Hydrogeology

Encyclopedia

**Hydrogeology**is the area of geology

Geology

Geology is the science comprising the study of solid Earth, the rocks of which it is composed, and the processes by which it evolves. Geology gives insight into the history of the Earth, as it provides the primary evidence for plate tectonics, the evolutionary history of life, and past climates...

that deals with the distribution and movement of groundwater

Groundwater

Groundwater is water located beneath the ground surface in soil pore spaces and in the fractures of rock formations. 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...

in the soil

Soil

Soil is a natural body consisting of layers of mineral constituents of variable thicknesses, which differ from the parent materials in their morphological, physical, chemical, and mineralogical characteristics...

and rocks

Rock (geology)

In geology, rock or stone is a naturally occurring solid aggregate of minerals and/or mineraloids.The Earth's outer solid layer, the lithosphere, is made of rock. In general rocks are of three types, namely, igneous, sedimentary, and metamorphic...

of the Earth's crust

Crust (geology)

In geology, the crust is the outermost solid shell of a rocky planet or natural satellite, which is chemically distinct from the underlying mantle...

, (commonly in aquifer

Aquifer

An aquifer is a wet underground layer of water-bearing permeable rock or unconsolidated materials from which groundwater can be usefully extracted using a water well. The study of water flow in aquifers and the characterization of aquifers is called hydrogeology...

s). The term

**geohydrology**is often used interchangeably. Some make the minor distinction between a hydrologist or engineer

Engineer

An engineer is a professional practitioner of engineering, concerned with applying scientific knowledge, mathematics and ingenuity to develop solutions for technical problems. Engineers design materials, structures, machines and systems while considering the limitations imposed by practicality,...

applying themselves to geology (geohydrology), and a geologist

Geologist

A geologist is a scientist who studies the solid and liquid matter that constitutes the Earth as well as the processes and history that has shaped it. Geologists usually engage in studying geology. Geologists, studying more of an applied science than a theoretical one, must approach Geology using...

applying themselves to hydrology

Hydrology

Hydrology is the study of the movement, distribution, and quality of water on Earth and other planets, including the hydrologic cycle, water resources and environmental watershed sustainability...

(hydrogeology).

## Introduction

Hydrogeology is an interdisciplinary subject; it can be difficult to account fully for the chemicalChemistry

Chemistry is the science of matter, especially its chemical reactions, but also its composition, structure and properties. Chemistry is concerned with atoms and their interactions with other atoms, and particularly with the properties of chemical bonds....

, physical

Engineering

Engineering is the discipline, art, skill and profession of acquiring and applying scientific, mathematical, economic, social, and practical knowledge, in order to design and build structures, machines, devices, systems, materials and processes that safely realize improvements to the lives of...

, biological

Biology

Biology is a natural science concerned with the study of life and living organisms, including their structure, function, growth, origin, evolution, distribution, and taxonomy. Biology is a vast subject containing many subdivisions, topics, and disciplines...

and even legal interactions between soil

Soil

Soil is a natural body consisting of layers of mineral constituents of variable thicknesses, which differ from the parent materials in their morphological, physical, chemical, and mineralogical characteristics...

, water

Water

Water is a chemical substance with the chemical formula H2O. A water molecule contains one oxygen and two hydrogen atoms connected by covalent bonds. Water is a liquid at ambient conditions, but it often co-exists on Earth with its solid state, ice, and gaseous state . Water also exists in a...

, nature

Biosphere

The biosphere is the global sum of all ecosystems. It can also be called the zone of life on Earth, a closed and self-regulating system...

and society

Urban planning

Urban planning incorporates areas such as economics, design, ecology, sociology, geography, law, political science, and statistics to guide and ensure the orderly development of settlements and communities....

. The study of the interaction between groundwater movement and geology can be quite complex. Groundwater does not always flow in the subsurface down-hill following the surface topography; groundwater follows pressure gradient

Pressure gradient

In atmospheric sciences , the pressure gradient is a physical quantity that describes in which direction and at what rate the pressure changes the most rapidly around a particular location. The pressure gradient is a dimensional quantity expressed in units of pressure per unit length...

s (flow from high pressure to low) often following fractures and conduits in circuitous paths. Taking into account the interplay of the different facets of a multi-component system often requires knowledge in several diverse fields at both the experiment

Experiment

An experiment is a methodical procedure carried out with the goal of verifying, falsifying, or establishing the validity of a hypothesis. Experiments vary greatly in their goal and scale, but always rely on repeatable procedure and logical analysis of the results...

al and theoretical

Theory

The English word theory was derived from a technical term in Ancient Greek philosophy. The word theoria, , meant "a looking at, viewing, beholding", and referring to contemplation or speculation, as opposed to action...

levels. The following is a more traditional introduction to the methods and nomenclature of saturated subsurface hydrology, or simply hydrogeology.

## 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 mediaPorous medium

A porous medium is a material containing pores . The skeletal portion of the material is often called the "matrix" or "frame". The pores are typically filled with a fluid...

(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

Soil science

Soil science is the study of 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; and these properties in relation to the use and management of soils.Sometimes terms which...

, agriculture

Agriculture

Agriculture is the cultivation of animals, plants, fungi and other life forms for food, fiber, and other products used to sustain life. Agriculture was the key implement in the rise of sedentary human civilization, whereby farming of domesticated species created food surpluses that nurtured the...

and civil engineering

Civil engineering

Civil engineering is a professional engineering discipline that deals with the design, construction, and maintenance of the physical and naturally built environment, including works like roads, bridges, canals, dams, and buildings...

