Problem 4 Emissimty As we learned from the lecture, one of the 'complications' for simple Stefan-Boltzmann models of the radiative balance of a planet with an atmosphere is emissivity or absorp- tivity e that is, what if the atmosphere only absorbs some faction (so, 5 is between 0 and 1} of the outgoing infrared radiation? Recall from lecture that we can modify the Stefan-Boltzmann equation to account for imperfect emissivity (we'll assume that e is constant over all wavelengths, which in reality it seldom is), which changes our absorber from a blackbody to a 'graybody': 3mm = \"'1'" (1) Consider the following simple model of the Earth system in Figure 2, with a single atmosphere layer and emissivity of that layer equal to e. 4 (1 6.)ng 30 Figure 2: Schematic of a one-layer atmosphere with less than complete absorption Calculate the planetary temperature T9 for this simple Earth if e is equal to 0.80. Compare this to the value we get (from lecture is ne, no need to calculate this value again here} if we assume the planet has an atmosphere that behaves like a blackhody. How do these two temperature values compare to the true average Earth temperature? So, what do you think might this suggest about the Earth's atmosphere, with respect to whether it behaves like a blackbody or graybody