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.