Solar radiation, Fs Atmosphere \\at temp T1 ' I Earth surface at temp T0 Figure 8.38: A simple schematic of earth and atmosphere system (not to scale) with atmosphere approximated as a layer above earth's surface. (Globe ilr lustration by u3dShutterstock.com) 8.11. PROBLEMS 8.18 Modeling Earth's Greenhouse Effect We will build a simple model of the greenhouse effect of the atmosphere. Here the atmosphere will be treated as an isothermal layer at temperature T1 at some small dis tance from the earth's surface whose temperature is To. The solar ux outside the atmosphere is F S W/m2 and is incident only on the plane facing the sun. The spectral property of the atmosphere is assumed as follows: For solar radiation, the atmospheric layer has a reectivity of ,0 (includes reection from earth's surface), and zero ah~ sorptivity, both properties averaged over all wavelengths. For radiation emitted by the earth's surface that is incident on the atmosphere, the absorptivity of the atmosphere is or, averaged over all wavelengths. The spectral property of the earth is assumed as follows: For solar radiation, the earth's surface has an absorptivity of l. Reectivity of solar radiation from the earth's surface is included in p, so no additional reection needs to be considered. The radius of the earth and the atmosphere can be considered the same (say R). Those interested in learning more can see Jacob (1999). 1) Perform a radiative energy balance of the earth + atmosphere system at the outer layer of atmosphere (at the dashed line as shown in Figure 8.38), considering this system to be at steady state with no other sources of heat generation or transport (conduction 0r convection). (Him: What radiation enters this system (dashed line)? How much radiutianfmm this system leaves the dashed line?) 2) Perform a radiative energy balance of the atmosphere only, assuming it to be at steady state. (Hint: How 303 much radiative energy is absorbed by the atmosphere? How much radiative energy is released by the atmosphere?) 3) Combining 1) and 2), calculate the earth's surface temperature when the solar ux is F; = 1353 W/mz, a = 0.75, and p = 0.28. 4) What would happen to the calculated earth's surface temperature if the absorptivity of the atmosphere, or, increases