ESE315 Assignment 2

Required:

1. Mars is 2.3e8 km away from the Sun; its albedo is 0.15. Its only source of heat is solar radiation. (a) Calculate the effective temperature of Mars. (b) The temperature observed at the surface of Mars is 220 K. What do you conclude about the Martian atmosphere?
2. The "Faint Young Sun" paradox has been puzzling scientists since the 1970s. Assuming that the distance between the Sun and the Earth has not changed significantly since the time of the Earth's formation 4.6 billion years ago. Use python to make a 2-D contour plot of the Earth's effective temperature (Te) for a range of solar constant and a range of albedos.

Extra credit:

The following questions are not part of the assignment that you are required to hand in. You can do them as extra credit. Or, you can use these as inspiration for your term project.

Based on the MODTRAN model:

• Demonstrate the Band Saturation Effect by making a plot of Iout as a function of a greenhouse gas concentration, from say 0 to 1000 ppm, with lots of points at low concentrations.
• Calculate the average temperature that the Earth radiates to space by setting the model Iout to epsilon sigma T4 and solving for T. What altitude is this (assuming the light is coming from the troposphere, the lowermost region in the temperature profile plot)? How does this altitude change as you change the greenhouse gas concentration?
• What is the effect of clouds on the upwelling IR to space, and to the downwelling IR seen from the ground?
• Compare CO2 vs. methane as greenhouse gases. Which would be the stronger if they had the same concentrations? Which is stronger given their current concentrations?

Simulate the temperature response to greenhouse gas IR forcing by adjusting the ground temperature to maintain a constant Iout as you increase the gas concentration. Demonstrate the water vapor feedback effect by doing this using both options of constant vapor pressure and constant relative humidity.