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Encyclopedia > Hydrogeology

Hydrogeology (hydro- meaning water, and -geology meaning the study of the Earth) is the part of hydrology that deals with the distribution and movement of groundwater in the soil and rocks of the Earth's crust, (commonly in aquifers). The term geohydrology is often used interchangeably. Some make the minor distinction between a hydrologist or engineer applying themselves to geology (geohydrology), and a geologist applying themselves to hydrology (hydrogeology). Water covers 70% of the Earths surface. ... Groundwater is water located beneath the ground surface in soil pore spaces and in the fractures of geologic formations. ... Loess field in Germany Surface-water-gley developed in glacial till, Northern Ireland Technically, soil forms the pedosphere: the interface between the lithosphere (rocky part of the planet) and the biosphere, atmosphere, and hydrosphere. ... This balancing rock, Steamboat Rock stands in Garden of the Gods park in Colorado Springs, CO The rocky side of a mountain creek near OrosÃ­, Costa Rica. ... Earth cutaway from core to exosphere. ... An aquifer is an underground layer of water-bearing permeable rock or unconsolidated materials (gravel, sand, silt, or clay) from which groundwater can be usefully extracted using a water well. ...

## Hydrogeology in relation to other fields

Hydrogeology, as stated above, is a branch of the earth sciences dealing with the flow of water through aquifers and other shallow porous media (typically less than 450 m or 1,500 ft below the land surface.) The very shallow flow of water in the subsurface (the upper 3 m or 10 ft) is pertinent to the fields of soil science, agriculture and civil engineering, as well as to hydrogeology. The general flow of fluids (water, hydrocarbons, geothermal fluids, etc.) in deeper formations is also a concern of geologists, geophysicists and petroleum geologists. Groundwater is a slow-moving, viscous fluid (with a Reynolds number less than unity); many of the empirically derived laws of groundwater flow can be alternately derived in fluid mechanics from the special case of Stokes flow (viscosity and pressure terms, but no inertial term). Groundwater is water located beneath the ground surface in soil pore spaces and in the fractures of geologic formations. ... An aquifer is an underground layer of water-bearing permeable rock or unconsolidated materials (gravel, sand, silt, or clay) from which groundwater can be usefully extracted using a water well. ... A porous medium or a porous material is a solid (often called frame or matrix) permeated by an interconnected network of pores (voids) filled with a fluid (liquid or gas). ... The metre (American English:meter) is a measure of length. ... A foot (plural: feet or foot;[1] symbol or abbreviation: ft or, sometimes, â€² â€“ a prime) is a unit of length, in a number of different systems, including English units, Imperial units, and United States customary units. ... Soil science deals with soil as a natural resource on the surface of the earth including soil formation, classification and mapping; physical, chemical, biological, and fertility properties of soils per se; and these properties in relation to the use and management of soils. ... This article does not cite any references or sources. ... A fluid is defined as a substance that continually deforms (flows) under an applied shear stress regardless of the magnitude of the applied stress. ... In chemistry, a hydrocarbon is a cleaning solution consisting only of carbon (C) and hydrogen (H). ... Earth cutaway from core to exosphere. ... This article includes a list of works cited but its sources remain unclear because it lacks in-text citations. ... â€¹ The template below has been proposed for deletion. ... Petroleum geology is a term used to refer to the specific set of geological disciplines that are applied to the search for hydrocarbons (oil exploration). ... Viscosity is a measure of the resistance of a fluid to deform under shear stress. ... In fluid mechanics, the Reynolds number is the ratio of inertial forces (vsÏ) to viscous forces (Î¼/L) and consequently it quantifies the relative importance of these two types of forces for given flow conditions. ... Fluid mechanics is the subdiscipline of continuum mechanics that studies fluids, that is, liquids and gases. ...

The mathematical relationships used to describe the flow of water through porous media are the diffusion and Laplace equations, which have applications in many diverse fields. Steady groundwater flow (Laplace equation) has been simulated using electrical, elastic and heat conduction analogies. Transient groundwater flow is analogous to the diffusion of heat in a solid, therefore some solutions to hydrological problems have been adapted from heat transfer literature. Incorrect shortening of Mathematics. ... The heat equation or diffusion equation is an important partial differential equation which describes the variation of temperature in a given region over time. ... Laplaces equation is a partial differential equation named after its discoverer Pierre-Simon Laplace. ... The article on electrical energy is located elsewhere. ... Look up elastic in Wiktionary, the free dictionary. ... Heat conduction or thermal conduction is the spontaneous transfer of thermal energy through matter, from a region of higher temperature to a region of lower temperature, and hence acts to even out temperature differences. ... In thermal physics, heat transfer is the passage of thermal energy from a hot to a cold body. ...

