Groundwater models are

computer models Computer simulation is the running of a mathematical model on a computer, the model being designed to represent the behaviour of, or the outcome of, a real-world or physical system. The reliability of some mathematical models can be determin ...

groundwater Groundwater is the water present beneath Earth's surface in rock and Pore space in soil, soil pore spaces and in the fractures of stratum, rock formations. About 30 percent of all readily available fresh water in the world is groundwater. A unit ...

flow systems, and are used by

hydrologist Hydrology () is the scientific study of the movement, distribution, and management of water on Earth and other planets, including the water cycle, water resources, and drainage basin sustainability. A practitioner of hydrology is called a hydro ...

s and hydrogeologists. Groundwater models are used to simulate and predict

aquifer An aquifer is an underground layer of water-bearing material, consisting of permeability (Earth sciences), permeable or fractured rock, or of unconsolidated materials (gravel, sand, or silt). Aquifers vary greatly in their characteristics. The s ...

conditions.

Characteristics

An unambiguous definition of "groundwater model" is difficult to give, but there are many common characteristics. A

model may be a

scale model A scale model is a physical model that is geometrically similar to an object (known as the ''prototype''). Scale models are generally smaller than large prototypes such as vehicles, buildings, or people; but may be larger than small protot ...

or an electric model of a groundwater situation or

. Groundwater models are used to represent the natural groundwater flow in the environment. Some groundwater models include (chemical) quality aspects of the groundwater. Such groundwater models try to predict the fate and movement of the chemical in natural, urban or hypothetical scenario. Groundwater models may be used to predict the effects of hydrological changes (like groundwater pumping or irrigation developments) on the behavior of the aquifer and are often named groundwater simulation models. Groundwater models are used in various water management plans for urban areas. As the computations in

mathematical Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...

groundwater models are based on groundwater flow equations, which are differential equations that can often be solved only by approximate methods using a

numerical analysis Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic computation, symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of ...

, these models are also called ''mathematical, numerical, or computational groundwater models''. The mathematical or the numerical models are usually based on the real physics the groundwater flow follows. These mathematical equations are solved using numerical codes such as MODFLOW, ParFlow, HydroGeoSphere
OpenGeoSys
etc. Various types of ''numerical solutions'' like the

finite difference method In numerical analysis, finite-difference methods (FDM) are a class of numerical techniques for solving differential equations by approximating Derivative, derivatives with Finite difference approximation, finite differences. Both the spatial doma ...

and the

finite element method Finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical problem areas of interest include the traditional fields of structural analysis, heat tran ...

are discussed in the article on "

Hydrogeology Hydrogeology (''hydro-'' meaning water, and ''-geology'' meaning the study of the Earth) is the area of geology that deals with the distribution and movement of groundwater in the soil and rock (geology), rocks of the Earth's crust (ge ...

Inputs

For the calculations one needs inputs like: *hydrological inputs, *operational inputs, *external conditions:

initial In a written or published work, an initial is a letter at the beginning of a word, a chapter (books), chapter, or a paragraph that is larger than the rest of the text. The word is ultimately derived from the Latin ''initiālis'', which means '' ...

and boundary conditions, *(hydraulic) parameters. The model may have chemical components like water salinity,

soil salinity Soil salinity is the salt (chemistry), salt content in the soil; the process of increasing the salt content is known as salinization (also called salination in American and British English spelling differences, American English). Salts occur nat ...

and other quality indicators of water and soil, for which inputs may also be needed.

Hydrological inputs

The primary coupling between groundwater and hydrological inputs is the

unsaturated zone The vadose zone (from the Latin word for "shallow"), also termed the unsaturated zone, is the part of Earth between the land surface and the top of the phreatic zone, the position at which the groundwater (the water in the soil's pores) is at ...

vadose zone The vadose zone (from the Latin word for "shallow"), also termed the unsaturated zone, is the part of Earth between the land surface and the top of the phreatic zone, the position at which the groundwater (the water in the soil's pores) is at ...

