Model is any device or constructs that represent an approximation of a field situation or real world situation . Mathematical or numerical model is solving an equation or set of equations that describes the behavior of the real-world system (or at least some components of it). Most of the principal governing equations for groundwater systems are differential equation, which are distinguished by the presence of at least one differential in the equation.
The solution to a differential equation (at least in cases where the dependent variable is contained in a differential) is an algebraic equation. Equation 1 requires transforming into an algebraic equation. The algebraic equation can then be used to compute the value of hydraulic head at a specific location and time. The form of the algebraic equations (solutions) can vary greatly depending on the boundary and initial conditions. Solutions to differential equations that can be found by methods of integration are called “analytical solutions”. These analytical solutions are exact for the problem domain for which they are solved. Many differential equations cannot be solved analytically for certain problem domain geometries or boundary or initial conditions. Then it is necessary to find a “numerical solution” to the differential equation that is approximate for the problem domain for which it is solved. There are lots of numerical solution techniques for differential equations which are finite difference method, finite element method, control volume method.
Purpose of Numerical Model
Models are essential in performing complex analyses and in making informed predictions. Worst case scenario, best case scenario of a real-world scenario. Any environmental policy making needs the help of numerical model to find worst case scenario of hazardous environmental activity. For example, dumping nuclear waste in fractured low permeable rock can be harmful to surrounding geology. Numerical model can predict the best case scenario and worst case scenario.
Controversy of Numerical Model
There is controversy regarding the numerical model. Few says, Numerical models are worthless because they require too many data and therefore are too expensive to assemble and run. Furthermore, they can never be proved to be correct and suffer from a lack of scientific certainty. They can’t be trusted because you can make a model do anything you want. But, models are becoming more and more accepted as a mainstream and reliable tool for the investigation if models are correctly used and adequately documented though models </ref name = Anderson and Woessner/ >. Nowadays, availability of model calibration, verification tools make models more reliable to believe.
- Anderson, M.P. and Woessner, W.W. (1992). " Applied Groundwater Modeling: Simulation of Flow and Advective Transport " p. 373. Elsevier Science, ISBN 9780080886947