Traditionally, the movement of groundwater has been studied separately from surface water, climatology, and even the chemical and microbiological aspects of hydrogeology (the processes are uncoupled). As the field of hydrogeology matures, the strong interactions between groundwater, surface water, water chemistry, soil moisture and even climate are becoming more clear. Water covers 70% of the Earths surface. ... Climatology is the study of climate, scientifically defined as weather conditions averaged over a period of time,[1] and is a branch of the atmospheric sciences. ... Chemistry - the study of interactions of chemical substances with one another and energy based on the structure of atoms, molecules and other kinds of aggregrates Chemistry (from Egyptian kÄ“me (chem), meaning earth[1]) is the science concerned with the composition, structure, and properties of matter, as well as the... This article does not cite any references or sources. ... Groundwater is water located beneath the ground surface in soil pore spaces and in the fractures of geologic formations. ... This bridge across the Danube River links Hungary with Slovakia. ... The field of geochemistry involves study of the chemical composition of the Earth and other planets, chemical processes and reactions that govern the composition of rocks and soils, and the cycles of matter and energy that transport the Earths chemical components in time and space, and their interaction with... Loess field in Germany Surface-water-gley developed in glacial till, Northern Ireland Technically, soil forms the pedosphere: the interface between the lithosphere (rocky part of the planet) and the biosphere, atmosphere, and hydrosphere. ...

## Definitions and material properties

Main article: Aquifer

One of the main tasks a hydrogeologist typically performs is the prediction of future behavior of an aquifer system, based on analysis of past and present observations. Some hypothetical, but characteristic questions asked would be: An aquifer is an underground layer of water-bearing permeable rock or unconsolidated materials (gravel, sand, silt, or clay) from which groundwater can be usefully extracted using a water well. ...

• Can the aquifer support another subdivision?
• Will the river dry up if the farmer doubles his irrigation?
• Did the chemicals from the dry cleaning facility travel through the aquifer to my well and make me sick?
• Will the plume of effluent leaving my neighbor's septic system flow to my drinking water well?

Most of these questions can be addressed through simulation of the hydrologic system (using numerical models or analytic equations). Accurate simulation of the aquifer system requires knowledge of the aquifer properties and boundary conditions. Therefore a common task of the hydrogeologist is determining aquifer properties using aquifer tests. This bridge across the Danube River links Hungary with Slovakia. ... Irrigation is the artificial application of water to the soil. ... Dry cleaning is any cleaning process for clothing and textiles using an organic solvent other than water â€” generally known as dry cleaning fluid, and typically this is tetrachloroethylene. ... An Aquifer test is conducted to evaluate an aquifer by stimulating the aquifer through constant pumping, and observing the aquifers response (drawdown) in observation wells. ...

In order to further characterize aquifers and aquitards some primary and derived physical properties are introduced below. Aquifers are broadly classified as being either confined or unconfined (water table aquifers), and either saturated or unsaturated; the type of aquifer affects what properties control the flow of water in that medium (e.g., the release of water from storage for confined aquifers is related to the storativity, while it is related to the specific yield for unconfined aquifers). An aquifer is an underground layer of water-bearing permeable rock or unconsolidated materials (gravel, sand, silt, or clay) from which groundwater can be usefully extracted using a water well. ... Cross section showing the water table varying with surface topography as well as a perched water table The water table or phreatic surface is the surface where the water pressure is equal to atmospheric pressure. ...

Changes in hydraulic head (h) are the driving force which causes water to move from one place to another. It is composed of pressure head (ψ) and elevation head (z). The head gradient is the change in hydraulic head per length of flowpath, and appears in Darcy's law as being proportional to the discharge. It has been suggested that Hydraulic head (hydrology) and Head (hydraulic) be merged into this article or section. ... In fluid dynamics, Darcys law is a phenomologically derived constitutive equation that describes the flow of a fluid through a porous medium. ...

Hydraulic head is a directly measurable property, which can take on any value (because of the arbitrary datum involved in the z term); ψ can be measured with a pressure transducer (this value can be negative, e.g., suction, but is positive in saturated aquifers), and z can be measured relative to a surveyed datum (typically the top of the well casing). Commonly, in wells tapping unconfined aquifers the water level in a well is used as a proxy for hydraulic head, assuming there is no vertical gradient of pressure. Often only changes in hydraulic head through time are needed, so the constant elevation head term can be left out (Δh = Δψ). A transducer is a device, usually electrical or electronic, that converts one type of energy to another. ... Cable tool water well drilling rig in Kimball, West Virginia. ...

A record of hydraulic head through time at a well is a hydrograph or, the changes in hydraulic head recorded during the pumping of a well in a test are called drawdown. There are two meanings for hydrographs both coming from hydro- meaning water, and -graph meaning chart. ... Drawdown has two distinct meanings: change in hydraulic head in an aquifer, typically due to pumping a well, this is found in drawdown_(hydrology) unrealized losses in economics, found in drawdown_(economics) This is a disambiguation page &#8212; a navigational aid which lists other pages that might otherwise share the...