, as well as to hydrogeology. The general flow of fluid

Fluid

In physics, a fluid is a substance that continually deforms under an applied shear stress. Fluids are a subset of the phases of matter and include liquids, gases, plasmas and, to some extent, plastic solids....

s (water, hydrocarbons, geothermal fluids, etc.) in deeper formations is also a concern of geologists, geophysicists

Geophysics

Geophysics is the physics of the Earth and its environment in space; also the study of the Earth using quantitative physical methods. The term geophysics sometimes refers only to the geological applications: Earth's shape; its gravitational and magnetic fields; its internal structure and...

and petroleum geologists

Petroleum geology

Petroleum geology refers to the specific set of geological disciplines that are applied to the search for hydrocarbons .-Sedimentary basin analysis:...

. Groundwater is a slow-moving, viscous

Viscosity

Viscosity is a measure of the resistance of a fluid which is being deformed by either shear or tensile stress. In everyday terms , viscosity is "thickness" or "internal friction". Thus, water is "thin", having a lower viscosity, while honey is "thick", having a higher viscosity...

fluid (with a Reynolds number less than unity); many of the empirically derived laws of groundwater flow can be alternately derived in fluid mechanics

Fluid mechanics

Fluid mechanics is the study of fluids and the forces on them. Fluid mechanics can be divided into fluid statics, the study of fluids at rest; fluid kinematics, the study of fluids in motion; and fluid dynamics, the study of the effect of forces on fluid motion...

from the special case of Stokes flow (viscosity and pressure

Pressure

Pressure is the force per unit area applied in a direction perpendicular to the surface of an object. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure.- Definition :...

terms, but no inertial term).

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

Elasticity (physics)

In physics, elasticity is the physical property of a material that returns to its original shape after the stress that made it deform or distort is removed. The relative amount of deformation is called the strain....

and heat conduction

Heat conduction

In heat transfer, conduction is a mode of transfer of energy within and between bodies of matter, due to a temperature gradient. Conduction means collisional and diffusive transfer of kinetic energy of particles of ponderable matter . Conduction takes place in all forms of ponderable matter, viz....

analogies. Transient groundwater flow is analogous to the diffusion of heat

Heat

In physics and thermodynamics, heat is energy transferred from one body, region, or thermodynamic system to another due to thermal contact or thermal radiation when the systems are at different temperatures. It is often described as one of the fundamental processes of energy transfer between...

in a solid, therefore some solutions to hydrological problems have been adapted from heat transfer

Heat transfer

Heat transfer is a discipline of thermal engineering that concerns the exchange of thermal energy from one physical system to another. Heat transfer is classified into various mechanisms, such as heat conduction, convection, thermal radiation, and phase-change transfer...

literature.

Traditionally, the movement of groundwater has been studied separately from surface water, climatology

Climatology

Climatology is the study of climate, scientifically defined as weather conditions averaged over a period of time, and is a branch of the atmospheric sciences...

, and even the chemical and microbiological

Microbiology

Microbiology is the study of microorganisms, which are defined as any microscopic organism that comprises either a single cell , cell clusters or no cell at all . This includes eukaryotes, such as fungi and protists, and prokaryotes...

aspects of hydrogeology (the processes are uncoupled). As the field of hydrogeology matures, the strong interactions between groundwater, surface water

River

A river is a natural watercourse, usually freshwater, flowing towards an ocean, a lake, a sea, or another river. In a few cases, a river simply flows into the ground or dries up completely before reaching another body of water. Small rivers may also be called by several other names, including...

, water chemistry

Geochemistry

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, water, and soils, and the cycles of matter and energy that transport the Earth's chemical components in time and space, and...

, soil moisture and even climate

Climate

Climate encompasses the statistics of temperature, humidity, atmospheric pressure, wind, rainfall, atmospheric particle count and other meteorological elemental measurements in a given region over long periods...

are becoming more clear.

For example: Aquifer drawdown

Drawdown

Drawdown has four distinct meanings:* Drawdown , a lowering of a reservoir or a change in hydraulic head in an aquifer, typically due to pumping a well.* Drawdown , decline in the value of an investment, below its all-time high....

or overdrafting

Overdrafting

Overdrafting is the process of extracting groundwater beyond the safe yield or equilibrium yield of the aquifer.Since every groundwater basin recharges at a different rate depending upon precipitation, vegetative cover and soil conservation practises, the quantity of groundwater that can be safely...

and the pumping of fossil water

Fossil water

Fossil water or paleowater is groundwater that has remained sealed in an aquifer for a long period of time. Water can rest underground in "fossil aquifers" for thousands or even millions of years...

increases the total amount of water within the hydrosphere

Hydrosphere

A hydrosphere in physical geography describes the combined mass of water found on, under, and over the surface of a planet....

subject to transpiration

Transpiration

Transpiration is a process similar to evaporation. It is a part of the water cycle, and it is the loss of water vapor from parts of plants , especially in leaves but also in stems, flowers and roots. Leaf surfaces are dotted with openings which are collectively called stomata, and in most plants...

and evaporation

Evaporation

Evaporation is a type of vaporization of a liquid that occurs only on the surface of a liquid. The other type of vaporization is boiling, which, instead, occurs on the entire mass of the liquid....

processes, thereby causing accretion in water vapour and cloud cover, the primary absorbers of infrared

Infrared

Infrared light is electromagnetic radiation with a wavelength longer than that of visible light, measured from the nominal edge of visible red light at 0.74 micrometres , and extending conventionally to 300 µm...

radiation in the earth's atmosphere. Adding water to the system has a forcing effect

Global warming

Global warming refers to the rising average temperature of Earth's atmosphere and oceans and its projected continuation. In the last 100 years, Earth's average surface temperature increased by about with about two thirds of the increase occurring over just the last three decades...

on the whole earth system

Gaia hypothesis

The Gaia hypothesis, also known as Gaia theory or Gaia principle, proposes that all organisms and their inorganic surroundings on Earth are closely integrated to form a single and self-regulating complex system, maintaining the conditions for life on the planet.The scientific investigation of the...

