2.1 Numerical mathematical modeling
When the dynamics of a system are well known and one can formulate a
mathematical equation for its behavior, numerical modeling can be used
to run the system in otherwise unexplored conditions or settings,
changing parameters to investigate their influence on the system’s
behavior. Good examples for this are weather and climate models. These
models often consist of equations derived from known physical processes
that occur in the atmosphere for which mathematical formulations exist.
Examples are fluid dynamics, evaporation and condensation, chemical
reactions and radiation. Although each of these processes is well
understood in isolation, their interaction makes the system
unpredictable. Combining them in a computer model enables us to
calculate how the system might behave in the future based on specific
initial conditions. Comparing the model outcome with historical and
present day observations shows the accuracy of the model and how well we
can trust its predictions of future climate observations.