### Porosity

Main article: Porosity

Porosity (n) is a directly measurable aquifer property; it is a fraction between 0 and 1 indicating the amount of pore space between unconsolidated soil particles or within a fractured rock. Typically, the majority of groundwater (and anything dissolved in it) moves through the porosity available to flow (sometimes called effective porosity). Porosity is a measure of the void spaces in a material, and is measured as a fraction, between 0â€“1, or as a percentage between 0â€“100%. The term porosity is used in multiple fields including manufacturing, earth sciences and construction. ... Loess field in Germany Surface-water-gley developed in glacial till, Northern Ireland Technically, soil forms the pedosphere: the interface between the lithosphere (rocky part of the planet) and the biosphere, atmosphere, and hydrosphere. ...

Porosity does not directly affect the distribution of hydraulic head in an aquifer, but it has a very strong effect on the migration of dissolved contaminants, since it affects groundwater flow velocities through an inversely proportional relationship.

### Water content

Main article: water content

Water content (θ) is also a directly measurable property; it is the fraction of the total rock which is filled with liquid water. This is also a fraction between 0 and 1, but it must also be less than or equal to the total porosity. Water content is a ratio used in hydrogeology and soil mechanics to indicate the amount of water a porous medium contains. ...

The water content is very important in vadose zone hydrology, where the hydraulic conductivity is a strongly nonlinear function of water content; this complicates the solution of the unsaturated groundwater flow equation. The vadose zone, also termed the unsaturated zone, is the portion of Earth between the land surface and the water table, and is thus not considered groundwater (vadose is Latin for shallow). It comprises the unsaturated portion of the soil, regolith or bedrock, as well as the saturated capillary fringe... written by AmerHydraulic conductivity, mathematically represented as , is a property of soil or rock, in the vadose zone or groundwater, that describes the ease with which water can move through pore spaces or fractures. ... To do: 20th century mathematics chaos theory, fractals Lyapunov stability and non-linear control systems non-linear video editing See also: Aleksandr Mikhailovich Lyapunov Dynamical system External links http://www. ...

### Hydraulic conductivity

Main article: Hydraulic conductivity

Hydraulic conductivity (K) and transmissivity (T) are indirect aquifer properties (they cannot be measured directly). T is the K integrated over the vertical thickness (b) of the aquifer (T=Kb when K is constant over the entire thickness). These properties are measures of an aquifer's ability to transmit water. Intrinsic permeability (κ) is a secondary medium property which does not depend on the viscosity and density of the fluid (K and T are specific to water); it is used more in the petroleum industry. written by AmerHydraulic conductivity, mathematically represented as , is a property of soil or rock, in the vadose zone or groundwater, that describes the ease with which water can move through pore spaces or fractures. ... An aquifer is an underground layer of water-bearing permeable rock or unconsolidated materials (gravel, sand, silt, or clay) from which groundwater can be usefully extracted using a water well. ... Impact from a water drop causes an upward rebound jet surrounded by circular capillary waves. ... In the earth sciences, permeability (commonly symbolized as Îº, or k) is a measure of the ability of a material (typically, a rock or unconsolidated material) to transmit fluids. ... Viscosity is a measure of the resistance of a fluid to deform under shear stress. ... In physics, density is mass m per unit volume V. For the common case of a homogeneous substance, it is expressed as: where, in SI units: Ï (rho) is the density of the substance, measured in kgÂ·m-3 m is the mass of the substance, measured in kg V is...

### Specific storage and specific yield

Main article: Specific storage

Specific storage (Ss) and its depth-integrated equivalent, storativity (S=Ssb), are indirect aquifer properties (they cannot be measured directly); they indicate the amount of groundwater released from storage due to a unit depressurization of a confined aquifer. They are fractions between 0 and 1. Specific storage (Ss), storativity (S), specific yield (Sy) and specific capacity are aquifer properties; they are measures of the ability of an aquifer to release groundwater from storage, due to a unit decline in hydraulic head. ...

Specific yield (Sy) is also a ratio between 0 and 1 (Sy ≤ porosity) which indicates the amount of water released due to drainage, from lowering the water table in an unconfined aquifer. Typically Sy is orders of magnitude larger than Ss. Often the porosity or effective porosity is used as an upper bound to the specific yield. Porosity is a measure of the void spaces in a material, and is measured as a fraction, between 0â€“1, or as a percentage between 0â€“100%. The term porosity is used in multiple fields including manufacturing, earth sciences and construction. ...

### Contaminant transport properties

Often we are interested in how the moving groundwater water will move dissolved contaminants around (the sub-field of contaminant hydrogeology). The contaminants can be man-made (e.g., petroleum products, nitrate or Chromium) or naturally occurring (e.g., arsenic, salinity). Besides needing to understand where the groundwater is flowing, based on the other hydrologic properties discussed above, there are additional aquifer properties which affect how dissolved contaminants move with groundwater. BTEX is an acronym that stands for Benzene, Toluene, Ethylbenzene, and Xylenes. ... An electrostatic potential map of the nitrate ion. ... General Name, Symbol, Number chromium, Cr, 24 Chemical series transition metals Group, Period, Block 6, 4, d Appearance silvery metallic Standard atomic weight 51. ... General Name, Symbol, Number arsenic, As, 33 Chemical series metalloids Group, Period, Block 15, 4, p Appearance metallic gray Standard atomic weight 74. ... Annual mean sea surface salinity for the World Ocean. ...