. An accurate estimate of the climatic forcing effect due to this hydrogeological fact is yet to be quantified.

## Definitions and material properties

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:- Can the aquifer support another subdivisionSubdivision (land)Subdivision is the act of dividing land into pieces that are easier to sell or otherwise develop, usually via a plat. The former single piece as a whole is then known in the United States as a subdivision...

? - Will the riverRiverA river is a natural watercourse, usually freshwater, flowing towards an ocean, a lake, a sea, or another river. In a few cases, a river simply flows into the ground or dries up completely before reaching another body of water. Small rivers may also be called by several other names, including...

dry up if the farmer doubles his irrigationIrrigationIrrigation may be defined as the science of artificial application of water to the land or soil. It is used to assist in the growing of agricultural crops, maintenance of landscapes, and revegetation of disturbed soils in dry areas and during periods of inadequate rainfall...

? - Did the chemicals from the dry cleaningDry cleaningDry cleaning is any cleaning process for clothing and textiles using a chemical solvent other than water. The solvent used is typically tetrachloroethylene , abbreviated "perc" in the industry and "dry-cleaning fluid" by the public...

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 test

Aquifer test

An aquifer test is conducted to evaluate an aquifer by "stimulating" the aquifer through constant pumping, and observing the aquifer's "response" in observation wells...

s.

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

Water table

The water table is the level at which the submarine pressure is far from atmospheric pressure. It may be conveniently visualized as the 'surface' of the subsurface materials that are saturated with groundwater in a given vicinity. However, saturated conditions may extend above the water table as...

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).

### Hydraulic head

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 lawDarcy's law

Darcy's law is a phenomenologically derived constitutive equation that describes the flow of a fluid through a porous medium. The law was formulated by Henry Darcy based on the results of experiments on the flow of water through beds of sand...

as being proportional to the discharge.

Hydraulic head is a directly measurable property that can take on any value (because of the arbitrary datum involved in the z term); ψ can be measured with a pressure transducer

Transducer

A transducer is a device that converts one type of energy to another. Energy types include electrical, mechanical, electromagnetic , chemical, acoustic or thermal energy. While the term transducer commonly implies the use of a sensor/detector, any device which converts energy can be considered a...

(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

Water well

A water well is an excavation or structure created in the ground by digging, driving, boring or drilling to access groundwater in underground aquifers. The well water is drawn by an electric submersible pump, a trash pump, a vertical turbine pump, a handpump or a mechanical pump...

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 record of hydraulic head through time at a well is a hydrograph

Hydrograph

A hydrograph is a graph showing the rate of flow versus time past a specific point in a river, or other channel or conduit carrying flow...

or, the changes in hydraulic head recorded during the pumping of a well in a test are called drawdown

Drawdown (hydrology)

In water-related science and engineering there are two similar but distinct definitions in use for drawdown.*In subsurface hydrogeology, drawdown is the change in hydraulic head observed at a well in an aquifer, typically due to pumping a well as part of an aquifer test or well test.*In surface...

.

### 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 soilSoil

Soil is a natural body consisting of layers of mineral constituents of variable thicknesses, which differ from the parent materials in their morphological, physical, chemical, and mineralogical characteristics...

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

Effective porosity

The term effective porosity lacks a single or straightforward definition. Even some of the terms used in its mathematical description have multiple definitions. However, it is most commonly considered to represent the porosity of a rock or sediment available to contribute to fluid flow through...

).

**Permeability**is an expression of the connectedness of the pores. For instance, an unfractured rock unit may have a high porosity (it has lots of holes between its constituent grains), but a low permeability (none of the pores are connected). An example of this phenomenon is pumice

Pumice

Pumice is a textural term for a volcanic rock that is a solidified frothy lava typically created when super-heated, highly pressurized rock is violently ejected from a volcano. It can be formed when lava and water are mixed. This unusual formation is due to the simultaneous actions of rapid...

, which, when in its unfractured state, can make a poor aquifer.

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

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.The water content is very important in vadose zone

Vadose zone

The vadose zone, also termed the unsaturated zone, is the portion of Earth between the land surface and the top of the phreatic zone i.e. the position at which the groundwater is at atmospheric pressure . Hence the vadose zone extends from the top of the ground surface to the water table...

hydrology, where the hydraulic conductivity

Hydraulic conductivity

Hydraulic conductivity, symbolically represented as K, is a property of vascular plants, soil or rock, that describes the ease with which water can move through pore spaces or fractures. It depends on the intrinsic permeability of the material and on the degree of saturation...

is a strongly nonlinear function of water content; this complicates the solution of the unsaturated groundwater flow equation.

### 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 aquiferAquifer

An aquifer is a wet underground layer of water-bearing permeable rock or unconsolidated materials from which groundwater can be usefully extracted using a water well. The study of water flow in aquifers and the characterization of aquifers is called hydrogeology...

's ability to transmit water

Water

Water is a chemical substance with the chemical formula H2O. A water molecule contains one oxygen and two hydrogen atoms connected by covalent bonds. Water is a liquid at ambient conditions, but it often co-exists on Earth with its solid state, ice, and gaseous state . Water also exists in a...

. Intrinsic permeability

Permeability (fluid)

Permeability in fluid mechanics and the earth sciences is a measure of the ability of a porous material to allow fluids to pass through it.- Units :...

