# Atmospheric sciences

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1. suppose a gas that absorbs solar radiation has a uniform mixing ratio of 1g kg^-1 and an absorption cross section of 5m^2kg^-1. At what altitude will the maximum rate of energy absorption per unit volume occur? Assume an isothermal atmosphere with T=260k, and a surface pressure of 1.025 x 10^5Pa and that the sun is directly overhead.

2. In the problem above, if the frequency range at which the absorption is taking place contains 5% of the total solar energy flux, what is the heating rate in degrees per day at the level of maximum energy absorption? What is the heating rate one scale height above and below the level of maximum energy absorption? Use the globally averaged insolation.

3. use the model in fig 3.10, but distribute the solar heating such that 0.3sigmaTe^4 is absorbed in each of the two atmospheric layers and the remaining 0.4sigmaTe^4 is absorbed at the surface. Calculate the new radiative equilibrium temperature profile. How does it differ from the case where all of the solar heating is applied at the surface?

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