DispersivityL, αT) is an empirical factor which quantifies how much contaminants stray away from the path of the groundwater which is carrying it. Some of the contaminants will be "behind" or "ahead" the mean groundwater, giving rise to a longitudinal dispersivity (αL), and some will be "to the sides of" the pure advective groundwater flow, leading to a transverse dispersivity (αT).

Dispersivity is actually a factor which represents our lack of information about the system we are simulating. There are many small details about the aquifer which are being averaged when using a macroscopic approach (e.g., tiny beds of gravel and clay in sand aquifers), they manifest themselves as an apparent dispersivity. Because of this, α is often claimed to be dependent on the length scale of the problem — the dispersivity found for transport through 1 m³ of aquifer is different than that for transport through 1 cm³ of the same aquifer material. Macroscopic is commonly used to describe physical objects that are measurable and observable by the naked eye. ...

Hydrodynamic dispersion (D) is a positive physical parameter which describes the molecule-scale movement of solute away from the mean flow; it is a result of Brownian motion. This is the same mechanism as dye uniformly spreading out in a still bucket of water. The dispersion coefficient is typically quite small (typically orders of magnitude smaller than α), and can often be considered negligible (unless groundwater flow velocities are extremely low, as they are in clay aquitards). Three different views of Brownian motion, with 32 steps, 256 steps, and 2048 steps denoted by progressively lighter colors. ...

It is important not to confuse hydrodynamic dispersion with dispersivity, as the former is a physical phenomenon and the latter is an empirical factor which is cast into a similar form as dispersion, because we already know how to solve that problem.

## Governing equations

### Darcy's Law

Main article: Darcy's law

Darcy's law is a Constitutive equation (empirically derived by Henri Darcy, in 1856) which states the amount of groundwater discharging through a given portion of aquifer is proportional to the cross-sectional area to flow, the hydraulic head gradient and the hydraulic conductivity. In fluid dynamics, Darcys law is a phenomologically derived constitutive equation that describes the flow of a fluid through a porous medium. ... In structural analysis, constitutive relations connect applied stresses or forces to strains or deformations. ... Henry Philibert Gaspard Darcy (June 10, 1803 - January 3, 1858), was a French scientist who made several important contributions to hydraulics. ... Groundwater is water located beneath the ground surface in soil pore spaces and in the fractures of geologic formations. ... An aquifer is an underground layer of water-bearing permeable rock or unconsolidated materials (gravel, sand, silt, or clay) from which groundwater can be usefully extracted using a water well. ... written by AmerHydraulic conductivity, mathematically represented as , is a property of soil or rock, in the vadose zone or groundwater, that describes the ease with which water can move through pore spaces or fractures. ...

### Groundwater flow equation

Main article: Groundwater flow equation

The groundwater flow equation, in its most general form, describes the movement of groundwater in a porous medium (aquifers and aquitards). It is known in mathematics as the diffusion equation, and has many analogs in other fields. Many solutions for groundwater flow problems were borrowed or adapted from existing heat transfer solutions. The groundwater flow equation is the mathematical relationship which is used to describe the flow of groundwater through a porous medium (e. ... The heat equation or diffusion equation is an important partial differential equation which describes the variation of temperature in a given region over time. ... In thermal physics, heat transfer is the passage of thermal energy from a hot to a cold body. ...

It is often derived from a physical basis using Darcy's law and a conservation of mass for a small control volume. The equation is often used to predict flow to wells, which have radial symmetry, so the flow equation is commonly solved in polar or cylindrical coordinates. In fluid dynamics, Darcys law is a phenomologically derived constitutive equation that describes the flow of a fluid through a porous medium. ... Cable tool water well drilling rig in Kimball, West Virginia. ... This article describes some of the common coordinate systems that appear in elementary mathematics. ... This article describes some of the common coordinate systems that appear in elementary mathematics. ...

The Theis equation is one of the most commonly used and fundamental solutions to the groundwater flow equation; it can be used to predict the transient evolution of head, due to the effects of pumping one or a number of pumping wells. An Aquifer test is conducted to evaluate an aquifer by stimulating the aquifer through constant pumping, and observing the aquifers response (drawdown) in observation wells. ...

The Thiem equation is a solution to the steady state groundwater flow equation (Laplace's Equation). Unless there are large sources of water nearby (a river or lake), true steady-state is rarely achieved in reality. An Aquifer test is conducted to evaluate an aquifer by stimulating the aquifer through constant pumping, and observing the aquifers response (drawdown) in observation wells. ...