(κ) is a secondary medium property which does not depend on the viscosity

Viscosity

Viscosity is a measure of the resistance of a fluid which is being deformed by either shear or tensile stress. In everyday terms , viscosity is "thickness" or "internal friction". Thus, water is "thin", having a lower viscosity, while honey is "thick", having a higher viscosity...

and density

Density

The mass density or density of a material is defined as its mass per unit volume. The symbol most often used for density is ρ . In some cases , density is also defined as its weight per unit volume; although, this quantity is more properly called specific weight...

of the fluid (K and T are specific to water); it is used more in the petroleum industry.

### Specific storage and specific yield

Specific storage (S_{s}) and its depth-integrated equivalent, storativity (S=S

_{s}b), 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 yield (S

_{y}) is also a ratio between 0 and 1 (S

_{y}≤ porosity) and indicates the amount of water released due to drainage from lowering the water table in an unconfined aquifer. The value for specific yield is less than the value for porosity because some water will remain in the medium even after drainage due to molecular forces. Often the porosity

Porosity

Porosity or void fraction is a measure of the void spaces in a material, and is a fraction of the volume of voids over the total volume, between 0–1, or as a percentage between 0–100%...

or effective porosity is used as an upper bound to the specific yield. Typically S

_{y}is orders of magnitude larger than S

_{s}.

### 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 productsBTEX

BTEX is an acronym that stands for benzene, toluene, ethylbenzene, and xylenes. These compounds are some of the volatile organic compounds found in petroleum derivatives such as petrol . Toluene, ethylbenzene, and xylenes have harmful effects on the central nervous system.BTEX compounds are...

, nitrate

Nitrate

The nitrate ion is a polyatomic ion with the molecular formula NO and a molecular mass of 62.0049 g/mol. It is the conjugate base of nitric acid, consisting of one central nitrogen atom surrounded by three identically-bonded oxygen atoms in a trigonal planar arrangement. The nitrate ion carries a...

or Chromium

Chromium

Chromium is a chemical element which has the symbol Cr and atomic number 24. It is the first element in Group 6. It is a steely-gray, lustrous, hard metal that takes a high polish and has a high melting point. It is also odorless, tasteless, and malleable...

) or naturally occurring (e.g., arsenic

Arsenic

Arsenic is a chemical element with the symbol As, atomic number 33 and relative atomic mass 74.92. Arsenic occurs in many minerals, usually in conjunction with sulfur and metals, and also as a pure elemental crystal. It was first documented by Albertus Magnus in 1250.Arsenic is a metalloid...

, salinity

Salinity

Salinity is the saltiness or dissolved salt content of a body of water. It is a general term used to describe the levels of different salts such as sodium chloride, magnesium and calcium sulfates, and bicarbonates...

). 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.

#### Hydrodynamic dispersion

Hydrodynamic dispersivity (α_{L}, α

_{T}) 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 (α

_{L}), and some will be "to the sides of" the pure advective groundwater flow, leading to a transverse dispersivity (α

_{T}). Dispersion in groundwater is because each water "particle", passing beyond a soil particle, must choose where to go, whether left or right or up or down, so that the water "particles" (and their solute) are gradually spread in all directions around the mean path. This is the "microscopic" mechanism, on the scale of soil particles. More important, on long distances, can be the macroscopic inhomogeneities of the aquifer, which can have regions of larger or smaller permeability, so that some water can find a preferential path in one direction, some other in a different direction, so that the contaminant can be spread in a completely irregular way, like in a (three-dimensional) delta of a river.

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

Macroscopic

The macroscopic scale is the length scale on which objects or processes are of a size which is measurable and observable by the naked eye.When applied to phenomena and abstract objects, the macroscopic scale describes existence in the world as we perceive it, often in contrast to experiences or...

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.

#### Molecular Diffusion

Diffusion is a fundamental physical phenomenon, by which Einstein explained Brownian motionBrownian motion

Brownian motion or pedesis is the presumably random drifting of particles suspended in a fluid or the mathematical model used to describe such random movements, which is often called a particle theory.The mathematical model of Brownian motion has several real-world applications...

, which describes the random thermal movement of molecules and small particles in gases and liquids. It is an important phenomenon for small distances (it is essential for the achievement of thermodinamic equilibria), but, as the time necessary to cover a distance by diffusion is proportional to the square of the distance itself, it is ineffective for spreading a solute over macroscopic distances. The diffusion coefficient, D, is typically quite small, and its effect can often be considered negligible (unless groundwater flow velocities are extremely low, as they are in clay aquitards).

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

#### Retardation by adsorption

The retardation factor is another very important feature that make the motion of the contaminant to deviate from the average groundwater motion. It is analogous to the retardation factorRetardation factor

In chromatography, the retardation factor is defined as the fraction of an analyte in the mobile phase of a chromatographic system.. In planar chromatography in particular, the retardation factor is defined as the ratio of the distance traveled by the center of a spot to the distance traveled by...

of chromatography

Chromatography

Chromatography is the collective term for a set of laboratory techniques for the separation of mixtures....

. Unlike diffusion and dispersion, which simply spread the contaminant, the retardation factor changes its global average velocity, so that it can be much slower than that of water. This is due to a chemico-physical effect: the adsorption

Adsorption

Adsorption is the adhesion of atoms, ions, biomolecules or molecules of gas, liquid, or dissolved solids to a surface. This process creates a film of the adsorbate on the surface of the adsorbent. It differs from absorption, in which a fluid permeates or is dissolved by a liquid or solid...

to the soil, which holds the contaminant back and does not allow it to progress until the quantity corresponding to the chemical adsorption equilibrium has been adsorbed. This effect is particularly important for less soluble contaminants, which thus can move even hundreds or thousands times slower than water. The effect of this phenomenon is that only more soluble species can cover long distances. The retardation factor depends on the chemical nature of both the contaminant and the aquifer.

