Simulation models are computer programs that represent actual systems. We use them to predict how the system would behave under different conditions. When I worked as an industrial engineer, we often used simulation models to help design and plan manufacturing processes. For example, suppose we had an assembly line of 20 workstations that made washing machine parts. We would "describe" the assembly line using data in a computer simulation program. Then we would enter information about each workstation—how long it took, number of defects (say, 1 out of 10 parts failed), how often the workstation needed to be shut down for repair or maintenance, etc. Then, we would run the model to see what would happen if we made changes. What if we added a workstation? or removed one? Would our output change? What if we retooled or retrained and quality improved so that we only had 1 in 50 defects? What if the number of orders we got suddenly doubled, how far behind would we get? We would use the output of these models to help us make business and management decisions. Each set of what if conditions is called a scenario.
"Mathematical models are used not only in the natural sciences and engineering disciplines (such as physics, biology, earth science, meteorology, and engineering) but also in the social sciences (such as economics, psychology, sociology and political science); physicists, engineers, computer scientists, and economists use mathematical models most extensively." (Wikipedia: Mathematical Model [2]) (I don't usually use Wikipedia as a source, but in this case the information is general, well stated, and widely accepted.)
We model many, many things—business processes, financial systems, whole economies, Internet traffic, network traffic, air traffic, automobile traffic, human behavior, cellular behavior...and so on! The Weather Channel will often show multiple possible paths for an incoming storm and the reporter will refer to different "models." These are weather models. Each model is based on a set of equations and data representing the weather system. Given a set of conditions (a scenario), the model predicts what the weather will do.
In the previous section, I used weather models as an example of using models to simulate different "what-if" scenarios. In the following sections we are going to talk about using models to study climate change. Before going there, let's pause and consider the important differences between "weather" and "climate." NASA has devoted an entire page to "What's the Difference between Weather and Climate?" [3] If you have time, check it out. Here are key excerpts:
The IPCC uses climate simulation models to predict future climate change and its impact. The IPCC Working Group I describes a climate model as,
A numerical representation of the climate system based on the physical, chemical and biological properties of its components, their interactions and feedback processes, and accounting for some of its known properties. The climate system can be represented by models of varying complexity, that is, for any one component or combination of components a spectrum or hierarchy of models can be identified, differing in such aspects as the number of spatial dimensions, the extent to which physical, chemical or biological processes are explicitly represented or the level at which empirical parameterizations are involved. Coupled Atmosphere–Ocean General Circulation Models (AOGCMs) provide a representation of the climate system that is near or at the most comprehensive end of the spectrum currently available. There is an evolution towards more complex models with interactive chemistry and biology. Climate models are applied as a research tool to study and simulate the climate, and for operational purposes, including monthly, seasonal, and interannual climate predictions. (from Annex III: Glossary)
FAQ 9.1 Are Climate Models Getting Better, and How Would We Know? [4] (AR5 WGI Chapter 9 Evaluation of Climate Models)
Links
[1] http://www.isgtw.org/feature/forecasting-el-nino-half-century-ahead
[2] http://en.wikipedia.org/wiki/Mathematical_model
[3] http://www.nasa.gov/mission_pages/noaa-n/climate/climate_weather.html
[4] https://www.e-education.psu.edu/egee401/sites/www.e-education.psu.edu.egee401/files/AR5%20WG1%20FAQ%209%201%20Are%20climate%20models%20getting%20better%20and%20who%20would%20we%20know.pdf