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Groundwater Energy Balance
The groundwater energy balance is the energy balance of a groundwater body in terms of incoming hydraulic energy associated with groundwater inflow into the body, energy associated with the outflow, energy conversion into heat due to friction of flow, and the resulting change of energy status and groundwater level. Theory When multiplying the horizontal velocity of groundwater (dimension, for example, m3/day per m2 cross-sectional area) with the groundwater potential (dimension energy per m3 water, or ''E''/m3) one obtains an energy flow (flux) in ''E''/day per m2 cross-sectional area. Summation or integration of the energy flux in a vertical cross-section of unit width (say 1 m) from the lower flow boundary (the impermeable layer or base) up to the water table in an unconfined aquifer gives the energy flow ''Fe'' through the cross-section in ''E''/day per m width of the aquifer. While flowing, the groundwater loses energy due to friction of flow, i.e. hydraulic energy is conver ...
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Groundwater
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 Groundwater is also often withdrawn for agricultural, municipal, and industrial use by constructing and operating extraction wells.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, perma ...
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Iteration
Iteration is the repetition of a process in order to generate a (possibly unbounded) sequence of outcomes. Each repetition of the process is a single iteration, and the outcome of each iteration is then the starting point of the next iteration. In mathematics and computer science, iteration (along with the related technique of recursion) is a standard element of algorithms. Mathematics In mathematics, iteration may refer to the process of iterating a function, i.e. applying a function repeatedly, using the output from one iteration as the input to the next. Iteration of apparently simple functions can produce complex behaviors and difficult problems – for examples, see the Collatz conjecture and juggler sequences. Another use of iteration in mathematics is in iterative methods which are used to produce approximate numerical solutions to certain mathematical problems. Newton's method is an example of an iterative method. Manual calculation of a number's square root is a co ...
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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 fields. H ...
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Aquifers
An aquifer is an underground layer of water-bearing, permeable rock, rock fractures, or unconsolidated materials (gravel, sand, or silt). Groundwater from aquifers can be extracted using a water well. Aquifers vary greatly in their characteristics. The study of water flow in aquifers and the characterization of aquifers is called hydrogeology. Related terms include aquitard, which is a bed of low permeability along an aquifer, and aquiclude (or ''aquifuge''), which is a solid, impermeable area underlying or overlying an aquifer, the pressure of which could create a confined aquifer. The classification of aquifers is as follows: Saturated versus unsaturated; aquifers versus aquitards; confined versus unconfined; isotropic versus anisotropic; porous, karst, or fractured; transboundary aquifer. Challenges for using groundwater include: overdrafting (extracting groundwater beyond the equilibrium yield of the aquifer), groundwater-related subsidence of land, groundwater becoming sa ...
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Hydrogeology
Hydrogeology (''hydro-'' meaning water, and ''-geology'' meaning the study of the Earth) is the area of geology that deals with the distribution and movement of groundwater in the soil and rocks of the Earth's crust (commonly in aquifers). The terms groundwater hydrology, geohydrology, and hydrogeology are often used interchangeably. Hydrogeology is the study of the laws governing the movement of subterranean water, the mechanical, chemical, and thermal interaction of this water with the porous solid, and the transport of energy, chemical constituents, and particulate matter by flow (Domenico and Schwartz, 1998). Groundwater engineering, another name for hydrogeology, is a branch of engineering which is concerned with groundwater movement and design of wells, pumps, and drains. The main concerns in groundwater engineering include groundwater contamination, conservation of supplies, and water quality.Walton, William C. (November 1990). ''Principles of Groundwater Engin ...
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Groundwater Flow Equation
Used in hydrogeology, the groundwater flow equation is the mathematical relationship which is used to describe the flow of groundwater through an aquifer. The transient flow of groundwater is described by a form of the diffusion equation, similar to that used in heat transfer to describe the flow of heat in a solid (heat conduction). The steady-state flow of groundwater is described by a form of the Laplace equation, which is a form of potential flow and has analogs in numerous fields. The groundwater flow equation is often derived for a small representative elemental volume (REV), where the properties of the medium are assumed to be effectively constant. A mass balance is done on the water flowing in and out of this small volume, the flux terms in the relationship being expressed in terms of head by using the constitutive equation called Darcy's law, which requires that the flow is laminar. Other approaches are based on Agent Based Models to incorporate the effect of complex aqui ...
