Applied Mathematics

Modeling and Simulation

Can a mathematical model be too complex?

Yes, mathematical models can be too complex for a number of reasons. For example, if we wanted to model the development of a hurricane, we would take data from a forming storm—water vapor, pressure, temperature, and so on—and incorporate it into our model. In this way, we would try to develop as close to a white-box model of the hurricane system as possible.

But in reality a collection of such a huge amount of data—not to mention the computational cost—would effectively inhibit the use of such a weather model. There is also uncertainty because the development of a hurricane is an overly complex system, mainly because each separate part of a hurricane and its development causes some amount of variance in the model. For example, not only would we have to know about the details of the hurricane’s development, but other factors would come into play, such as the ocean-interaction variables that contribute to the hurricane, variability of solar radiation, and even how periodic events such as El Niño—a periodic warming of the waters off the South America coast—affect the hurricane. Thus, meteorologists usually use some approximations to make the mathematical model more manageable, which is also why we still can’t predict where and how much rain, wind, and tornadoes will occur during a hurricane.


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