Richards Equation
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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 porous ...
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Vadose Zone
The vadose zone, 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 ("vadose" is from the Latin word for "shallow"). 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. Engl ...
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Retention Water Capacity
Retention may refer to: General * Recall (memory), in learning, the ability to recall facts and figures in memory * Memory and retention in learning * Selective retention * Cultural retention * Customer retention * University student retention * Employee retention, the ability to keep employees within an organization * Forced retention * Grade retention, in schools, keeping a student in the same grade for another year (that is, not promoting the student to the next higher grade with his/her classmates) * Retention basin, * Retention election, in the United States court system, a process whereby a judge is periodically subject to a vote in order to remain in the position of judge * Retention rate * Retention ratio, in company earnings * Retention of vision, in magic * Water retention (medicine), abnormal accumulation of fluid in the body * Urinary retention, the lack or inability to urinate * Variable retention, in land management and forestry conservation Information and record ...
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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 tensiometer. ...
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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 sol ...
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