. The soil acts to partition hydrological inputs such as rainfall or snowmelt into

surface runoff Surface runoff (also known as overland flow or terrestrial runoff) is the unconfined flow of water over the ground surface, in contrast to ''channel runoff'' (or ''stream flow''). It occurs when excess rainwater, stormwater, meltwater, or other ...

soil moisture Soil moisture is the water content of the soil. It can be expressed in terms of volume or weight. Soil moisture measurement can be based on ''in situ'' probes (e.g., capacitance probes, neutron probes) or remote sensing methods. Water that enters ...

evapotranspiration Evapotranspiration (ET) refers to the combined processes which move water from the Earth's surface (open water and ice surfaces, bare soil and vegetation) into the Atmosphere of Earth, atmosphere. It covers both water evaporation (movement of w ...

and

groundwater recharge Groundwater recharge or deep drainage or deep percolation is a hydrologic process, where water moves downward from surface water to groundwater. Recharge is the primary method through which water enters an aquifer. This process usually occurs in ...

. Flows through the

that couple surface water to

and

can be upward or downward, depending upon the gradient of

hydraulic head Hydraulic head or piezometric head is a measurement related to liquid pressure (normalized by specific weight) and the liquid elevation above a vertical datum., 410 pages. See pp. 43–44., 650 pages. See p. 22, eq.3.2a. It is usually meas ...

in the soil, can be modeled using the numerical solution of Richards' equation partial differential equation, or the ordinary differential equation Finite Water-Content method as validated for modeling

and

interactions.

Operational inputs

The operational inputs concern human interferences with the ''water management'' like

irrigation Irrigation (also referred to as watering of plants) is the practice of applying controlled amounts of water to land to help grow crops, landscape plants, and lawns. Irrigation has been a key aspect of agriculture for over 5,000 years and has bee ...

drainage Drainage is the natural or artificial removal of a surface's water and sub-surface water from an area with excess water. The internal drainage of most agricultural soils can prevent severe waterlogging (anaerobic conditions that harm root gro ...

, pumping from wells, watertable control, and the operation of retention or infiltration basins, which are often of an hydrological nature.
These inputs may also vary in time and space. Many groundwater models are made for the purpose of assessing the effects

hydraulic engineering Hydraulic engineering as a sub-discipline of civil engineering is concerned with the flow and conveyance of fluids, principally water and sewage. One feature of these systems is the extensive use of gravity as the motive force to cause the move ...

measures.

Boundary and initial conditions

''Boundary conditions'' can be related to levels of the

water table The water table is the upper surface of the phreatic zone or zone of saturation. The zone of saturation is where the pores and fractures of the ground are saturated with groundwater, which may be fresh, saline, or brackish, depending on the loc ...

, artesian pressures, and

along the boundaries of the model on the one hand (the ''head conditions''), or to groundwater inflows and outflows along the boundaries of the model on the other hand (the ''flow conditions''). This may also include quality aspects of the water like salinity. The ''initial conditions'' refer to initial values of elements that may increase or decrease in the course of the time ''inside'' the model domain and they cover largely the same phenomena as the boundary conditions do. The initial and boundary conditions may vary from place to place. The boundary conditions may be kept either constant or be made variable in time.

Parameters

The parameters usually concern the

geometry Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician w ...

of and

distance Distance is a numerical or occasionally qualitative measurement of how far apart objects, points, people, or ideas are. In physics or everyday usage, distance may refer to a physical length or an estimation based on other criteria (e.g. "two co ...

s in the domain to be modelled and those physical properties of the aquifer that are more or less constant with time but that may be variable in space. Important parameters are the

topography Topography is the study of the forms and features of land surfaces. The topography of an area may refer to the landforms and features themselves, or a description or depiction in maps. Topography is a field of geoscience and planetary sci ...

, thicknesses of soil / rock layers and their horizontal/vertical

hydraulic conductivity In science and engineering, hydraulic conductivity (, in SI units of meters per second), is a property of porous materials, soils and Rock (geology), rocks, that describes the ease with which a fluid (usually water) can move through the porosity, ...

(permeability for water), aquifer transmissivity and resistance, aquifer porosity and storage coefficient, as well as the capillarity of the unsaturated zone. For more details see the article on

hydrogeology Hydrogeology (''hydro-'' meaning water, and ''-geology'' meaning the study of the Earth) is the area of geology that deals with the distribution and movement of groundwater in the soil and rock (geology), rocks of the Earth's crust (ge ...