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Groundwater Discharge
Groundwater discharge is the volumetric flow rate of groundwater through an aquifer. Total groundwater discharge, as reported through a specified area, is similarly expressed as: :Q = \fracKA where :''Q'' is the total groundwater discharge ( 3·T−1 m3/s), :''K'' is the hydraulic conductivity of the aquifer ( ·T−1 m/s), :''dh/dl'' is the hydraulic gradient ( ·L−1 unitless), and :''A'' is the area which the groundwater is flowing through ( 2 m2) For example, this can be used to determine the flow rate of water flowing along a plane with known geometry. The discharge potential The discharge potential is a potential in groundwater mechanics which links the physical properties, hydraulic head, with a mathematical formulation for the energy as a function of position. The discharge potential, \Phi 3·T−1 is defined in such way that its gradient equals the discharge vector. Q_x = -\frac Q_y = -\frac Thus the hydraulic head may be calculated in terms of the discharge pot ...
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DPHM-RS
DPHM-RS (Semi-Distributed Physically based Hydrologic Model using Remote Sensing and GIS) is a semi-distributed hydrologic model developed at University of Alberta, Canada. Model description The semi-distributed DPHM-RS (Semi-Distributed Physically based Hydrologic Model using Remote Sensing and GIS) sub-divides a river basin to a number of sub-basins, computes the evapotranspiration, soil moisture and surface runoff using energy and rainfall forcing data in a sub-basin scale. It consists of six basic components: interception of rainfall, evapotranspiration, soil moisture, saturated subsurface flow, surface flow and channel routing, as described in Biftu and Gan. The interception of precipitation from the atmosphere by the canopy is modeled using the Rutter Interception Model. The land surface evaporation and vegetation transpiration are computed separately using the Two Source Model of Shuttleworth and Gurney, which is based on the energy balance above canopy, within c ...
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Conservation Of Mass
In physics and chemistry, the law of conservation of mass or principle of mass conservation states that for any system closed to all transfers of matter and energy, the mass of the system must remain constant over time, as the system's mass cannot change, so quantity can neither be added nor be removed. Therefore, the quantity of mass is conserved over time. The law implies that mass can neither be created nor destroyed, although it may be rearranged in space, or the entities associated with it may be changed in form. For example, in chemical reactions, the mass of the chemical components before the reaction is equal to the mass of the components after the reaction. Thus, during any chemical reaction and low-energy thermodynamic processes in an isolated system, the total mass of the reactants, or starting materials, must be equal to the mass of the products. The concept of mass conservation is widely used in many fields such as chemistry, mechanics, and fluid dynamics. Historic ...
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Continuity Equation
A continuity equation or transport equation is an equation that describes the transport of some quantity. It is particularly simple and powerful when applied to a conserved quantity, but it can be generalized to apply to any extensive quantity. Since mass, energy, momentum, electric charge and other natural quantities are conserved under their respective appropriate conditions, a variety of physical phenomena may be described using continuity equations. Continuity equations are a stronger, local form of conservation laws. For example, a weak version of the law of conservation of energy states that energy can neither be created nor destroyed—i.e., the total amount of energy in the universe is fixed. This statement does not rule out the possibility that a quantity of energy could disappear from one point while simultaneously appearing at another point. A stronger statement is that energy is ''locally'' conserved: energy can neither be created nor destroyed, ''nor'' can it " t ...
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Darcy's Law
Darcy's law is an equation that describes the flow of a fluid through a porous medium. The law was formulated by Henry Darcy based on results of experiments on the flow of water through beds of sand, forming the basis of hydrogeology, a branch of earth sciences. It is analogous to Ohm's law in electrostatics, linearly relating the volume flow rate of the fluid to the hydraulic head difference (which is often just proportional to the pressure difference) via the hydraulic conductivity. Background Darcy's law was first determined experimentally by Darcy, but has since been derived from the Navier–Stokes equations via homogenization methods. It is analogous to Fourier's law in the field of heat conduction, Ohm's law in the field of electrical networks, and Fick's law in diffusion theory. One application of Darcy's law is in the analysis of water flow through an aquifer; Darcy's law along with the equation of conservation of mass simplifies to the groundwater flow equation, one of ...
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Drainage Equation
A drainage equation is an equation describing the relation between depth and spacing of parallel subsurface drains, depth of the watertable, depth and hydraulic conductivity of the soils. It is used in drainage design. A well known steady-state drainage equation is the Hooghoudt drain spacing equation. Its original publication is in Dutch. The equation was introduced in the USA by van Schilfgaarde. Hooghoudt's equation Hooghoudt's equation can be written as:. :Q L2 = 8 Kb d (Dd - Dw) + 4 Ka (Dd - Dw)2 where: * Q = steady state drainage discharge rate (m/day) * Ka = hydraulic conductivity of the soil above drain level (m/day) * Kb = hydraulic conductivity of the soil below drain level (m/day) * Di = depth of the impermeable layer below drain level (m) * Dd = depth of the drains (m) * Dw = steady state depth of the watertable midway between the drains (m) * L = spacing between the drains (m) * d = equivalent depth, a function of L, (Di-Dd), and r * r = drain radius (m) ...
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