### Darcy's Law

Darcy's law is a Constitutive equationConstitutive equation

In physics, a constitutive equation is a relation between two physical quantities that is specific to a material or substance, and approximates the response of that material to external forces...

(empirically derived by Henri Darcy, in 1856) that states the amount of groundwater

Groundwater

Groundwater is water located beneath the ground surface in soil pore spaces and in the fractures of rock formations. 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...

discharging through a given portion of aquifer

Aquifer

An aquifer is a wet underground layer of water-bearing permeable rock or unconsolidated materials from which groundwater can be usefully extracted using a water well. The study of water flow in aquifers and the characterization of aquifers is called hydrogeology...

is proportional to the cross-sectional area of flow, the hydraulic head gradient, and the hydraulic conductivity

Hydraulic conductivity

Hydraulic conductivity, symbolically represented as K, is a property of vascular plants, soil or rock, that describes the ease with which water can move through pore spaces or fractures. It depends on the intrinsic permeability of the material and on the degree of saturation...

.

### 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 transferHeat transfer

Heat transfer is a discipline of thermal engineering that concerns the exchange of thermal energy from one physical system to another. Heat transfer is classified into various mechanisms, such as heat conduction, convection, thermal radiation, and phase-change transfer...

solutions.

It is often derived from a physical basis using Darcy's law

Darcy's law

Darcy's law is a phenomenologically derived constitutive equation that describes the flow of a fluid through a porous medium. The law was formulated by Henry Darcy based on the results of experiments on the flow of water through beds of sand...

and a conservation of mass for a small control volume. The equation is often used to predict flow to wells

Water well

A water well is an excavation or structure created in the ground by digging, driving, boring or drilling to access groundwater in underground aquifers. The well water is drawn by an electric submersible pump, a trash pump, a vertical turbine pump, a handpump or a mechanical pump...

, which have radial symmetry, so the flow equation is commonly solved in polar or cylindrical coordinates.

The Theis equation

Aquifer test

An aquifer test is conducted to evaluate an aquifer by "stimulating" the aquifer through constant pumping, and observing the aquifer's "response" in observation wells...

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.

The Thiem equation is a solution to the steady state groundwater flow equation (Laplace's Equation) for flow to a well. Unless there are large sources of water nearby (a river or lake), true steady-state is rarely achieved in reality.

Both above equations are used in aquifer test

Aquifer test

An aquifer test is conducted to evaluate an aquifer by "stimulating" the aquifer through constant pumping, and observing the aquifer's "response" in observation wells...

s (pump tests).

The Hooghoudt equation

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....

is a groundwater flow equation applied to subsurface drainage

Drainage system (Agriculture)

An agricultural drainage system is a system by which the water level on or in the soil is controlled to enhance agricultural crop production.-Classification:Figure 1 classifies the various types of drainage systems...

by pipes, tile drains

Tile drainage

Tile drainage is an agriculture practice that removes excess water from soil subsurface. Whereas irrigation is the practice of adding additional water when the soil is naturally too dry, drainage brings soil moisture levels down for optimal crop growth...

or ditches. An alternative subsurface drainage method is drainage by wells for which groundwater flow equations are also available.

## 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

Partial differential equation

In mathematics, partial differential equations are a type of differential equation, i.e., a relation involving an unknown function of several independent variables and their partial derivatives with respect to those variables...

(PDE) must be solved. The most common means of analytically solving the diffusion equation in the hydrogeology literature are:

- Laplace, HankelHankel transformIn mathematics, the Hankel transform expresses any given function f as the weighted sum of an infinite number of Bessel functions of the first kind Jν. The Bessel functions in the sum are all of the same order ν, but differ in a scaling factor k along the r-axis...

and FourierFourier transformIn mathematics, Fourier analysis is a subject area which grew from the study of Fourier series. The subject began with the study of the way general functions may be represented by sums of simpler trigonometric functions...

transforms (to reduce the number of dimensionDimensionIn physics and mathematics, the dimension of a space or object is informally defined as the minimum number of coordinates needed to specify any point within it. Thus a line has a dimension of one because only one coordinate is needed to specify a point on it...

s of the PDE), - similaritySimilarity-Specific definitions:Different fields provide differing definitions of similarity:-In computer science:* string metric, aka string similarity* semantic similarity in computational linguistics-In other fields:...

transform (also called the Boltzmann transform) is commonly how the Theis solutionAquifer test

is derived, - separation of variablesSeparation of variablesIn mathematics, separation of variables is any of several methods for solving ordinary and partial differential equations, in which algebra allows one to rewrite an equation so that each of two variables occurs on a different side of the equation....

, which is more useful for non-Cartesian coordinates, and - Green's functionGreen's functionIn mathematics, a Green's function is a type of function used to solve inhomogeneous differential equations subject to specific initial conditions or boundary conditions...

s, which is another common method for deriving the Theis solution — from the fundamental solutionFundamental solutionIn 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 Green's function...

to the diffusion equation in free space.

No matter which method we use to solve the groundwater flow equation

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...

, 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).

There are two broad categories of how the (PDE) would be solved; either

analytical

Mathematical analysis

Mathematical analysis, which mathematicians refer to simply as analysis, has its beginnings in the rigorous formulation of infinitesimal calculus. It is a branch of pure mathematics that includes the theories of differentiation, integration and measure, limits, infinite series, and analytic functions...

methods, numerical

Numerical analysis

Numerical analysis is the study of algorithms that use numerical approximation for the problems of mathematical analysis ....

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.