. Some parameters may be influenced by changes in the groundwater situation, like the thickness of a soil layer that may reduce when the water table drops and/the hydraulic pressure is reduced. This phenomenon is called

subsidence Subsidence is a general term for downward vertical movement of the Earth's surface, which can be caused by both natural processes and human activities. Subsidence involves little or no horizontal movement, which distinguishes it from slope mov ...

. The thickness, in this case, is variable in time and not a parameter proper.

Applicability

The applicability of a groundwater model to a real situation depends on the accuracy of the input data and the parameters. Determination of these requires considerable study, like collection of hydrological data (

rainfall Rain is a form of precipitation where water droplets that have condensed from atmospheric water vapor fall under gravity. Rain is a major component of the water cycle and is responsible for depositing most of the fresh water on the Earth. ...

) and determination of the parameters mentioned before including pumping tests. As many parameters are quite variable in space, expert judgment is needed to arrive at representative values. The models can also be used for the if-then analysis: if the value of a parameter is A, then what is the result, and if the value of the parameter is B instead, what is the influence? This analysis may be sufficient to obtain a rough impression of the groundwater behavior, but it can also serve to do a ''sensitivity analysis'' to answer the question: which factors have a great influence and which have less influence. With such information one may direct the efforts of investigation more to the influential factors. When sufficient data have been assembled, it is possible to determine some of missing information by calibration. This implies that one assumes a range of values for the unknown or doubtful value of a certain parameter and one runs the model repeatedly while comparing results with known corresponding data. For example, if

salinity Salinity () is the saltiness or amount of salt (chemistry), salt dissolved in a body of water, called saline water (see also soil salinity). It is usually measured in g/L or g/kg (grams of salt per liter/kilogram of water; the latter is dimensio ...

figures of the groundwater are available and the value of

is uncertain, one assumes a range of conductivities and the selects that value of conductivity as "true" that yields salinity results close to the observed values, meaning that the groundwater flow as governed by the hydraulic conductivity is in agreement with the salinity conditions. This procedure is similar to the measurement of the flow in a river or canal by letting very saline water of a known salt concentration drip into the channel and measuring the resulting salt concentration downstream.

Dimensions

Groundwater models can be one-dimensional, two-dimensional, three-dimensional and semi-three-dimensional. Two and three-dimensional models can take into account the

anisotropy Anisotropy () is the structural property of non-uniformity in different directions, as opposed to isotropy. An anisotropic object or pattern has properties that differ according to direction of measurement. For example, many materials exhibit ve ...

of the aquifer with respect to the

, i.e. this property may vary in different directions.

One-, two- and three-dimensional

#One-dimensional models can be used for the vertical flow in a system of parallel horizontal layers. #

Two-dimensional A two-dimensional space is a mathematical space with two dimensions, meaning points have two degrees of freedom: their locations can be locally described with two coordinates or they can move in two independent directions. Common two-dimension ...

models apply to a vertical plane while it is assumed that the groundwater conditions repeat themselves in other parallel vertical planes (Fig. 4). Spacing equations of subsurface drains and the groundwater energy balance applied to drainage equations are examples of two-dimensional groundwater models. #

Three-dimensional In geometry, a three-dimensional space (3D space, 3-space or, rarely, tri-dimensional space) is a mathematical space in which three values (''coordinates'') are required to determine the position (geometry), position of a point (geometry), poi ...

models like Modflow require

discretization In applied mathematics, discretization is the process of transferring continuous functions, models, variables, and equations into discrete counterparts. This process is usually carried out as a first step toward making them suitable for numeri ...

of the entire flow domain. To that end the flow region must be subdivided into smaller elements (or cells), in both horizontal and vertical sense. Within each cell the parameters are maintained constant, but they may vary between the cells (Fig. 5). Using numerical solutions of groundwater flow equations, the flow of groundwater may be found as horizontal, vertical and, more often, as intermediate.

