Models in Irrigation andWater Management - Practices of Irrigation and On-farm Water Management - page 388

10.2.3.5 Model Validation
Verification/validation : The process of determining that a model implementation
accurately represents the developer's conceptual description of the model and the
solution to the model.
10.2.3.6 Confidence and Uncertainty
Confidence : Probability that a numerical estimate will lie within a specified range.
Uncertainty : A potential deficiency in any phase or activity of the modeling or
experimentation process that is due to inherent variability or lack of knowledge.
10.2.3.7 Implicit Vs Explicit Scheme/Method, and Stability Issue
Numerical solution schemes are often referred to as being explicit or implicit. When
a direct computation of the dependent variables can be made in terms of known
quantities, the computation is said to be explicit. One can compute values on new
level (time or space) by explicit formula.
When the dependent variables are defined by coupled sets of equations, and either
a matrix or iterative technique is needed to obtain the solution, the numerical method
is said to be implicit. To find a value on new level, one must solve the linear system
of equations.
The limitation of an explicit scheme is that there is a certain stability criterion
associated with it, so that the size of the time steps can not exceed a certain value.
However, the use of an explicit scheme is justified by the fact that it saves a large
amount of computer memory which would be required by a matrix solver used in
an implicit scheme.
10.2.3.8 Finite Element and Finite Difference Scheme/Method
Finite Element Method
The finite element method is a method through which any continuous function
can be approximated by a discrete model, which consists of a set of values of the
given function at a finite number of pre-selected points in its domain, together with
piecewise approximation of the function over a finite number of connected disjunct
sub-domains. These sub-domains are called finite elements and are determined by
the pre-selected points. The pre-selected points are called nodal points or nodes.
Finite Difference Method
Finite difference methods are numerical methods for approximating the solutions to
differential equations using finite different scheme. It consists of replacing (trans-
forming) the partial derivative expression with approximately equivalent difference
quotients (equations) over a small interval. That is, it transforms the continuous
domain of the state variables by a network or mesh of discrete points.