EARTH 002: GAIA-THE EARTH SYSTEM

Fall 2009

PROBLEM SET #6 (Due Fri Dec 4)

1. You will seek to produce an alternative version of KCC Figure 12-12, using the simple “one layer atmosphere” energy balance model (see lecture #8). We will assume that carbon dioxide concentrations remain fixed at their current value of about 388 ppm. “Te” will simply be represented by the “blackbody” case where the emissivity is always set to epsilon=0. Ts will be represented by taking into account the non-zero emissivity of the atmosphere due to the greenhouse effect, and representing the positive water vapor feedback in a very simple way, where epsilon increases towards the current value (epsilon=0.77) as the solar constant increases towards its current value S=S0.

To construct the curves, calculate Te and Ts for following cases:

Time (BY BP) S/S0 epsilon

4.5 0.725 0.745

3 0.8 0.75

2 0.85 0.755

1 0.92 0.763

0 1.0 0.77

Briefly interpret your results in the context of the “Faint Young Sun” paradox.

2. KCC Chapter #14, Critical-Thinking Problem #1