### Analytic methods

Analytic methods typically use the structure of mathematicsMathematics

Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

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 that 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

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...

, typically used to analyze the results of an aquifer test

Aquifer test

or slug test

Slug test

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 methodsNumerical analysis

Numerical analysis is the study of algorithms that use numerical approximation for the problems of mathematical analysis ....

is quite large, obviously being of use to most fields of engineering

Engineering

Engineering is the discipline, art, skill and profession of acquiring and applying scientific, mathematical, economic, social, and practical knowledge, in order to design and build structures, machines, devices, systems, materials and processes that safely realize improvements to the lives of...

and science

Science

Science is a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe...

in general. Numerical methods have been around much longer than computer

Computer

A computer is a programmable machine designed to sequentially and automatically carry out a sequence of arithmetic or logical operations. The particular sequence of operations can be changed readily, allowing the computer to solve more than one kind of problem...

s have (In the 1920s Richardson

Lewis Fry Richardson

Lewis Fry Richardson, FRS was an English mathematician, physicist, meteorologist, psychologist and pacifist who pioneered modern mathematical techniques of weather forecasting, and the application of similar techniques to studying the causes of wars and how to prevent them...

developed some of the finite difference

Finite difference

A finite difference is a mathematical expression of the form f − f. If a finite difference is divided by b − a, one gets a difference quotient...

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 computer

Personal computer

A personal computer is any general-purpose computer whose size, capabilities, and original sales price make it useful for individuals, and which is intended to be operated directly by an end-user with no intervening computer operator...

s. A quick survey of the main numerical methods used in hydrogeology, and some of the most basic principles is shown below and further discussed in the article "Groundwater model

Groundwater model

Groundwater models are computer models of groundwater flow systems, and are used by hydrogeologists. Groundwater models are used to simulate and predict aquifer conditions.-Characteristics:...

".

There are two broad categories of numerical methods: gridded or discretized methods and non-gridded or mesh-free methods. In the common finite difference

Finite difference

A finite difference is a mathematical expression of the form f − f. If a finite difference is divided by b − a, one gets a difference quotient...

method and finite element method

Finite element method

The finite element method is a numerical technique for finding approximate solutions of partial differential equations as well as integral equations...

(FEM) the domain is completely gridded ("cut" into a grid or mesh of small elements). The analytic element method

Analytic element method

The analytic element method is a numerical method used for the solution of partial differential equations. It was initially developed by O.D.L. Strack at the University of Minnesota...

(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.

#### General properties of gridded methods

Gridded Methods like finite differenceFinite difference

A finite difference is a mathematical expression of the form f − f. If a finite difference is divided by b − a, one gets a difference quotient...

and finite element methods solve the groundwater flow equation by breaking the problem area (domain) into many small elements (squares, rectangles, triangles, blocks, tetrahedra

Tetrahedron

In geometry, a tetrahedron is a polyhedron composed of four triangular faces, three of which meet at each vertex. A regular tetrahedron is one in which the four triangles are regular, or "equilateral", and is one of the Platonic solids...

, 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

Conservation of mass

The law of conservation of mass, also known as the principle of mass/matter conservation, states that the mass of an isolated system will remain constant over time...

across the boundaries between the elements (similar to the divergence theorem

Divergence theorem

In vector calculus, the divergence theorem, also known as Gauss' theorem , Ostrogradsky's theorem , or Gauss–Ostrogradsky theorem is a result that relates the flow of a vector field through a surface to the behavior of the vector field inside the surface.More precisely, 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).

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

Taylor series

In mathematics, a Taylor series is a representation of a function as an infinite sum of terms that are calculated from the values of the function's derivatives at a single point....

). For example the first-order time derivative is often approximated using the following forward finite difference, where the subscripts indicate a discrete time location,

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

LU decomposition

In linear algebra, LU decomposition is a matrix decomposition which writes a matrix as the product of a lower triangular matrix and an upper triangular matrix. The product sometimes includes a permutation matrix as well. This decomposition is used in numerical analysis to solve systems of linear...

or Cholesky decomposition

Cholesky decomposition

In linear algebra, the Cholesky decomposition or Cholesky triangle is a decomposition of a Hermitian, positive-definite matrix into the product of a lower triangular matrix and its conjugate transpose. It was discovered by André-Louis Cholesky for real matrices...

). 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

Parallel computing

Parallel computing is a form of computation in which many calculations are carried out simultaneously, operating on the principle that large problems can often be divided into smaller ones, which are then solved concurrently . There are several different forms of parallel computing: bit-level,...

, since one node depends only on its immediate neighbors). Rather than the finite difference method, sometimes the Galerkin FEM

Finite element method

The finite element method is a numerical technique for finding approximate solutions of partial differential equations as well as integral equations...

approximation is used in space (this is different from the type of FEM often used in structural engineering

Structural engineering

Structural engineering is a field of engineering dealing with the analysis and design of structures that support or resist loads. Structural engineering is usually considered a specialty within civil engineering, but it can also be studied in its own right....

) with finite differences still used in time.

#### Application of finite difference models

MODFLOWMODFLOW

MODFLOW is the U.S. Geological Survey modular finite-difference flow model, which is a computer code that solves the groundwater flow equation. The program is used by hydrogeologists to simulate the flow of groundwater through aquifers...

