2. A Two-Layer Model. Insert another atmospheric layer into the model, just like

Question

2. A Two-Layer Model. Insert another atmospheric layer into the model, just like the first one.
The layer is transparent to visible light but a blackbody for infrared.
a) Write the energy budgets for both atmospheric layers, for the ground, and for the Earth as a
whole, like we did for the One-Layer Model.
b) Manipulate the budget for the Earth as a whole to obtain the temperature T2
of the top
atmospheric layer, labeled Atmospheric layer 2 in Figure 3-5. Does this part of the exercise
seem familiar in any way? Does the term ring any bells?
c) Insert the value you found for T2 into the energy budget for layer 2, and solve for the
temperature of layer 1 in terms of layer 2. How much bigger is T1 than T2?
d) Now insert the value you found for T1 into the budget for atmospheric layer 1 to obtain the
temperature of the ground, Tground. Is the greenhouse effect stronger or weaker because of
the second layer?

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Explanation / Answer

I think you should also give reference of the one layer model question for solving these efficiently.

b) The temperature of Layer 2 is the same as the top layer of the one-layer model, or the temperature of the bare rock with no atmosphere (the skin temperature).

c) T1 =4sqrt(2) T2

d) Tground = 4sqrt(3) T2. Greenhouse effect is stronger.

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