# Radiation Balance in the Atmosphere

One of the many challenges in teaching students about climate change arises from the complexity in the climate system. Global Climate Models (GCMs) are designed to try to account for the complex interactions and feedback between various components of the climate system and to estimate the sensitivity of climate to various forcing mechanisms. In introducing students to the climate system, it's helpful to start with a very simple, or zero-dimensional, model of Earth's energy balance. Calculating Earth's radiative equilibrium surface temperature allows students to take a first step toward understanding the factors that drive climate. This calculation introduces students to a very simple numerical model that allows them to explore one of the fundamental factors driving climate on Earth. What follows here is a suggested strategy for introducing students to this simple model.

**Background Information:** Students should be familiar with the concept of energy conservation, the relationship between radiation and temperature, and the difference between shortwave and longwave radiation (e.g., Stefan-Boltzmann Law and Wien's Law).

**Discuss the model with words/diagrams/equations:** To begin, an instructor might ask students to identify the primary factor in determining the average temperature of the Earth (the Sun). Then ask students how we might determine the relationship between the Sun and the surface temperature of the Earth. This leads into the concept of radiative equilibrium: incoming energy must equal outgoing energy. (An instructor may work with students to generate a diagram like the one on this page, with or without equations, depending on the level of the course.)

Students will wonder why the calculated temperature is so cold, and this is a good opportunity to discuss the limitations of this calculation.

**Meta-model discussion:** At this point, an instructor can remind students that what we have done here is create a very simple model. We have found the surface temperature of the Earth (without an atmosphere). This would be a good opportunity to hypothesize outcomes of different scenarios. For example: How would Earth's surface temperature be different if the Earth were covered in ice? (Or a dark-colored rock?) Could we use this model to find the temperature of other planets? Have students calculate the surface temperature of another planet and compare those values with actual temperatures of other planets.

An instructor might discuss factors that are missing in the model, and ask what factors students would like to include to make the model more realistic. Students could brainstorm factors that improve the estimate of Earth's surface temperature, such as the addition of the greenhouse effect, or latent and sensible transfer of heat away from the surface. Logic diagrams could be incorporated to build a conceptual model of climate that incorporates more of these additional climate processes. For those interested in using STELLA, teaching activities using STELLA to model the Earth's climate system can be found in the SERC activity collection.