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In this lesson, we began to explore the use of theoretical models of the climate system. We saw that:

- a simple
*zero-dimensional energy balance model*can be used to estimate the surface temperature of the Earth, as well as the response of surface temperatures to changes external (including human-induced perturbations). The model balances the incoming solar radiation absorbed at Earth's surface and the outgoing longwave radiation emitted from Earth's surface; - a simple linear approximation can be used in the zero dimensional EBM to represent the outgoing longwave radiation, leading to a mathematical simplification and a simple formula for global surface temperature;
- using the simplest,
*black body*approximation for the outgoing longwave radiation gives a global surface temperature of about 255K, i.e., 18C below freezing—obviously way too cold; - the
*gray body approximation*provides a simple fix to the zero-dimensional EBM that incorporates, at least crudely, the atmospheric greenhouse effect; - using appropriate values of the
*gray body*model coefficients, we can accurately predict both the Earth's surface temperature (roughly 288K, i.e., approximately 15°C), and the response of surface temperatures to perturbations such as increasing greenhouse gas concentrations (roughly 3°C for a doubling of atmospheric CO_{2}).

This lesson also introduced us to the important concept of equilibrium climate sensitivity—a concept we will encounter again and again throughout this course.

### Reminder - Complete all of the lesson tasks!

You have finished Lesson 4. Double-check the list of requirements on the first page of this lesson to make sure you have completed all of the activities listed there before beginning the next lesson.