Semi three-dimensional

In semi 3-dimensional models the horizontal flow is described by 2-dimensional flow equations (i. e. in horizontal x and y direction). Vertical flows (in z-direction) are described (a) with a 1-dimensional flow equation, or (b) derived from a

water balance The law of water balance states that the inflows to any water system or area is equal to its outflows plus change in storage during a time interval. In hydrology, a water balance equation can be used to describe the flow of water in and out of ...

of horizontal flows converting the excess of horizontally incoming over the horizontally outgoing groundwater into vertical flow under the assumption that water is

incompressible Incompressible may refer to: * Incompressible flow, in fluid mechanics * incompressible vector field, in mathematics * Incompressible surface, in mathematics * Incompressible string, in computing {{Disambig ...

. There are two classes of semi 3-dimensional models: *''Continuous models'' or ''radial models'' consisting of 2 dimensional submodels in vertical radial planes intersecting each other in one single axis. The flow pattern is repeated in each vertical plane fanning out from the central axis. *''Discretized models'' or ''prismatic models'' consisting of submodels formed by vertical blocks or prisms for the horizontal flow combined with one or more methods of superposition of the vertical flow.

Continuous radial model

An example of a non-discretized radial model is the description of groundwater flow moving radially towards a deep well in a network of wells from which water is abstracted. The radial flow passes through a vertical, cylindrical, cross-section representing the hydraulic equipotential of which the

surface A surface, as the term is most generally used, is the outermost or uppermost layer of a physical object or space. It is the portion or region of the object that can first be perceived by an observer using the senses of sight and touch, and is ...

diminishes in the direction of the axis of intersection of the radial planes where the well is located. Garmsar

Prismatically discretized model

Prismatically discretized models like SahysModILRI, 1995. ''SahysMod: Spatial Agro-Hydro-Salinity Model. Description of Principles, User Manual, and Case Studies''. International Institute for Land Reclamation and Improvement (ILRI), Wageningen, Netherlands. On line

/ref> have a grid over the land surface only. The 2-dimensional grid network consists of triangles, squares, rectangles or

polygons In geometry, a polygon () is a plane figure made up of line segments connected to form a closed polygonal chain. The segments of a closed polygonal chain are called its '' edges'' or ''sides''. The points where two edges meet are the polygon' ...

. Hence, the flow domain is subdivided into vertical blocks or prisms. The prisms can be discretized into ''horizontal'' layers with different characteristics that may also vary between the prisms. The groundwater flow between neighboring prisms is calculated using 2-dimensional horizontal groundwater flow equations. Vertical flows are found by applying one-dimensional flow equations in a vertical sense, or they can be derived from the water balance: excess of horizontal inflow over horizontal outflow (or vice versa) is translated into vertical flow, as demonstrated in the article

Hydrology (agriculture) Agricultural hydrology is the study of water balance components intervening in farm water, agricultural water management, especially in irrigation and drainage. Water balance components The water balance components can be grouped into componen ...

. In semi 3-dimensional models, intermediate flow between horizontal and vertical is not modelled like in truly 3-dimensional models. Yet, like the truly 3-dimensional models, such models do permit the introduction of horizontal and vertical subsurface drainage systems. Semiconfined aquifers with a slowly permeable layer overlying the aquifer (the

aquitard An aquifer is an underground layer of water-bearing material, consisting of permeability (Earth sciences), permeable or fractured rock, or of unconsolidated materials (gravel, sand, or silt). Aquifers vary greatly in their characteristics. The s ...

) can be included in the model by simulating vertical flow through it under influence of an overpressure in the aquifer proper relative to the level of the watertable inside or above the aquitard.

Groundwater modeling software and references

* Analytic Element Method * FEFLOW
PORFLOW
* SVFlux * FEHM * HydroGeoSphere * Integrated Water Flow Model
MicroFEM
* MODFLOW ** GMS ** Visual MODFLOW ** Processing Modflow
OpenGeoSys
* SahysMod, Spatial agro-hydro-salinity-aquifer model, online

US Geological Survey Water Resources Ground Water Software

MARTHE from the French Geological Survey (BRGM)
* ZOOMQ3D

Footnotes

{{DEFAULTSORT:Groundwater Model Scientific simulation software Hydrogeology Hydrology models