## Calculation of groundwater flow

To use the groundwater flow equation to estimate the distribution of hydraulic heads, or the direction and rate of groundwater flow, this partial differential equation (PDE) must be solved. The most common means of analytically solving the diffusion equation in the hydrogeology literature are: In mathematics, a partial differential equation (PDE) is a relation involving an unknown function of several independent variables and its partial derivatives with respect to those variables. ...

No matter which method we use to solve the groundwater flow equation, we need both initial conditions (heads at time (t) = 0) and boundary conditions (representing either the physical boundaries of the domain, or an approximation of the domain beyond that point). Often the initial conditions are supplied to a transient simulation, by a corresponding steady-state simulation (where the time derivative in the groundwater flow equation is set equal to 0). In mathematics, the Laplace transform is a technique for analyzing linear time-invariant systems such as electrical circuits, harmonic oscillators, optical devices, and mechanical systems. ... In mathematics, the Hankel transform of order Î½ of a function f(r) is given by: where JÎ½ is the Bessel function of the first kind of order Î½ with Î½ â‰¥ âˆ’1/2. ... In mathematics, the Fourier transform is a certain linear operator that maps functions to other functions. ... 2-dimensional renderings (ie. ... Look up similarity in Wiktionary, the free dictionary. ... An Aquifer test is conducted to evaluate an aquifer by stimulating the aquifer through constant pumping, and observing the aquifers response (drawdown) in observation wells. ... In mathematics, separation of variables is any of several methods for solving ordinary and partial differential equations, in which algebra allows one to re-write an equation so that each of two variables occurs on a different side of the equation. ... In mathematics, a Greens function is a type of function used to solve inhomogeneous differential equations subject to boundary conditions. ... In mathematics, a fundamental solution for a linear partial differential operator L is a formulation in the language of distribution theory of the older idea of a Greens function. ... The groundwater flow equation is the mathematical relationship which is used to describe the flow of groundwater through a porous medium (e. ... In mathematics, boundary conditions are imposed on the solutions of ordinary differential equations and partial differential equations, to fit the solutions to the actual problem. ...

There are two broad categories of how the (PDE) would be solved; either analytical methods, numerical methods, or something possibly in between. Typically, analytic methods solve the groundwater flow equation under a simplified set of conditions exactly, while numerical methods solve it under more general conditions to an approximation. Analysis has its beginnings in the rigorous formulation of calculus. ... Numerical analysis is the study of approximate methods for the problems of continuous mathematics (as distinguished from discrete mathematics). ...

### Analytic methods

Analytic methods typically use the structure of mathematics to arrive at a simple, elegant solution, but the required derivation for all but the simplest domain geometries can be quite complex (involving non-standard coordinates, conformal mapping, etc.). Analytic solutions typically are also simply an equation, which can give a quick answer based on a few basic parameters. The Theis equation is a very simple (yet still very useful) analytic solution to the groundwater flow equation, typically used to analyze the results of an aquifer test or slug test. Euclid, Greek mathematician, 3rd century BC, as imagined by by Raphael in this detail from The School of Athens. ... See Cartesian coordinate system or Coordinates (elementary mathematics) for a more elementary introduction to this topic. ... In mathematics, a mapping w = f(z) is angle-preserving or (more usually) conformal at a point z0, if it preserves oriented angles between curves through z0, as well as their orientation, i. ... An Aquifer test is conducted to evaluate an aquifer by stimulating the aquifer through constant pumping, and observing the aquifers response (drawdown) in observation wells. ... The groundwater flow equation is the mathematical relationship which is used to describe the flow of groundwater through a porous medium (e. ... An Aquifer test is conducted to evaluate an aquifer by stimulating the aquifer through constant pumping, and observing the aquifers response (drawdown) in observation wells. ... A slug test is a particular type of aquifer test where water is quickly added or removed from a groundwater well, and the change in hydraulic head is monitored through time, to determine the near-well aquifer characteristics. ...

### Numerical methods

The topic of numerical methods is quite large, obviously being of use to most fields of engineering and science in general. Numerical methods have been around much longer than computers have (In the 1920s Richardson developed some of the finite difference schemes still in use today, but they were calculated by hand, using paper and pencil, by human "calculators"), but they have become very important through the availability of fast and cheap personal computers. A quick survey of the main numerical methods used in hydrogeology, and some of the most basic principles is below. Numerical analysis is the study of approximate methods for the problems of continuous mathematics (as distinguished from discrete mathematics). ... Engineering is the design, analysis, and/or construction of works for practical purposes. ... Part of a scientific laboratory at the University of Cologne. ... The NASA Columbia Supercomputer. ... Lewis Fry Richardson (October 11, 1881 - September 30, 1953) was a mathematician, physicist and psychologist. ... A finite difference is a mathematical expression of the form f(x + b) âˆ’ f(x +a). ...

