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Solving for ground temperature using atmospheric layer models and energy budgets

  1. Oct 4, 2009 #1
    1. The problem statement, all variables and given/known data

    Imagine that our simple single layer atmosphere model derived in class now has 2 atmospheric layers. It is transparent to visible light but a blackbody for IR

    a) Write the energy budgets for both atmospheric layers, for the ground, and for the Earth as a whole.
    b) Rearrange the balanced budget for the Earth as a whole and compute the temperature (T for atm 2) of the top atmospheric layer. This should seem familiar to what we did with a one layer model using I (1-α) = 1000 Wm-2
    c)Insert the value you compute for Tatm2 into the energy budget for layer 2 to solve for the temperature of atmospheric layer 1 (Tatm1) in terms of layer 2. How much bigger is Tatm1 than Tatm2?
    d) Now insert the value you found for Tatm1 into the budget for atmospheric layer 1 to solve for the temperature for the ground, Tgnd. Is the greenhouse effect stronger or weaker because of the second layer?


    2. Relevant equations

    I have been using this basic equation for each step 2εσT= εσT and then substituting the various layers in.


    3. The attempt at a solution

    I've actually reached the final answer, but I've never done this before so I'm not sure if its right. I went through with each step and solved it as the problem told me to. So for atmosphere 2, I found a temperature of 257.685 K. Then I used that temperature in the atmosphere 1 energy budget in order to find a temperature of 306.4408 K for atmosphere 1. Finally, I used that temperature in the final energy budget to finish with a ground temperature of 76.91 K. This seems awfully low to me. Could some one check this and then give me hints on how to solve it if this is not right? Thanks :)
     
  2. jcsd
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