The simplest definition of a model is that a model is a simplification of reality. As such
it also needs to be an abstraction of reality, because in order to simplify we need to
aggregate and describe the system in more abstract, general terms.
Einstein is attributed the saying that “The best explanation is as simple as possible, but
no simpler”. The best model, indeed, should balance between realism and simplicity.
Models may be used to gain a better understanding of the system that they represent, i.e. the structure of real-world systems and the way they work. Different elements of the model and their interrelations may be manipulated by changing variables, attributes, equations and parameters. As such, it is possible to experiment using a model instead of with the real-world system (even if that would at all be possible, simulating flooding under real-world conditions is usually not possible or feasible). These kind of models are used abundantly in science.
Models can also be used to predict the future behaviour of a system, with or without interventions. It is important is to ensure that the model represents future behaviour accurately enough (usually based on knowledge about current behaviour or historical trends). Simple extrapolations may not always be desirable, as results obtained from the past are no guarantee for future behaviour!
Scenarios based on simulations may be used to sketch possible future developments. A possible future is constructed based on a well-described initial situation. Over time, several changes occur or are introduced, thereby changing the predictions. Scenarios are particularly useful when used in comparison with other scenarios (starting from the same initial situation). Scenario models and model predictions are typically used in policy studies.
In many applications it is not sufficient to only know what is happening (qualitative). Usually we also need to know to what extent something is happening (quantitative). Such quantification is common in, for example, engineering, finance and economics, environmental sciences and physical geography. Quantitative measurements can be obtained by direct measurement (from prototypes, scale models or analogue models) or by calculation. In the latter case, scientists need quantitative information to answer questions such as “What traffic volumes are to be expected on this new bridge?” or “How large is this deforested area?” In the first question, the object or system has not yet been realized if the bridge is not already built and operating, so only a predictive model can help. If such a model is a mathematical model, then the different variables (quantities) that are considered to be important and their interrelationships are expressed in equations (formulas), after which mathematical operations can be executed (to predict, to control, to optimize). In the second question, the deforestation has already taken place and direct measurement is possible (e.g. through a NDVI).
An example of a model we often deal with is a map. When your friend explains how
to get to his house, he draws a scheme of roads and streets, in fact building a model for
you to better understand the directions. His model will surely lack a lot of detail about
the landscape that you may see on your way, but if it is a good model it will contain
all the information you need to get to his house. If it is a bad model you lose your way
and do not reach his house without additional help. For more sophisticated situations
or to examine some of the “what if” questions that typify many development-related
problems in which various alternative interventions might be investigated, for example,
we can use Geographic Information Systems with spatial analysis and scenario
building tools in which dynamics are becoming increasingly important.
Note that the models we build are defined by the purposes that they are to serve. If
you only want your friend to get to your house, you will draw a very simple diagram,
avoiding the description of various places of interest on her way. However, if you
want her to take notice of a particular location, you might also show her a photograph,
which is also a model. Its purpose is very different and so are the implementation, the
scale, or the details.