There are two broad categories of numerical methods: gridded or discretized methods and non-gridded or mesh-free methods. In the common finite difference method and finite element method (FEM) the domain is completely gridded ("cut" into a grid or mesh of small elements). The analytic element method (AEM) and the boundary integral equation method (BIEM — sometimes also called BEM, or Boundary Element Method) are only discretized at boundaries or along flow elements (line sinks, area sources, etc.), the majority of the domain is mesh-free. A finite difference is a mathematical expression of the form f(x + b) âˆ’ f(x +a). ... Mathematically, the finite element method (FEM) is used for finding approximate solution of partial differential equations (PDE) as well as of integral equations such as the heat transport equation. ... The analytic element method (AEM) is a numerical method used for the solution of partial differential equations. ...

#### General properties of gridded methods

Gridded Methods like finite difference and finite element methods solve the groundwater flow equation by breaking the problem area (domain) into many small elements (squares, rectangles, triangles, blocks, tetrahedra, etc.) and solving the flow equation for each element (all material properties are assumed constant or possibly linearly variable within an element), then linking together all the elements using conservation of mass across the boundaries between the elements (similar to the divergence theorem). This results in a system which overall approximates the groundwater flow equation, but exactly matches the boundary conditions (the head or flux is specified in the elements which intersect the boundaries). A finite difference is a mathematical expression of the form f(x + b) âˆ’ f(x +a). ... Finite element analysis (FEA) or finite element method (FEM) is a numerical technique for solution of boundary-value problems. ... A tetrahedron (plural: tetrahedra) is a polyhedron composed of four triangular faces, three of which meet at each vertex. ... The law of conservation of mass/matter, also known as law of mass/matter conservation (or the Lomonosov-Lavoisier law), states that the mass of a closed system of substances will remain constant, regardless of the processes acting inside the system. ... In vector calculus, the divergence theorem, also known as Gauss theorem, Ostrogradskys theorem, or Gauss-Ostrogradsky theorem is a result that relates the flow (that is, flux) of a vector field through a surface to the behaviour of the vector field inside the surface. ...

Finite differences are a way of representing continuous differential operators using discrete intervals (Δx and Δt), and the finite difference methods are based on these (they are derived from a Taylor series). For example the first-order time derivative is often approximated using the following forward finite difference, where the subscripts indicate a discrete time location, There are two subfields of mathematics that concern themselves with finite differences. ... In mathematics, a differential operator is a linear operator defined as a function of the differentiation operator. ... As the degree of the Taylor series rises, it approaches the correct function. ...

$frac{partial h}{partial t} = h'(t_i) approx frac{h_i - h_{i-1}}{Delta t}.$

The forward finite difference approximation is unconditionally stable, but leads to an implicit set of equations (that must be solved using matrix methods, e.g. LU or Cholesky decomposition). The similar backwards difference is only conditionally stable, but it is explicit and can be used to "march" forward in the time direction, solving one grid node at a time (or possibly in parallel, since one node depends only on its immediate neighbors). Rather than the finite difference method, sometimes the Galerkin FEM approximation is used in space (this is different from the type of FEM often used in structural engineering) with finite differences still used in time. In linear algebra, the LU decomposition is a matrix decomposition which writes a matrix as the product of a lower and upper triangular matrix. ... In mathematics, the Cholesky decomposition, named after AndrÃ©-Louis Cholesky, is a matrix decomposition of a symmetric positive-definite matrix into a lower triangular matrix and the transpose of the lower triangular matrix. ... Parallel computing is the simultaneous execution of the same task (split up and specially adapted) on multiple processors in order to obtain results faster. ... Mathematically, the finite element method (FEM) is used for finding approximate solution of partial differential equations (PDE) as well as of integral equations such as the heat transport equation. ... Taipei 101, the worlds tallest building as of 2004. ...

#### Application of finite difference models

MODFLOW is a well-known example of a general finite difference groundwater flow model. It is developed by the US Geological Survey as a modular and extensible simulation tool for modeling groundwater flow. It is free software developed, documented and distributed by the USGS. Many commercial products have grown up around it, providing graphical user interfaces to its input file based interface, and typically incorporating pre- and post-processing of user data. Many other models have been developed to work with MODFLOW input and output, making linked models which simulate several hydrologic processes possible (flow and transport models, surface water and groundwater models and chemical reaction models), because of the simple, well documented nature of MODFLOW. MODFLOW (modular flow) is a computer code which solves the groundwater flow equation using finite differences. ... The United States Geological Survey (USGS) is a scientific agency of the United States government. ... Clockwise from top: The logo of the GNU Project (the GNU head), the Linux kernel mascot Tux the Penguin, and the FreeBSD daemon Free software is a term coined by Richard Stallman and the Free Software Foundation[1] to refer to software that can be used, studied, and modified without... A graphical user interface (GUI) is a type of user interface which allows people to interact with a computer and computer-controlled devices which employ graphical icons, visual indicators or special graphical elements called widgets, along with text labels or text navigation to represent the information and actions available to... Surface water is water on the ground or in a stream, river, lake, sea or ocean; as opposed to groundwater. ... Groundwater is water located beneath the ground surface in soil pore spaces and in the fractures of geologic formations. ...

