Models in Irrigation andWater Management - Practices of Irrigation and On-farm Water Management - page 389

10.2.4 Basic Considerations in Model Development
and Formulation of Model Structure

10.2.4.1 Basic Considerations

Successful model development always begins with a question or hypothesis, and
the model complexity and scale should match those of the question. At that point, a
decision must be made about the type of mathematical model the researcher will
develop. For all cases, developing a model may not necessary. Simply develop-
ing a clear conceptual model can answer to a question. However, many complex
problems (having complex interactions among different processes) cannot be solved
with conceptual model alone. The process of developing a mathematical model can
be extremely helpful in clarifying the relevant processes. It directs or forces the
modeler to think clearly about the important processes and relationships that govern
important features of the problem.
The key features that should be considered during development of any model are:

• simplifying assumptions must be made;

• boundary conditions or initial conditions must be identified;

• the range of applicability of the model should be understood.

10.2.4.2 Formulation of Model

Modeling process begins with a definition of goals. The goal may be find from the
answer of the question - What will be the model be used for - to solve a specific
problem, to learn more about the system, to evaluate alternative management strate-
gies, etc? The answer will help in determining the structure of the model, the data
required, and the expected output.
The next step is a conceptualization of the prototype, including selection of scales
of time and space, dimensionality, and discretization. This is followed by formula-
tion as a set of differential equations, statistical properties, empirical expressions, or
combinations of these. Computational representation of model formulation implic-
itly requires selection of a method of solution. For illustration, a conceptualization
of a simple irrigation scheduling model (conceptual model) is depicted in Fig. 10.2 .
At this stage, the model is tested functionally under hypothetical but realistic
boundary conditions using best estimates of uncertain parameters in the governing
equations. Calibration of the model requires adjustment of parameters for a given
set of boundary conditions and assumed values of key state variables. The modeler
will decide whether agreement between model and prototype is acceptable or not.
Once the model is calibrated with a specific set of parameter values, it may be
tested again against another set of prototype data in a process of verification to ascer-
tain whether the degree of conformity with the prototype under the new conditions
is consistent with that of calibration. If the model fails this test, recalibration may
be necessary. Calibration/verification is sometimes considered a single process in
model development, termed as validation .