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

Free software

Free software, software libre or libre software is software that can be used, studied, and modified without restriction, and which can be copied and redistributed in modified or unmodified form either without restriction, or with restrictions that only ensure that further recipients can also do...

developed, documented and distributed by the USGS. Many commercial products have grown up around it, providing graphical user interface

Graphical user interface

In computing, a graphical user interface is a type of user interface that allows users to interact with electronic devices with images rather than text commands. GUIs can be used in computers, hand-held devices such as MP3 players, portable media players or gaming devices, household appliances and...

s 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

Surface water

Surface water is water collecting on the ground or in a stream, river, lake, wetland, or ocean; it is related to water collecting as groundwater or atmospheric water....

and groundwater

Groundwater

Groundwater is water located beneath the ground surface in soil pore spaces and in the fractures of rock formations. 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...

models and chemical reaction models), because of the simple, well documented nature of MODFLOW.

#### 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; HydrusHYDRUS (software)

Hydrus is a suite of Windows-based modeling software that can be used for analysis of water flow, heat and solute transport in variably saturated porous media . HYDRUS suite of software is supported by an interactive graphics-based interface for data-preprocessing, discretization of the soil...

, a commercial unsaturated flow model; FEFLOW

FEFLOW

FEFLOW is a computer program for simulating groundwater flow, mass transfer and heat transfer in porous media...

, a commercial modeling environment for subsurface flow, solute and heat transport processes; and COMSOL Multiphysics

COMSOL Multiphysics

COMSOL Multiphysics is a finite element analysis, solver and Simulation software / FEA Software package for various physics and engineering applications, especially coupled phenomena, or multiphysics. COMSOL Multiphysics also offers an extensive interface to MATLAB and its toolboxes for a large...

(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

University

A university is an institution of higher education and research, which grants academic degrees in a variety of subjects. A university is an organisation that provides both undergraduate education and postgraduate education...

and laboratory

Laboratory

A laboratory is a facility that provides controlled conditions in which scientific research, experiments, and measurement may be performed. The title of laboratory is also used for certain other facilities where the processes or equipment used are similar to those in scientific laboratories...

environments, where specialized models solve non-standard forms of the flow equation (unsaturated

Vadose zone

The vadose zone, also termed the unsaturated zone, is the portion of Earth between the land surface and the top of the phreatic zone i.e. the position at which the groundwater is at atmospheric pressure . Hence the vadose zone extends from the top of the ground surface to the water table...

flow, density

Density

The mass density or density of a material is defined as its mass per unit volume. The symbol most often used for density is ρ . In some cases , density is also defined as its weight per unit volume; although, this quantity is more properly called specific weight...

dependent flow, coupled heat

Heat transfer

Heat transfer is a discipline of thermal engineering that concerns the exchange of thermal energy from one physical system to another. Heat transfer is classified into various mechanisms, such as heat conduction, convection, thermal radiation, and phase-change transfer...

and groundwater flow, etc.)

#### Application of finite volume models

The finite volume method is a method for representing and evaluating partial differential equations as algebraic equations [LeVeque, 2002; Toro, 1999]. Similar to the finite difference method, values are calculated at discrete places on a meshed geometry. "Finite volume" refers to the small volume surrounding each node point on a mesh. In the finite volume method, volume integrals in a partial differential equation that contain a divergence term are converted to surface integrals, using the divergence theorem. These terms are then evaluated as fluxes at the surfaces of each finite volume. Because the flux entering a given volume is identical to that leaving the adjacent volume, these methods are conservative. Another advantage of the finite volume method is that it is easily formulated to allow for unstructured meshes. The method is used in many computational fluid dynamics packages.**PORFLOW**software package is a comprehensive mathematical model for simulation of Ground Water Flow and Nuclear Waste Management developed by Analytic & Computational Research, Inc., ACRi]ACRi

The

**FEHM**

software package is available free from Los Alamos National Laboratory

FEHM

FEHM is a groundwater model that has been developed in the at Los Alamos National Laboratory over the past 30 years. The executable is available free at the . The capabilities of the code have expanded over the years to include multiphase flow of heat and mass with air, water, and CO2, methane...

Los Alamos National Laboratory

Los Alamos National Laboratory is a United States Department of Energy national laboratory, managed and operated by Los Alamos National Security , located in Los Alamos, New Mexico...

and can be accessed at the FEHM Website. This versatile porous flow simulator includes capabilities to model multiphase, thermal, stress, and multicomponent reactive chemistry. Current work using this code includes simulation of methane hydrate formation, CO

_{2}sequestration, oil shale extraction, migration of both nuclear and chemical contaminants, environmental isotope migration in the unsaturated zone, and karst formation.

#### Other methods

These include mesh-free methods like the Analytic Element MethodAnalytic element method

The analytic element method is a numerical method used for the solution of partial differential equations. It was initially developed by O.D.L. Strack at the University of Minnesota...

(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 yet.

## See also

- Aquifer testAquifer test

s or well tests are common methods used by hydrogeologist to analyze aquifers and wells; - Environmental engineeringEnvironmental engineeringEnvironmental engineering is the application of science and engineering principles to improve the natural environment , to provide healthy water, air, and land for human habitation and for other organisms, and to remediate polluted sites...

and Earth scienceEarth scienceEarth science is an all-embracing term for the sciences related to the planet Earth. It is arguably a special case in planetary science, the Earth being the only known life-bearing planet. There are both reductionist and holistic approaches to Earth sciences...

are broad categories hydrogeology fits into; - FlownetFlownetA flownet is a graphical representation of two-dimensional steady-state groundwater flow through aquifers. Construction of a flownet is often used for solving groundwater flow problems where the geometry makes analytical solutions impractical...

is an analysis tool for steady-state flow; - GroundwaterGroundwater

: general description of issues; - Groundwater energy balanceGroundwater energy balanceThe 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 flow equations based on the energy balance; - Groundwater modelGroundwater modelGroundwater models are computer models of groundwater flow systems, and are used by hydrogeologists. Groundwater models are used to simulate and predict aquifer conditions.-Characteristics:...

