# Groundwater model

**Groundwater models** are conceptual, analytical or numerical tools that provide the necessary information for the quantitative and qualitative management of an aquifer ( aquifer ).

## General

A groundwater model enables the simulation of various variables such as

- the flow field in the unsaturated or saturated soil area,
- the diffusive , dispersive and convective transport of dissolved water constituents (material transport model) and the
- Heat propagation .

## Mathematical model

A mathematical groundwater flow model essentially consists of a combination of the Darcy equation with a balance relationship , as it is e.g. B. represents the Laplace equation . A mass transport model is based on the calculated flow field and uses the advection dispersion equation , a combination of the dispersion approach and a balance relationship to calculate the dispersion of the substances in the water. Alternatively, the heat propagation on the flow field can be calculated using the heat conduction equation.

The previous calculation of the flow field is therefore essential for the use of a mass transport or heat dissipation model.

## Numerical model

In addition to analytical approaches such as the flow network , which usually start from very simple (one-dimensional or two-dimensional) model concepts with simple geometric boundary conditions and homogeneous relationships in the model area, there are numerical models for solving the equations of the mathematical model.

For practical applications with complex boundary conditions, mathematical models can only be solved approximately, but allow the simulation of heterogeneous and anisotropic, three-dimensional systems.

The solution with a numerical model takes place either with so-called Euler's approaches such as the finite difference method , finite volume method or the finite element method, or by Lagrangian approaches such as *particle tracking* and the *random walk method* .

The groundwater model takes into account the geological and hydrogeological knowledge of the model area ( concept model or hydrogeological model ) or the specifications of an experimental setup. Part of numerical groundwater modeling is the calibration of the model and the implementation of a sensitivity analysis .

## calibration

The calibration represents the verification of the result calculated by the model with the given (in practice: the groundwater levels, substance concentrations or temperatures measured in the field) results as well as the adaptation of the model properties to minimize the deviations. The difference between the measured and the calculated results as well the groundwater balance of the model, which should be as balanced as possible, is a measure of the quality of the calibration, which is stationary, i.e. H. time-independent or unsteady, d. H. time-dependent, can take place.

## Stochastic Analysis

Since the (hydro) geological findings on which the model is based (e.g. the hydraulic permeability coefficient ) can often not be quantified unambiguously and above all not across the board through field tests, it is advisable to vary these parameters within the framework of a sensitivity analysis and thus their influence on the model result to estimate.

## application

On the basis of the calibrated groundwater model, given conditions and model concepts can be checked using the calibrated parameter set or, through the use of predicted, also time-dependent boundary conditions (e.g. groundwater recharge ), future developments and the effects of planned anthropogenic interventions can be simulated; historical conditions can also be reconstructed (e.g. E.g. when searching for sources of pollution, tracing migration routes).

## literature

- Kinzelbach, W. & Rausch, R. (1995):
*Groundwater modeling - an introduction with exercises.*284 p., 223 fig., 15 tab., 2 diskettes; Berlin, Stuttgart (Borntraeger), ISBN 3-443-01032-6 . - Zipfel Klaus, Battermann Gerhard (1997):
*Main thing groundwater - groundwater models, possibilities, experiences, perspectives.*Ed. Technologieberatung Groundwater and Environment (TGU). Koblenz, OCLC 177343255 . - Chiang, WH, Kinzelbach, W., Rausch, R. (1998):
*Aquifer simulation model for Windows [media combination]: 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 . - Rausch, R., Schäfer, W., Wagner, C. (2002):
*Introduction to transport modeling in groundwater: with 9 tables in the text.*193 p .; Berlin, Stuttgart (Borntraeger), ISBN 3-443-01048-2 . - Rausch, R., Schäfer, W., Therrien, R., Wagner, C. (2005):
*Solute transport modeling: an introduction to models and solution strategies; with 11 tables.*205 p .; Berlin, Stuttgart (Borntraeger), ISBN 3-443-01055-5 . - Diersch, H.-J. (2014): FEFLOW -
*Finite Element Modeling of Flow, Mass and Heat Transport in Porous and Fractured Media*. 996 p .; Heidelberg (Springer), ISBN 978-3-642-38738-8 .