#### Application of finite element models

Finite Element programs are more flexible in design (triangular elements vs. the block elements most finite difference models use) and there are some programs available (SUTRA, a 2D or 3D density-dependent flow model by the USGS; Hydrus, a commercial unsaturated flow model; FEFLOW, a commercial modeling environment for subsurface flow, solute and heat transport processes; and COMSOL Multiphysics (FEMLAB) a commercial general modeling environment), but unless they are gaining in importance they are still not as popular in with practicing hydrogeologists as MODFLOW is. Finite element models are more popular in university and laboratory environments, where specialized models solve non-standard forms of the flow equation (unsaturated flow, density dependent flow, coupled heat and groundwater flow, etc.) Representation of a university class, 1350s. ... This article does not cite any references or sources. ... The vadose zone, also termed the unsaturated zone, is the portion of Earth between the land surface and the water table, and is thus not considered groundwater (vadose is Latin for shallow). It comprises the unsaturated portion of the soil, regolith or bedrock, as well as the saturated capillary fringe... In physics, density is mass m per unit volume V. For the common case of a homogeneous substance, it is expressed as: where, in SI units: Ï (rho) is the density of the substance, measured in kgÂ·m-3 m is the mass of the substance, measured in kg V is... In thermal physics, heat transfer is the passage of thermal energy from a hot to a cold body. ...

#### Other methods

These include mesh-free methods like the Analytic Element Method (AEM) and the Boundary Element Method (BEM), which are closer to analytic solutions, but they do approximate the groundwater flow equation in some way. The BEM and AEM exactly solve the groundwater flow equation (perfect mass balance), while approximating the boundary conditions. These methods are more exact and can be much more elegant solutions (like analytic methods are), but have not seen as widespread use outside academic and research groups. The analytic element method (AEM) is a numerical method used for the solution of partial differential equations. ...

### General hydrogeology

• Domenico, P.A. & Schwartz, W., 1998. Physical and Chemical Hydrogeology Second Edition, Wiley. — Good book for consultants, it has many real-world examples and covers additional topics (e.g. heat flow, multi-phase and unsaturated flow). ISBN 0-471-59762-7
• Driscoll, Fletcher, 1986. Groundwater and Wells, US Filter / Johnson Screens. — Practical book illustrating the actual process of drilling, developing and utilizing water wells, but it is a trade book, so some of the material is slanted towards the products made by Johnson Well Screens. ISBN 0-9616456-0-1
• Freeze, R.A. & Cherry, J.A., 1979. Groundwater, Prentice-Hall. — A classic text; like an older version of Domenico and Schwartz. ISBN 0-13-365312-9
• de Marsily, G., 1986. Quantitative Hydrogeology: Groundwater Hydrology for Engineers, Academic Press, Inc., Orlando Florida. — Classic book intended for engineers with mathematical background but it can be read by hydrologists and geologists as well. ISBN 0-12-208916-2
• Porges, Robert E. & Hammer, Matthew J., 2001. The Compendium of Hydrogeology, National Ground Water Association, ISBN 1-56034-100-9. Written by practicing hydrogeologists, this inclusive handbook provides a concise, easy-to-use reference for hydrologic terms, equations, pertinent physical parameters, and acronyms
• Todd, David Keith, 1980. Groundwater Hydrology Second Edition, John Wiley & Sons. — Case studies and real-world problems with examples. ISBN 0-471-87616-X

### Numerical groundwater modeling

• Anderson, Mary P. & Woessner, William W., 1992 Applied Groundwater Modeling, Academic Press. — An introduction to groundwater modeling, a little bit old, but the methods are still very applicable. ISBN 0-12-059485-4
• Chiang, W.-H., Kinzelbach, W., Rausch, R. (1998): Aquifer Simulation Model for WINdows - Groundwater flow and transport modeling, an integrated program. - 137 p., 115 fig., 2 tab., 1 CD-ROM; Berlin, Stuttgart (Borntraeger). ISBN 3-443-01039-3
• Elango, L and Jayakumar, R (Eds.)(2001) Modelling in Hydrogeology, UNESCO-IHP Publication, Allied Publ., Chennai, ISBN 81-7764-218-9
• Rausch, R., Schäfer W., Therrien, R., Wagner, C., 2005 Solute Transport Modelling - An Introduction to Models and Solution Strategies. - 205 p., 66 fig., 11 tab.; Berlin, Stuttgart (Borntraeger). ISBN 3-443-01055-5
• Rushton, K.R., 2003, Groundwater Hydrology: Conceptual and Computational Models. John Wiley and Sons Ltd. ISBN 0-470-85004-3
• Zheng, C., and Bennett, G.D., 2002, Applied Contaminant Transport Modeling Second Edition, John Wiley & Sons — A very good, modern treatment of groundwater flow and transport modeling, by the author of MT3D. ISBN 0-471-38477-1

