This module introduces the student to the process of mathematical modeling. It shows how the process starts in the 4real world! with a physical system and some observations or an experiment. In a zero-dimensional energy balance model, the Earth's climate system is described in terms of a single variable, namely the temperature of the Earth's surface averaged over the entire globe. In general, this variable varies with time; its time evolution is governed by the amount of energy coming in from the Sun (in the form of ultraviolet radiation) and the amount of energy leaving the Earth (in the form of infrared radiation). The mathematical challenge is to find expressions for the incoming and outgoing energy that are consistent with the observed current state of the climate system, and then use the resulting energy balance model to see whether the climate system admits other equilibrium states and, if so, how a transition from one equilibrium state to another could be triggered. The module includes descriptions of several simple experiments that illustrate various concepts used in the discussion.
This material is based in part upon work supported by the National Science Foundation under Grants NSF DRL-1020166 and DMS-1053887. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.