You are going to build a very simple energy balance model for the earth. The model is based on the fact that, on average, the incoming energy (solar) is equal to the outgoing energy (from the earth). The parameters you will have to work with are:
S – is the solar constant.
A – planetary albedo of the earth.
T – temperature of the earth’s surface (Kelvin).
You will assume that the earth has no atmosphere. Thus you don’t have to be concerned about the greenhouse effect or transfer of energy by conduction and convection or by the transfer of latent heat.
1. Develop your energy balance model. Your model will be an equation which expresses the energy balance using the above variables S, A, and T. You will use the Stefan Boltzmann Law for the outgoing energy. The constant σ is 5.67 x 10-8 Wm-2K-4.
2. Solve the equation algebraically for T. Using the solar constant and mean planetary albedo, calculate a surface temperature for this simple model. If solved correctly you should see that the incoming solar radiation (units of W/m2) is the solar constant scaled by a factor of 4.
3. Using this equation for T, answer the following:
a) If albedo increases, what happens to T?
b) If incoming solar radiation increases, what happens to T?
c) If the snow and ice on the earth decreases, resulting in an albedo of .17, what is the temperature of the earth (T)?
4. Add an atmosphere with a greenhouse effect factor G to your model, where do you think G would go in the equation for T? Why?
5. Could you use the same model to calculate the temperature of Mars (assuming it has no atmosphere)? If yes, explain. If no, what would have to change?