1) Make a sketch (graph) of how the planetary albedo of a water-world could vary with its global mean temperature. Label the axes of the graph.
2) Make a sketch (graph) of how much radiation is absorbed by the planet as a result of it's changing albedo, as a function of its global mean temperature.
3) Find the relationship between the temperature of any object and how much energy it emits. Sketch this relationship as a graph and label the axes properly.
4) Combining the two graphs of energy absorbed and energy emitted and show the equilibrium points of the system. Label the stable and unstable equilibriums.
5) Referring to the energy in/out graph from (4),
a) Explain why the ice-house climate state is a stable equilibrium.
b) Explain why the hot-house climate state is a stable equilibrium.
c) Explain why the third equilibrium point, located in between the hot-house and ice-house states, is an unstable equilibrium.
6) How would increasing the greenhouse gas concentration of the atmosphere change the above graph? What effect would that change have on the equilibrium points?
7) Explain the meaning of 'Critical Transitions'.
8) What are two important characteristics of critical transitions in complex systems such as the Earth-system?
- Irreversibility of Critical Transitions.
1) Referring to your responses to Problem 1. Energy Balance and Equilibrium, construct a trajectory of Earth's equilibrium temperature values (along vertical axis) vs. CO2 concentrations (horizontal axis) as they increase. Mark the critical temperatures and CO2 concentrations with the labels T+ and C+ respectively. Also use an arrow to indicate the direction of the trajectory.
2) Same as above, but for decreasing CO2 concentrations. Mark the critical temperatures and CO2 concentrations with the labels T- and C-, respectively. Also use an arrow to indicate the direction of the trajectory. (HINT: The + and - values should not be the same)
3) Translate your understanding of (a) and (b) into the context of the present anthropogenic climate change.
Sample Solution