: particulars on the solution of groundwater flow equations; - Heat conductionHeat conductionIn heat transfer, conduction is a mode of transfer of energy within and between bodies of matter, due to a temperature gradient. Conduction means collisional and diffusive transfer of kinetic energy of particles of ponderable matter . Conduction takes place in all forms of ponderable matter, viz....

is a field which solves the same equation as groundwater flow; - Hydraulic conductivityHydraulic conductivityHydraulic conductivity, symbolically represented as K, is a property of vascular plants, soil or rock, that describes the ease with which water can move through pore spaces or fractures. It depends on the intrinsic permeability of the material and on the degree of saturation...

: general information on aquifer permeability - Isotope hydrologyIsotope hydrologyIsotope hydrology is a field of hydrology that uses isotopic dating to estimate the age and origins of water and of movement within the hydrologic cycle. The techniques are used for water-use policy, mapping aquifers, conserving water supplies, and controlling pollution...

is often used to understand sources and travel times in groundwater systems; - List of publications in geology#Hydrogeology : important publications;
- SahysModSahysModSahysMod is a computer program for the prediction of the salinity of soil moisture, groundwater and drainage water, the depth of the watertable, and the drain discharge in irrigated agricultural lands, using different hydrogeologic and aquifer conditions, varying water management options, including...

is a spatial agro-hydro-salinity model with groundwater flow in a polygonal network; - Water cycleWater cycleThe water cycle, also known as the hydrologic cycle or H2O cycle, describes the continuous movement of water on, above and below the surface of the Earth. Water can change states among liquid, vapor, and solid at various places in the water cycle...

, hydrosphereHydrosphereA hydrosphere in physical geography describes the combined mass of water found on, under, and over the surface of a planet....

and water resourcesWater resourcesWater resources are sources of water that are useful or potentially useful. Uses of water include agricultural, industrial, household, recreational and environmental activities. Virtually all of these human uses require fresh water....

are larger concepts which hydrogeology is a part of; - Water wellWater wellA water well is an excavation or structure created in the ground by digging, driving, boring or drilling to access groundwater in underground aquifers. The well water is drawn by an electric submersible pump, a trash pump, a vertical turbine pump, a handpump or a mechanical pump...

, spring (hydrosphere)Spring (hydrosphere)A spring—also known as a rising or resurgence—is a component of the hydrosphere. Specifically, it is any natural situation where water flows to the surface of the earth from underground...

, and municipal water system are subjects the hydrogeologist is concerned about; - Hydrology (agriculture)Hydrology (agriculture)Agricultural hydrology is the study of water balance components intervening in agricultural water management, notably in irrigation and drainage.-Water balance components:...

### 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 Good, accessible overview of hydrogeological processes.
- 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
- Fetter, C.W. Contaminant Hydrogeology Second Edition, Prentice Hall. ISBN 0137512155
- Fetter, C.W. Applied Hydrogeology Fourth Edition, Prentice Hall. ISBN 0130882399

### 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
- Wang H. F., Theory of Linear Poroelasticity with Applications to Geomechanics and Hydrogeology, Princeton Press, (2000). Good introduction to fundamentals of poroelasticity.
- Waltham T., Foundations of Engineering Geology, 2nd Edition, Taylor & Francis, (2001). General introduction.
- Yang X. S., Mathematical Modelling for Earth Sciences, Dunedin Academic Press, (2008). Good introduction to mathematical and numerical techniques in flow in porous media.
- 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 methodAnalytic element methodThe analytic element method is a numerical method used for the solution of partial differential equations. It was initially developed by O.D.L. Strack at the University of Minnesota...

(AEM). ISBN 0-12-316550-4 - Harr, Milton E., 1962. Groundwater and seepage, Dover. — a more civil engineeringCivil engineeringCivil engineering is a professional engineering discipline that deals with the design, construction, and maintenance of the physical and naturally built environment, including works like roads, bridges, canals, dams, and buildings...

view on groundwater; includes a great deal on flownetFlownetA flownet is a graphical representation of two-dimensional steady-state groundwater flow through aquifers. Construction of a flownet is often used for solving groundwater flow problems where the geometry makes analytical solutions impractical...

s. ISBN 0-486-66881-9 - Kovacs, Gyorgy, 1981. Seepage Hydaulics, Developments in Water Science; 10. Elsevier. - Conformal mapConformal mapIn mathematics, a conformal map is a function which preserves angles. In the most common case the function is between domains in the complex plane.More formally, a map,...

ping well explained. ISBN 0-444-99755-5, ISBN 0-444-99755-5 (series) - 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

## External links and sources

- UK Groundwater Forum — Groundwater in the UK
- Centre for Groundwater Studies — Groundwater Education and Research.
- EPA drinking water standards — the maximum contaminant levels (mcl) for dissolved species in US drinking water.
- US Geological Survey water resources homepage — a good place to find free data (for both US surface water and groundwater) and free groundwater modeling software like MODFLOWMODFLOWMODFLOW is the U.S. Geological Survey modular finite-difference flow model, which is a computer code that solves the groundwater flow equation. The program is used by hydrogeologists to simulate the flow of groundwater through aquifers...

. - US Geological Survey TWRI index — a series of instructional manuals covering common procedures in hydrogeology. They are freely available online as PDF files.
- International Ground Water Modeling Center (IGWMC) — an educational repository of groundwater modeling software which offers support for most software, some of which is free.
- The Hydrogeologist Time Capsule — a video collection of interviews of eminent hydrogeologists who have made a material difference to the profession.
- IGRAC International Groundwater Resources Assessment Centre
- US Army Geospatial Center — For information on OCONUS surface water and groundwater.