The diagram shows a more involved model of the greenhouse effect.

The average incoming radiation intensity $\frac{\mathrm{S}}{4}=350 \mathrm{W} {\mathrm{m}}^{-2}$. The albedo of the atmosphere is $0.300$. Assume that the fraction $t$ of the energy radiated by the earth actually escapes the earth and the surface behaves as a black body. The model assumes that part of the radiation from the earth is reflected back down from the atmosphere.

Show that as much energy enters the earth's atmosphere as leaves it.

Given $I_2=\frac{1-\alpha -t}{1-\alpha +t}\times \frac{(1-\alpha )S}{4}$ and $I_3=\frac{2t}{1-\alpha +t}\times \frac{(1-\alpha )S}{4}$

The diagram shows a more involved model of the greenhouse effect.

The average incoming radiation intensity $\frac{\mathrm{S}}{4}=350 \mathrm{W} {\mathrm{m}}^{-2}$. The albedo of the atmosphere is $0.300$. Assume that the fraction $t$ of the energy radiated by the earth actually escapes the earth and the surface behaves as a black body. The model assumes that part of the radiation from the earth is reflected back down from the atmosphere.

Show that a surface temperature of $\mathrm{T}= 288 \mathrm{K}$ implies that $t=0.556$

Given $I_2=\frac{1-\alpha -t}{1-\alpha +t}\times \frac{(1-\alpha )S}{4}$ and $I_3=\frac{2t}{1-\alpha +t}\times \frac{(1-\alpha )S}{4}$ and $I_1=\frac{(1-\alpha )S}{4}\times \frac{2}{1-\alpha +t}$, Solar constant $\mathrm{S}=1400 \mathrm{W} {\mathrm{m}}^{-2}$ Stefan's constant $\mathrm{\sigma }=5.6\times {10}^{-8 }\mathrm{W}/{\mathrm{m}}^2 {\mathrm{K}}^4$

The diagram shows a more involved model of the greenhouse effect.

The average incoming radiation intensity $\frac{\mathrm{S}}{4}=350 \mathrm{W} {\mathrm{m}}^{-2}$. The albedo of the atmosphere is $0.300$. Assume that the fraction $t$ $(t=0.556)$ of the energy radiated by the earth actually escapes the earth and the surface behaves as a black body. The model assumes that part of the radiation from the earth is reflected back down from the atmosphere.

Calculate the temperature of the atmosphere.

Given $I_2=\frac{1-\alpha -t}{1-\alpha +t}\times \frac{(1-\alpha )S}{4}$ and $I_3=\frac{2t}{1-\alpha +t}\times \frac{(1-\alpha )S}{4}$ and $I_1=\frac{(1-\alpha )S}{4}\times \frac{2}{1-\alpha +t}$,$\mathrm{\sigma }=5.6\times {10}^{-8 }\mathrm{W}/{\mathrm{m}}^2 {\mathrm{K}}^4,\mathrm{S}=1400 \mathrm{W} {\mathrm{m}}^{-2},\mathrm{t}=0.556$

The diagram shows two energy flow diagrams for thermal energy to and from specific areas of the surface of the earth. R represents net energy incident on the surface in the form of radiation,E is the thermal energy lost from the earth due to evaporation and C is the thermal energy conducted to the atmosphere because of the temperature difference between the surface and the atmosphere.Suggest whether the Earth area in each diagram is likely to be dry and cool or moist and warm.