.. [32 pts] Simple energy balance models a} Derive the equation for the basic planetary energy balance and solve for the surface temperature for the Earth {assume zero atmospheric layers}, T5, with radius R and a planetary albedo, A. Assume the Earth behaves as a blackbody. You will use the Stefan- Boltzmann constant 0 = 5.5? x 10'\" w of2 K1. [3] b] Extend the model in 0.1a to a twolayer to a two layer model. The lower layer A has emissivity EA and temperature TA. The upper layer B has emissivity EB and temperature TB. Draw a diagram with the radiative fluxes from the surface, layer A, layer B, and the top of the atmosphere. [5] c) Assume that all atmospheric layers behave as black bodies. Explain what the term blackbody means. Using equations for energy balance at the top of the atmosphere {TBA}, surface, and for each layer of the atmosphere, solve for Ta, Tu, and T5. Also assume that incoming and reected solar radiation does not interact with the atmospheric layers. [3] d] In reality, the emissivity of the atmosphere is around 0.8. Describe in words what this means? How do you expect this to change Ta, Ts, and T5? Solve for them to see if your hypothesis is correct. [8] e} Greenhouse gases in the lower atmosphere {layer A} increase the emissivity of that layer to 0.9. How does this impact the temperatures ofthe atmospheric layers and the surface? Show this is the case by either writing out equations or solving for the new temperatures. [8]