### Analytic groundwater modeling

• Haitjema, Henk M., 1995. Analytic Element Modeling of Groundwater Flow, Academic Press. — An introduction to analytic solution methods, especially the Analytic element method (AEM). ISBN 0-12-316550-4
• Harr, Milton E., 1962. Groundwater and seepage, Dover. — a more civil engineering view on groundwater; includes a great deal on flownets. ISBN 0-486-66881-9
• Lee, Tien-Chang, 1999. Applied Mathematics in Hydrogeology, CRC Press. — Great explanation of mathematical methods used in deriving solutions to hydrogeology problems (solute transport, finite element and inverse problems too). ISBN 1-56670-375-1
• Liggett, James A. & Liu, Phillip .L-F., 1983. The Boundary Integral Equation Method for Porous Media Flow, George Allen and Unwin, London. — Book on BIEM (sometimes called BEM) with examples, it makes a good introduction to the method. ISBN 0-04-620011-8

The analytic element method (AEM) is a numerical method used for the solution of partial differential equations. ... This article does not cite any references or sources. ... The construction of a Flownet is a graphical method used to solve two-dimensional steady-state groundwater flow problems through aquifers. ...

physical aquifer properties used in hydrogeology
hydraulic head | hydraulic conductivity | storativity | porosity | water content

Environmental engineering[1][2] is the application of science and engineering principles to improve the environment (air, water, and/or land resources), to provide healthy water, air, and land for human habitation and for other organisms, and to remediate polluted sites. ... Earth science (also known as geoscience, the geosciences or the Earth Sciences), is an all-embracing term for the sciences related to the planet Earth. ... The movement of water around, over, and through the Earth is called the water cycle. ... The movement of water around, over, and through the Earth is called the water cycle, a key process of the hydrosphere. ... Water resources are sources of water that are useful or potentially useful to humans. ... An Aquifer test is conducted to evaluate an aquifer by stimulating the aquifer through constant pumping, and observing the aquifers response (drawdown) in observation wells. ... This article discusses Water well testing; the testing of other wells, eg. ... Isotope hydrology is a fast, cheap, and reliable way to discover the age, origins, size, flow and fate of a water source for purposes of sound water-use policy, maping underground aquifers, conserving water supplies, and controling pollution. ... The construction of a Flownet is a graphical method used to solve two-dimensional steady-state groundwater flow problems through aquifers. ... Heat conduction or thermal conduction is the spontaneous transfer of thermal energy through matter, from a region of higher temperature to a region of lower temperature, and hence acts to even out temperature differences. ... Dye tracing is tracking and tracing various flows using dye added to the liquid in question. ... // Foundations Principles of Geology Author: Charles Lyell Publication data: 1830â€“1833. ... A municipal water system is a large system of reservoirs and large-scale piping which supplies fresh water, suitable for human consumption, to houses and other residences. ... Groundwater is water located beneath the ground surface in soil pore spaces and in the fractures of geologic formations. ... A natural spring on Mackinac Island in Michigan. ... Cable tool water well drilling rig in Kimball, West Virginia. ... Well water is drawn via mechanical pump from a source below the surface of the earth. ... An aquifer is an underground layer of water-bearing permeable rock or unconsolidated materials (gravel, sand, silt, or clay) from which groundwater can be usefully extracted using a water well. ... It has been suggested that Hydraulic head (hydrology) and Head (hydraulic) be merged into this article or section. ... written by AmerHydraulic conductivity, mathematically represented as , is a property of soil or rock, in the vadose zone or groundwater, that describes the ease with which water can move through pore spaces or fractures. ... Specific storage (Ss), storativity (S), specific yield (Sy) and specific capacity are aquifer properties; they are measures of the ability of an aquifer to release groundwater from storage, due to a unit decline in hydraulic head. ... Porosity is a measure of the void spaces in a material, and is measured as a fraction, between 0â€“1, or as a percentage between 0â€“100%. The term porosity is used in multiple fields including manufacturing, earth sciences and construction. ... Water content is a ratio used in hydrogeology and soil mechanics to indicate the amount of water a porous medium contains. ...

Results from FactBites:

 Hydrogeology - Wikipedia, the free encyclopedia (2323 words) Although the basic principles of hydrogeology are very intuitive (e.g., water flows "downhill"), the study of their interaction can be quite complex. Traditionally, the movement of groundwater has been studied separately from surface water, climatology, and even the chemical and microbiological aspects of hydrogeology (the processes are uncoupled). As the field of hydrogeology matures, the strong interactions between groundwater, surface water, water chemistry, soil moisture and even climate are becoming more clear.
 Contaminant Hydrogeology (1093 words) Hydrogeology is the study of water movement in rocks, and includes the behaviour of associated chemicals whether they are natural occurring or pollutants. This module is an intensive study of the basic concepts of hydrogeology, and includes aspects of geology and hydrology. The course will extend students´ knowledge of hydrogeology by discussing urban groundwater at the regional and local scales, with case studies of investigation and assessment.
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