of an is ... [...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. The soil moisture curve is characteristic for different soil types, and is also called the soil moisture characteristic. It is used to predict soil water storage, plant water supply (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, the 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Soil Water Diffusivity
Soil, also commonly referred to as earth, is a mixture of organic matter, minerals, gases, water, and organisms that together support the life of plants and soil organisms. Some scientific definitions distinguish dirt from ''soil'' by restricting the former term specifically to displaced soil. Soil consists of a solid collection of minerals and organic matter (the soil matrix), as well as a porous phase that holds gases (the soil atmosphere) and water (the soil solution). Accordingly, soil is a three-state system of solids, liquids, and gases. Soil is a product of several factors: the influence of climate, relief (elevation, orientation, and slope of terrain), organisms, and the soil's parent materials (original minerals) interacting over time. It continually undergoes development by way of numerous physical, chemical and biological processes, which include weathering with associated erosion. Given its complexity and strong internal connectedness, soil ecologists regard soil a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
